kakothegreat
Muhammad Awais
lease help me can anybody guide me how to make project on "cost minimization in consumer price indices" ? if any ony have any project of linear programming shopping please mail me at [email protected]
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Need Help in making project on :: cost minimization in consumer price indices
- Thread starter kakothegreat
- Start date
Re: linear programming
Consumer Price Index - November 2009
On a seasonally adjusted basis, the Consumer Price Index for All
Urban Consumers (CPI-U) rose 0.4 percent in November, the U.S. Bureau
of Labor Statistics reported today. Over the last 12 months the index
increased 1.8 percent before seasonal adjustment, the first positive
12-month change since February 2009.
The seasonally adjusted increase in the all items index was due to a
4.1 percent increase in the energy index. The index for gasoline rose
sharply and the indexes for electricity, fuel oil, and natural gas
also increased, creating the fourth consecutive rise in the energy
index and the largest increase since August. In contrast, the index
for all items less food and energy was unchanged in November, after
ten consecutive monthly increases. Declines in shelter indexes offset
increases in the indexes for new and used motor vehicles, medical
care, airline fares, and tobacco.
The food index rose slightly in November. As in October, the food
away from home index rose modestly while the index for food at home
was unchanged. Within the latter, three grocery store food groups
posted increases while three declined.
Table A. Percent changes in CPI for All Urban Consumers (CPI-U): U.S. city
average
Seasonally adjusted changes from
preceding month
Un-
adjusted
12-mos.
May June July Aug. Sep. Oct. Nov. ended
2009 2009 2009 2009 2009 2009 2009 Nov.
2009
All items.................. .1 .7 .0 .4 .2 .3 .4 1.8
Food...................... -.2 .0 -.3 .1 -.1 .1 .1 -.7
Food at home............. -.5 .0 -.5 .0 -.3 .0 .0 -2.9
Food away from home (1).. .1 .1 .1 .1 .1 .1 .2 2.1
Energy.................... .2 7.4 -.4 4.6 .6 1.5 4.1 7.4
Energy commodities....... 2.3 16.2 -.4 8.5 1.1 1.9 6.3 19.6
Gasoline (all types).... 3.1 17.3 -.8 9.1 1.0 1.6 6.4 23.6
Fuel oil................ -3.3 4.8 -1.5 6.2 1.5 6.3 9.0 -6.9
Energy services.......... -1.7 -1.2 -.3 .0 .1 .9 1.4 -5.1
Electricity............. -.4 -1.9 -.6 -.1 .6 .6 1.4 .1
Utility (piped) gas
service.............. -5.7 1.3 .9 .4 -1.7 1.9 1.5 -18.6
All items less food and
energy................. .1 .2 .1 .1 .2 .2 .0 1.7
Commodities less food and
energy commodities.... .2 .3 .2 -.3 .3 .4 .2 2.6
New vehicles............ .5 .7 .5 -1.3 .4 1.6 .6 4.9
Used cars and trucks.... 1.0 .9 .0 1.9 1.6 3.4 2.0 5.8
Apparel................. -.2 .7 .6 -.1 .1 -.4 -.3 1.0
Medical care commodities .4 .1 -.1 .5 .6 .2 .0 3.8
Services less energy
services.............. .1 .1 .0 .2 .1 .1 .0 1.4
Shelter................. .1 .1 -.2 .1 .0 .0 -.2 .3
Transportation services -.1 -.1 .5 .6 .7 .4 .6 3.6
Medical care services... .3 .2 .3 .2 .4 .2 .4 3.5
1 Not seasonally adjusted.
Consumer Price Index Data for November 2009
Food
The food index rose 0.1 percent in November, the same increase as in
October. The index for food away from home increased 0.2 percent
while the food at home index was unchanged. Among the food at home
groups, the dairy and related products index declined 0.7 percent in
November after rising 1.0 percent in October, and the index for other
food at home also declined in November following an October increase.
In contrast, the indexes for fruits and vegetables and for meats,
poultry, fish, and eggs both increased in November after declining in
October. The index for nonalcoholic beverages fell for the second
straight month, declining 0.3 percent in November, and the index for
cereals and bakery products rose 0.1 percent in November after being
unchanged in October. Over the past year, the food index has declined
0.7 percent. The food at home index has fallen 2.9 percent over the
last 12 months, with five of the six grocery store food groups
declining, but the index for food away from home has risen 2.1
percent.
Energy
The energy index rose 4.1 percent in November after increasing 1.5
percent in October. The index for energy commodities rose 6.3
percent, with the gasoline index increasing 6.4 percent. (Before
seasonal adjustment, gasoline prices rose 4.1 percent in November.)
The rise in the gasoline index accounted for over three-quarters of
the total energy increase. The remainder of the increase was due to
advances in all of the other energy components. The index for fuel
oil rose 9.0 percent in November following a 6.3 percent increase in
October. The index for energy services increased 1.4 percent in
November, with the electricity index rising 1.4 percent and the index
for natural gas advancing 1.5 percent. The energy index has risen 7.4
percent over the past 12 months, with the gasoline index rising 23.6
percent.
All items less food and energy
The index for all items less food and energy was unchanged in
November after rising 0.2 percent in October. The heavily weighted
index for shelter, unchanged in October, declined 0.2 percent in
November. Within the shelter group, the indexes for rent and owners'
equivalent rent both declined 0.1 percent and the lodging away from
home index fell 1.5 percent. Also declining in November were the
indexes for household furnishings and operations and for apparel,
both down 0.3 percent. Several indexes posted increases to offset
these declines. The new vehicles index rose 0.6 percent in November,
its tenth increase in the last eleven months. The index for used cars
and trucks advanced 2.0 percent in November and has now risen 11.1
percent since April. The index for airline fares rose 3.8 percent in
November and has increased 13.3 percent since June. The medical care
index increased 0.3 percent in November and the index for tobacco
advanced 1.0 percent. Over the past 12 months, the index for all
items less food and energy has risen 1.7 percent.
Not seasonally adjusted CPI measures
The Consumer Price Index for All Urban Consumers (CPI-U) increased
1.8 percent over the last 12 months to an index level of 216.330
(1982-84=100). For the month, the index increased 0.1 percent prior
to seasonal adjustment.
The Consumer Price Index for Urban Wage Earners and Clerical Workers
(CPI-W) increased 2.3 percent over the last 12 months to an index
level of 212.003 (1982-84=100). For the month, the index increased
0.2 percent prior to seasonal adjustment.
The Chained Consumer Price Index for All Urban Consumers (C-CPI-U)
increased 1.6 percent over the last 12 months. For the month, the
index was unchanged on a not seasonally adjusted basis. Please note
that the indexes for the post-2007 period are subject to revision.
The Consumer Price Index for December 2009 is scheduled to be
released on Friday, January 15, 2010, at 8:30 a.m. (EST).
Expenditure Weight Update
Effective with the January 2010 release the Bureau of Labor
Statistics (BLS) will update the consumption expenditure weights in
the Consumer Price Index for All Urban Consumers (CPI-U) and Consumer
Price Index for Urban Wage Earners and Clerical Workers (CPI-W) to
the 2007-08 period. The updated expenditure weights for these indexes
will replace the 2005-2006 weights that were introduced effective
with the January 2008 CPI release. CPI expenditure weights will
continue to be updated at two year intervals subsequent to the 2010
updating.
Facilities for Sensory Impaired
Information from this release will be made available to sensory
impaired individuals upon request. Voice phone: 202-691-5200,
Federal Relay Services: 1-800-877-8339.
Brief Explanation of the CPI
The Consumer Price Index (CPI) is a measure of the average change in
prices over time of goods and services purchased by households. The
Bureau of Labor Statistics publishes CPIs for two population groups:
(1) the CPI for Urban Wage Earners and Clerical Workers (CPI-W),
which covers households of wage earners and clerical workers that
comprise approximately 32 percent of the total population and (2) the
CPI for All Urban Consumers (CPI-U) and the Chained CPI for All Urban
Consumers (C-CPI-U), which cover approximately 87 percent of the
total population and include in addition to wage earners and clerical
worker households, groups such as professional, managerial, and
technical workers, the self-employed, short-term workers, the
unemployed, and retirees and others not in the labor force.
The CPIs are based on prices of food, clothing, shelter, and fuels,
transportation fares, charges for doctors' and dentists' services,
drugs, and other goods and services that people buy for day-to-day
living. Prices are collected each month in 87 urban areas across the
country from about 4,000 housing units and approximately 25,000
retail establishments-department stores, supermarkets, hospitals,
filling stations, and other types of stores and service
establishments. All taxes directly associated with the purchase and
use of items are included in the index. Prices of fuels and a few
other items are obtained every month in all 87 locations. Prices of
most other commodities and services are collected every month in the
three largest geographic areas and every other month in other areas.
Prices of most goods and services are obtained by personal visits or
telephone calls of the Bureau's trained representatives.
In calculating the index, price changes for the various items in each
location are averaged together with weights, which represent their
importance in the spending of the appropriate population group.
Local data are then combined to obtain a U.S. city average. For the
CPI-U and CPI-W separate indexes are also published by size of city,
by region of the country, for cross-classifications of regions and
population-size classes, and for 27 local areas. Area indexes do not
measure differences in the level of prices among cities; they only
measure the average change in prices for each area since the base
period. For the C-CPI-U data are issued only at the national level.
It is important to note that the CPI-U and CPI-W are considered final
when released, but the C-CPI-U is issued in preliminary form and
subject to two annual revisions.
The index measures price change from a designed reference date. For
the CPI-U and the CPI-W the reference base is 1982-84 equals 100.0.
The reference base for the C-CPI-U is December 1999 equals 100. An
increase of 16.5 percent from the reference base, for example, is
shown as 116.5. This change can also be expressed in dollars as
follows: the price of a base period market basket of goods and
services in the CPI has risen from $10 in 1982-84 to $11.65.
For further details visit the CPI home page on the Internet at
Consumer Price Index (CPI) or contact our CPI Information and Analysis
Section on (202) 691-7000.
Note on Sampling Error in the Consumer Price Index
The CPI is a statistical estimate that is subject to sampling error
because it is based upon a sample of retail prices and not the
complete universe of all prices. BLS calculates and publishes
estimates of the 1-month, 2-month, 6-month and 12-month percent
change standard errors annually, for the CPI-U. These standard error
estimates can be used to construct confidence intervals for
hypothesis testing. For example, the estimated standard error of the
1 month percent change is 0.04 percent for the U.S. All Items
Consumer Price Index. This means that if we repeatedly sample from
the universe of all retail prices using the same methodology, and
estimate a percentage change for each sample, then 95% of these
estimates would be within 0.08 percent of the 1 month percentage
change based on all retail prices. For example, for a 1-month change
of 0.2 percent in the All Items CPI for All Urban Consumers, we are
95 percent confident that the actual percent change based on all
retail prices would fall between 0.12 and 0.28 percent. For the
latest data, including information on how to use the estimates of
standard error, see "Variance Estimates for Price Changes in the
Consumer Price Index, January-December 2008". These data are
available on the CPI home page (Consumer Price Index (CPI)), or by using
the following link http://www.bls.gov/cpi/cpivar2008.pdf
Calculating Index Changes
Movements of the indexes from one month to another are usually
expressed as percent changes rather than changes in index points,
because index point changes are affected by the level of the index in
relation to its base period while percent changes are not. The
example below illustrates the computation of index point and percent
changes.
Percent changes for 3-month and 6-month periods are expressed as
annual rates and are computed according to the standard formula for
compound growth rates. These data indicate what the percent change
would be if the current rate were maintained for a 12-month period.
Index Point Change
CPI
202.416
Less previous index
201.800
Equals index point change
.616
Percent Change
Index point difference
.616
Divided by the previous index
201.800
Equals
0.003
Results multiplied by one hundred
0.003x100
Equals percent change
0.3
Regions Defined
The states in the four regions shown in Tables 3 and 6 are listed
below.
The Northeast--Connecticut, Maine, Massachusetts, New Hampshire, New
York, New Jersey, Pennsylvania, Rhode Island, and Vermont.
The Midwest--Illinois, Indiana, Iowa, Kansas, Michigan, Minnesota,
Missouri, Nebraska, North Dakota, Ohio, South Dakota, and Wisconsin.
The South--Alabama, Arkansas, Delaware, Florida, Georgia, Kentucky,
Louisiana, Maryland, Mississippi, North Carolina, Oklahoma, South
Carolina, Tennessee, Texas, Virginia, West Virginia, and the District
of Columbia.
The West--Alaska, Arizona, California, Colorado, Hawaii, Idaho,
Montana, Nevada, New Mexico, Oregon, Utah, Washington, and Wyoming.
A Note on Seasonally Adjusted and Unadjusted Data
Because price data are used for different purposes by different
groups, the Bureau of Labor Statistics publishes seasonally adjusted
as well as unadjusted changes each month.
For analyzing general price trends in the economy, seasonally
adjusted changes are usually preferred since they eliminate the
effect of changes that normally occur at the same time and in about
the same magnitude every year--such as price movements resulting from
changing climatic conditions, production cycles, model changeovers,
holidays, and sales.
The unadjusted data are of primary interest to consumers concerned
about the prices they actually pay. Unadjusted data also are used
extensively for escalation purposes. Many collective bargaining
contract agreements and pension plans, for example, tie compensation
changes to the Consumer Price Index before adjustment for seasonal
variation.
Seasonal factors used in computing the seasonally adjusted indexes
are derived by the X-12-ARIMA Seasonal Adjustment Method. Seasonally
adjusted indexes and seasonal factors are computed annually. Each
year, the last 5 years of seasonally adjusted data are revised. Data
from January 2004 through December 2008 were replaced in January
2009. Exceptions to the usual revision schedule were: the updated
seasonal data at the end of 1977 replaced data from 1967 through
1977; and, in January 2002, dependently seasonally adjusted series
were revised for January 1987-December 2001 as a result of a change
in the aggregation weights for dependently adjusted series. For
further information, please see "Aggregation of Dependently Adjusted
Seasonally Adjusted Series," in the October 2001 issue of the CPI
Detailed Report.
The seasonal movement of all items and 54 other aggregations is
derived by combining the seasonal movement of 73 selected components.
Each year the seasonal status of every series is reevaluated based
upon certain statistical criteria. If any of the 73 components
change their seasonal adjustment status from seasonally adjusted to
not seasonally adjusted, not seasonally adjusted data will be used in
the aggregation of the dependent series for the last 5 years, but the
seasonally adjusted indexes will be used before that period. Note:
47 of the 73 components are seasonally adjusted for 2009.
Seasonally adjusted data, including the all items index levels, are
subject to revision for up to five years after their original
release. For this reason, BLS advises against the use of these data
in escalation agreements.
Effective with the calculation of the seasonal factors for 1990, the
Bureau of Labor Statistics has used an enhanced seasonal adjustment
procedure called Intervention Analysis Seasonal Adjustment for some
CPI series. Intervention Analysis Seasonal Adjustment allows for
better estimates of seasonally adjusted data. Extreme values and/or
sharp movements which might distort the seasonal pattern are
estimated and removed from the data prior to calculation of seasonal
factors. Beginning with the calculation of seasonal factors for
1996, X-12-ARIMA software was used for Intervention Analysis Seasonal
Adjustment.
For the seasonal factors introduced in January 2009, BLS adjusted 29
series using Intervention Analysis Seasonal Adjustment, including
selected food and beverage items, motor fuels, electricity and
vehicles. For example, this procedure was used for the Motor fuel
series to offset the effects of events such as damage to oil
refineries from Hurricane Katrina.
For a complete list of Intervention Analysis Seasonal Adjustment
series and explanations, please refer to the article "Intervention
Analysis Seasonal Adjustment",
Consumer Price Index - November 2009
On a seasonally adjusted basis, the Consumer Price Index for All
Urban Consumers (CPI-U) rose 0.4 percent in November, the U.S. Bureau
of Labor Statistics reported today. Over the last 12 months the index
increased 1.8 percent before seasonal adjustment, the first positive
12-month change since February 2009.
The seasonally adjusted increase in the all items index was due to a
4.1 percent increase in the energy index. The index for gasoline rose
sharply and the indexes for electricity, fuel oil, and natural gas
also increased, creating the fourth consecutive rise in the energy
index and the largest increase since August. In contrast, the index
for all items less food and energy was unchanged in November, after
ten consecutive monthly increases. Declines in shelter indexes offset
increases in the indexes for new and used motor vehicles, medical
care, airline fares, and tobacco.
The food index rose slightly in November. As in October, the food
away from home index rose modestly while the index for food at home
was unchanged. Within the latter, three grocery store food groups
posted increases while three declined.
Table A. Percent changes in CPI for All Urban Consumers (CPI-U): U.S. city
average
Seasonally adjusted changes from
preceding month
Un-
adjusted
12-mos.
May June July Aug. Sep. Oct. Nov. ended
2009 2009 2009 2009 2009 2009 2009 Nov.
2009
All items.................. .1 .7 .0 .4 .2 .3 .4 1.8
Food...................... -.2 .0 -.3 .1 -.1 .1 .1 -.7
Food at home............. -.5 .0 -.5 .0 -.3 .0 .0 -2.9
Food away from home (1).. .1 .1 .1 .1 .1 .1 .2 2.1
Energy.................... .2 7.4 -.4 4.6 .6 1.5 4.1 7.4
Energy commodities....... 2.3 16.2 -.4 8.5 1.1 1.9 6.3 19.6
Gasoline (all types).... 3.1 17.3 -.8 9.1 1.0 1.6 6.4 23.6
Fuel oil................ -3.3 4.8 -1.5 6.2 1.5 6.3 9.0 -6.9
Energy services.......... -1.7 -1.2 -.3 .0 .1 .9 1.4 -5.1
Electricity............. -.4 -1.9 -.6 -.1 .6 .6 1.4 .1
Utility (piped) gas
service.............. -5.7 1.3 .9 .4 -1.7 1.9 1.5 -18.6
All items less food and
energy................. .1 .2 .1 .1 .2 .2 .0 1.7
Commodities less food and
energy commodities.... .2 .3 .2 -.3 .3 .4 .2 2.6
New vehicles............ .5 .7 .5 -1.3 .4 1.6 .6 4.9
Used cars and trucks.... 1.0 .9 .0 1.9 1.6 3.4 2.0 5.8
Apparel................. -.2 .7 .6 -.1 .1 -.4 -.3 1.0
Medical care commodities .4 .1 -.1 .5 .6 .2 .0 3.8
Services less energy
services.............. .1 .1 .0 .2 .1 .1 .0 1.4
Shelter................. .1 .1 -.2 .1 .0 .0 -.2 .3
Transportation services -.1 -.1 .5 .6 .7 .4 .6 3.6
Medical care services... .3 .2 .3 .2 .4 .2 .4 3.5
1 Not seasonally adjusted.
Consumer Price Index Data for November 2009
Food
The food index rose 0.1 percent in November, the same increase as in
October. The index for food away from home increased 0.2 percent
while the food at home index was unchanged. Among the food at home
groups, the dairy and related products index declined 0.7 percent in
November after rising 1.0 percent in October, and the index for other
food at home also declined in November following an October increase.
In contrast, the indexes for fruits and vegetables and for meats,
poultry, fish, and eggs both increased in November after declining in
October. The index for nonalcoholic beverages fell for the second
straight month, declining 0.3 percent in November, and the index for
cereals and bakery products rose 0.1 percent in November after being
unchanged in October. Over the past year, the food index has declined
0.7 percent. The food at home index has fallen 2.9 percent over the
last 12 months, with five of the six grocery store food groups
declining, but the index for food away from home has risen 2.1
percent.
Energy
The energy index rose 4.1 percent in November after increasing 1.5
percent in October. The index for energy commodities rose 6.3
percent, with the gasoline index increasing 6.4 percent. (Before
seasonal adjustment, gasoline prices rose 4.1 percent in November.)
The rise in the gasoline index accounted for over three-quarters of
the total energy increase. The remainder of the increase was due to
advances in all of the other energy components. The index for fuel
oil rose 9.0 percent in November following a 6.3 percent increase in
October. The index for energy services increased 1.4 percent in
November, with the electricity index rising 1.4 percent and the index
for natural gas advancing 1.5 percent. The energy index has risen 7.4
percent over the past 12 months, with the gasoline index rising 23.6
percent.
All items less food and energy
The index for all items less food and energy was unchanged in
November after rising 0.2 percent in October. The heavily weighted
index for shelter, unchanged in October, declined 0.2 percent in
November. Within the shelter group, the indexes for rent and owners'
equivalent rent both declined 0.1 percent and the lodging away from
home index fell 1.5 percent. Also declining in November were the
indexes for household furnishings and operations and for apparel,
both down 0.3 percent. Several indexes posted increases to offset
these declines. The new vehicles index rose 0.6 percent in November,
its tenth increase in the last eleven months. The index for used cars
and trucks advanced 2.0 percent in November and has now risen 11.1
percent since April. The index for airline fares rose 3.8 percent in
November and has increased 13.3 percent since June. The medical care
index increased 0.3 percent in November and the index for tobacco
advanced 1.0 percent. Over the past 12 months, the index for all
items less food and energy has risen 1.7 percent.
Not seasonally adjusted CPI measures
The Consumer Price Index for All Urban Consumers (CPI-U) increased
1.8 percent over the last 12 months to an index level of 216.330
(1982-84=100). For the month, the index increased 0.1 percent prior
to seasonal adjustment.
The Consumer Price Index for Urban Wage Earners and Clerical Workers
(CPI-W) increased 2.3 percent over the last 12 months to an index
level of 212.003 (1982-84=100). For the month, the index increased
0.2 percent prior to seasonal adjustment.
The Chained Consumer Price Index for All Urban Consumers (C-CPI-U)
increased 1.6 percent over the last 12 months. For the month, the
index was unchanged on a not seasonally adjusted basis. Please note
that the indexes for the post-2007 period are subject to revision.
The Consumer Price Index for December 2009 is scheduled to be
released on Friday, January 15, 2010, at 8:30 a.m. (EST).
Expenditure Weight Update
Effective with the January 2010 release the Bureau of Labor
Statistics (BLS) will update the consumption expenditure weights in
the Consumer Price Index for All Urban Consumers (CPI-U) and Consumer
Price Index for Urban Wage Earners and Clerical Workers (CPI-W) to
the 2007-08 period. The updated expenditure weights for these indexes
will replace the 2005-2006 weights that were introduced effective
with the January 2008 CPI release. CPI expenditure weights will
continue to be updated at two year intervals subsequent to the 2010
updating.
Facilities for Sensory Impaired
Information from this release will be made available to sensory
impaired individuals upon request. Voice phone: 202-691-5200,
Federal Relay Services: 1-800-877-8339.
Brief Explanation of the CPI
The Consumer Price Index (CPI) is a measure of the average change in
prices over time of goods and services purchased by households. The
Bureau of Labor Statistics publishes CPIs for two population groups:
(1) the CPI for Urban Wage Earners and Clerical Workers (CPI-W),
which covers households of wage earners and clerical workers that
comprise approximately 32 percent of the total population and (2) the
CPI for All Urban Consumers (CPI-U) and the Chained CPI for All Urban
Consumers (C-CPI-U), which cover approximately 87 percent of the
total population and include in addition to wage earners and clerical
worker households, groups such as professional, managerial, and
technical workers, the self-employed, short-term workers, the
unemployed, and retirees and others not in the labor force.
The CPIs are based on prices of food, clothing, shelter, and fuels,
transportation fares, charges for doctors' and dentists' services,
drugs, and other goods and services that people buy for day-to-day
living. Prices are collected each month in 87 urban areas across the
country from about 4,000 housing units and approximately 25,000
retail establishments-department stores, supermarkets, hospitals,
filling stations, and other types of stores and service
establishments. All taxes directly associated with the purchase and
use of items are included in the index. Prices of fuels and a few
other items are obtained every month in all 87 locations. Prices of
most other commodities and services are collected every month in the
three largest geographic areas and every other month in other areas.
Prices of most goods and services are obtained by personal visits or
telephone calls of the Bureau's trained representatives.
In calculating the index, price changes for the various items in each
location are averaged together with weights, which represent their
importance in the spending of the appropriate population group.
Local data are then combined to obtain a U.S. city average. For the
CPI-U and CPI-W separate indexes are also published by size of city,
by region of the country, for cross-classifications of regions and
population-size classes, and for 27 local areas. Area indexes do not
measure differences in the level of prices among cities; they only
measure the average change in prices for each area since the base
period. For the C-CPI-U data are issued only at the national level.
It is important to note that the CPI-U and CPI-W are considered final
when released, but the C-CPI-U is issued in preliminary form and
subject to two annual revisions.
The index measures price change from a designed reference date. For
the CPI-U and the CPI-W the reference base is 1982-84 equals 100.0.
The reference base for the C-CPI-U is December 1999 equals 100. An
increase of 16.5 percent from the reference base, for example, is
shown as 116.5. This change can also be expressed in dollars as
follows: the price of a base period market basket of goods and
services in the CPI has risen from $10 in 1982-84 to $11.65.
For further details visit the CPI home page on the Internet at
Consumer Price Index (CPI) or contact our CPI Information and Analysis
Section on (202) 691-7000.
Note on Sampling Error in the Consumer Price Index
The CPI is a statistical estimate that is subject to sampling error
because it is based upon a sample of retail prices and not the
complete universe of all prices. BLS calculates and publishes
estimates of the 1-month, 2-month, 6-month and 12-month percent
change standard errors annually, for the CPI-U. These standard error
estimates can be used to construct confidence intervals for
hypothesis testing. For example, the estimated standard error of the
1 month percent change is 0.04 percent for the U.S. All Items
Consumer Price Index. This means that if we repeatedly sample from
the universe of all retail prices using the same methodology, and
estimate a percentage change for each sample, then 95% of these
estimates would be within 0.08 percent of the 1 month percentage
change based on all retail prices. For example, for a 1-month change
of 0.2 percent in the All Items CPI for All Urban Consumers, we are
95 percent confident that the actual percent change based on all
retail prices would fall between 0.12 and 0.28 percent. For the
latest data, including information on how to use the estimates of
standard error, see "Variance Estimates for Price Changes in the
Consumer Price Index, January-December 2008". These data are
available on the CPI home page (Consumer Price Index (CPI)), or by using
the following link http://www.bls.gov/cpi/cpivar2008.pdf
Calculating Index Changes
Movements of the indexes from one month to another are usually
expressed as percent changes rather than changes in index points,
because index point changes are affected by the level of the index in
relation to its base period while percent changes are not. The
example below illustrates the computation of index point and percent
changes.
Percent changes for 3-month and 6-month periods are expressed as
annual rates and are computed according to the standard formula for
compound growth rates. These data indicate what the percent change
would be if the current rate were maintained for a 12-month period.
Index Point Change
CPI
202.416
Less previous index
201.800
Equals index point change
.616
Percent Change
Index point difference
.616
Divided by the previous index
201.800
Equals
0.003
Results multiplied by one hundred
0.003x100
Equals percent change
0.3
Regions Defined
The states in the four regions shown in Tables 3 and 6 are listed
below.
The Northeast--Connecticut, Maine, Massachusetts, New Hampshire, New
York, New Jersey, Pennsylvania, Rhode Island, and Vermont.
The Midwest--Illinois, Indiana, Iowa, Kansas, Michigan, Minnesota,
Missouri, Nebraska, North Dakota, Ohio, South Dakota, and Wisconsin.
The South--Alabama, Arkansas, Delaware, Florida, Georgia, Kentucky,
Louisiana, Maryland, Mississippi, North Carolina, Oklahoma, South
Carolina, Tennessee, Texas, Virginia, West Virginia, and the District
of Columbia.
The West--Alaska, Arizona, California, Colorado, Hawaii, Idaho,
Montana, Nevada, New Mexico, Oregon, Utah, Washington, and Wyoming.
A Note on Seasonally Adjusted and Unadjusted Data
Because price data are used for different purposes by different
groups, the Bureau of Labor Statistics publishes seasonally adjusted
as well as unadjusted changes each month.
For analyzing general price trends in the economy, seasonally
adjusted changes are usually preferred since they eliminate the
effect of changes that normally occur at the same time and in about
the same magnitude every year--such as price movements resulting from
changing climatic conditions, production cycles, model changeovers,
holidays, and sales.
The unadjusted data are of primary interest to consumers concerned
about the prices they actually pay. Unadjusted data also are used
extensively for escalation purposes. Many collective bargaining
contract agreements and pension plans, for example, tie compensation
changes to the Consumer Price Index before adjustment for seasonal
variation.
Seasonal factors used in computing the seasonally adjusted indexes
are derived by the X-12-ARIMA Seasonal Adjustment Method. Seasonally
adjusted indexes and seasonal factors are computed annually. Each
year, the last 5 years of seasonally adjusted data are revised. Data
from January 2004 through December 2008 were replaced in January
2009. Exceptions to the usual revision schedule were: the updated
seasonal data at the end of 1977 replaced data from 1967 through
1977; and, in January 2002, dependently seasonally adjusted series
were revised for January 1987-December 2001 as a result of a change
in the aggregation weights for dependently adjusted series. For
further information, please see "Aggregation of Dependently Adjusted
Seasonally Adjusted Series," in the October 2001 issue of the CPI
Detailed Report.
The seasonal movement of all items and 54 other aggregations is
derived by combining the seasonal movement of 73 selected components.
Each year the seasonal status of every series is reevaluated based
upon certain statistical criteria. If any of the 73 components
change their seasonal adjustment status from seasonally adjusted to
not seasonally adjusted, not seasonally adjusted data will be used in
the aggregation of the dependent series for the last 5 years, but the
seasonally adjusted indexes will be used before that period. Note:
47 of the 73 components are seasonally adjusted for 2009.
Seasonally adjusted data, including the all items index levels, are
subject to revision for up to five years after their original
release. For this reason, BLS advises against the use of these data
in escalation agreements.
Effective with the calculation of the seasonal factors for 1990, the
Bureau of Labor Statistics has used an enhanced seasonal adjustment
procedure called Intervention Analysis Seasonal Adjustment for some
CPI series. Intervention Analysis Seasonal Adjustment allows for
better estimates of seasonally adjusted data. Extreme values and/or
sharp movements which might distort the seasonal pattern are
estimated and removed from the data prior to calculation of seasonal
factors. Beginning with the calculation of seasonal factors for
1996, X-12-ARIMA software was used for Intervention Analysis Seasonal
Adjustment.
For the seasonal factors introduced in January 2009, BLS adjusted 29
series using Intervention Analysis Seasonal Adjustment, including
selected food and beverage items, motor fuels, electricity and
vehicles. For example, this procedure was used for the Motor fuel
series to offset the effects of events such as damage to oil
refineries from Hurricane Katrina.
For a complete list of Intervention Analysis Seasonal Adjustment
series and explanations, please refer to the article "Intervention
Analysis Seasonal Adjustment",
Re: linear programming
A consumer price index (CPI) is a measure estimating the average price of consumer goods and services purchased by households. A consumer price index measures a price change for a constant market basket of goods and services from one period to the next within the same area (city, region, or nation).[1] It is a price index determined by measuring the price of a standard group of goods meant to represent the typical market basket of a typical urban consumer.[2] Related, but different, terms are the United Kingdom's CPI, RPI, and RPIX. It is one of several price indices calculated by most national statistical agencies. The percent change in the CPI is a measure estimating inflation. The CPI can be used to index (i.e., adjust for the effect of inflation on the real value of money: the medium of exchange) wages, salaries, pensions, and regulated or contracted prices. The CPI is, along with the population census and the National Income and Product Accounts, one of the most closely watched national economic statistics.
introduction
Two basic types of data are needed to construct the CPI: price data and weighting data. The price data are collected for a sample of goods and services from a sample of sales outlets in a sample of locations for a sample of times. The weighting data are estimates of the shares of the different types of expenditure as fractions of the total expenditure covered by the index. These weights are usually based upon expenditure data obtained for sampled decades from a sample of households. Although some of the sampling is done using a sampling frame and probabilistic sampling methods, much is done in a commonsense way (purposive sampling) that does not permit estimation of confidence intervals. Therefore, the sampling variance is normally ignored, since a single estimate is required in most of the purposes for which the index is used. Stocks greatly affect this cause.
The index is usually computed yearly, or quarterly in some countries, as a weighted average of sub-indices for different components of consumer expenditure, such as food, housing, clothing, each of which is in turn a weighted average of sub-sub-indices. At the most detailed level, the elementary aggregate level, (for example, men's shirts sold in department stores in San Francisco), detailed weighting information is unavailable, so elementary aggregate indices are computed using an unweighted arithmetic or geometric mean of the prices of the sampled product offers. (However, the growing use of scanner data is gradually making weighting information available even at the most detailed level.) These indices compare prices each month with prices in the price-reference month. The weights used to combine them into the higher-level aggregates, and then into the overall index, relate to the estimated expenditures during a preceding whole year of the consumers covered by the index on the products within its scope in the area covered. Thus the index is a fixed-weight index, but rarely a true Laspeyres index, since the weight-reference period of a year and the price-reference period, usually a more recent single month, do not coincide. It takes time to assemble and process the information used for weighting which, in addition to household expenditure surveys, may include trade and tax data.
Ideally, the weights would relate to the composition of expenditure during the time between the price-reference month and the current month. There is a large technical economics literature on index formulae which would approximate this and which can be shown to approximate what economic theorists call a true cost of living index. Such an index would show how consumer expenditure would have to move to compensate for price changes so as to allow consumers to maintain a constant standard of living. Approximations can only be computed retrospectively, whereas the index has to appear monthly and, preferably, quite soon. Nevertheless, in some countries, notably in the United States and Sweden, the philosophy of the index is that it is inspired by and approximates the notion of a true cost of living (constant utility) index, whereas in most of Europe it is regarded more pragmatically.
The coverage of the index may be limited. Consumers' expenditure abroad is usually excluded; visitors' expenditure within the country may be excluded in principle if not in practice; the rural population may or may not be included; certain groups such as the very rich or the very poor may be excluded. Saving and investment are always excluded, though the prices paid for financial services provided by financial intermediaries may be included along with insurance.
The index reference period, usually called the base year, often differs both from the weight-reference period and the price reference period. This is just a matter of rescaling the whole time-series to make the value for the index reference-period equal to 100. Annually revised weights are a desirable but expensive feature of an index, for the older the weights the greater is the divergence between the current expenditure pattern and that of the weight reference-period.
Example: The prices of 95,000 items from 22,000 stores, and 35,000 rental units are added together and averaged. They are weighted this way: Housing: 41.4%, Food and Beverage: 17.4%, Transport: 17.0%, Medical Care: 6.9%, Other: 6.9%, Apparel: 6.0%, Entertainment: 4.4%. Taxes (43%) are not included in CPI computation
formula
CPI= (Productrep X Pricecurrent)/(Productrep X Price11987*)
Weighting
Weights and sub-indices
Weights can be expressed as fractions or ratios summing to one, as percentages summing to 100 or as per mille numbers summing to 1000.
In the European Union's Harmonised Index of Consumer Prices, for example, each country computes some 80 prescribed sub-indices, their weighted average constituting the national Harmonised Index. The weights for these sub-indices will consist of the sum of the weights of a number of component lower level indexes. The classification is according to use, developed in a national accounting context. This is not necessarily the kind of classification that is most appropriate for a Consumer Price Index. Grouping together of substitutes or of products whose prices tend to move in parallel might be more suitable.
For some of these lower level indexes detailed reweighing to make them be available, allowing computations where the individual price observations can all be weighted. This may be the case, for example, where all selling is in the hands of a single national organisation which makes its data available to the index compilers. For most lower level indexes, however, the weight will consist of the sum of the weights of a number of elementary aggregate indexes, each weight corresponding to its fraction of the total annual expenditure covered by the index. An 'elementary aggregate' is a lowest-level component of expenditure, one which has a weight but within which, weights of its sub-components are usually lacking. Thus, for example: Weighted averages of elementary aggregate indexes (e.g. for men’s shirts, raincoats, women’s dresses etc.) make up low level indexes (e.g. Outer garments),
Weighted averages of these in turn provide sub-indices at a higher, more aggregated level,(e.g. clothing) and weighted averages of the latter provide yet more aggregated sub-indices (e.g. Clothing and Footwear).
Some of the elementary aggregate indexes, and some of the sub-indexes can be defined simply in terms of the types of goods and/or services they cover, as in the case of such products as newspapers in some countries and postal services, which have nationally uniform prices. But where price movements do differ or might differ between regions or between outlet types, separate regional and/or outlet-type elementary aggregates are ideally required for each detailed category of goods and services, each with its own weight. An example might be an elementary aggregate for sliced bread sold in supermarkets in the Northern region.
Most elementary aggregate indexes are necessarily 'unweighted' averages for the sample of products within the sampled outlets. However in cases where it is possible to select the sample of outlets from which prices are collected so as to reflect the shares of sales to consumers of the different outlet types covered, self-weighted elementary aggregate indexes may be computed. Similarly, if the market shares of the different types of product represented by product types are known, even only approximately, the number of observed products to be priced for each of them can be made proportional to those shares.
Estimating weights
The outlet and regional dimensions noted above mean that the estimation of weights involves a lot more than just the breakdown of expenditure by types of goods and services, and the number of separately weighted indexes composing the overall index depends upon two factors:
The degree of detail to which available data permit breakdown of total consumption expenditure in the weight reference-period by type of expenditure, region and outlet type.
Whether there is reason to believe that price movements vary between these most detailed categories.
How the weights are calculated, and in how much detail, depends upon the availability of information and upon the scope of the index. In the UK the RPI does not relate to the whole of consumption, for the reference population is all private households with the exception of a) pensioner households that derive at least three-quarters of their total income from state pensions and benefits and b) “high income households” whose total household income lies within the top four per cent of all households. The result is that it is difficult to use data sources relating to total consumption by all population groups.
For products whose price movements can differ between regions and between different types of outlet:
The ideal, rarely realisable in practice, would consist of estimates of expenditure for each detailed consumption category, for each type of outlet, for each region.
At the opposite extreme, with no regional data on expenditure totals but only on population (e.g. 24% in the Northern region) and only national estimates for the shares of different outlet types for broad categories of consumption (e.g. 70% of food sold in supermarkets) the weight for sliced bread sold in supermarkets in the Northern region has to be estimated as the share of sliced bread in total consumption × 0.24 × 0.7.
The situation in most countries comes somewhere between these two extremes. The point is to make the best use of whatever data are available.
The nature of the data used for weighting
No firm rules can be suggested on this issue for the simple reason that the available statistical sources differ between countries. However, all countries conduct periodical Household Expenditure surveys and all produce breakdowns of Consumption Expenditure in their National Accounts. The expenditure classifications used there may however be different. In particular:
Household Expenditure surveys do not cover the expenditures of foreign visitors, though these may be within the scope of a Consumer Price Index.
National Accounts include imputed rents for owner-occupied dwellings which may not be within the scope of a Consumer Price Index.
Even with the necessary adjustments, the National Account estimates and Household Expenditure Surveys usually diverge.
The statistical sources required for regional and outlet-type breakdowns are usually weaker. Only a large-sample Household Expenditure survey can provide a regional breakdown. Regional population data are sometimes used for this purpose, but need adjustment to allow for regional differences in living standards and consumption patterns. Statistics of retail sales and market research reports can provide information for estimating outlet-type breakdowns, but the classifications they use rarely correspond to COICOP categories.
The increasingly widespread use of bar codes, scanners in shops has meant that detailed cash register printed receipts are provided by shops for an increasing share of retail purchases. This development makes possible improved Household Expenditure surveys, as Statistics Iceland has demonstrated. Survey respondents keeping a diary of their purchases need to record only the total of purchases when itemised receipts were given to them and keep these receipts in a special pocket in the diary. These receipts provide not only a detailed breakdown of purchases but also the name of the outlet. Thus response burden is markedly reduced, accuracy is increased, product description is more specific and point of purchase data are obtained, facilitating the estimation of outlet-type weights.
There are only two general principles for the estimation of weights: use all the available information and accept that rough estimates are better than no estimates.
Reweighing
Ideally, in computing an index, the weights would represent current annual expenditure patterns. In practice they necessarily reflect past expenditure patterns, using the most recent data available or, if they are not of high quality, some average of the data for more than one previous year. Some countries have used a three-year average in recognition of the fact that household survey estimates are of poor quality. In some cases some of the data sources used may not be available annually, in which case some of the weights for lower level aggregates within higher level aggregates are based on older data than the higher level weights.
Infrequent reweighing saves costs for the national statistical office but delays the introduction into the index of new types of expenditure. For example, subscriptions for Internet Service entered index compilation with a considerable time lag in some countries, and account could be taken of digital camera prices between re-weightings only by including some digital cameras in the same elementary aggregate as film cameras.
A consumer price index (CPI) is a measure estimating the average price of consumer goods and services purchased by households. A consumer price index measures a price change for a constant market basket of goods and services from one period to the next within the same area (city, region, or nation).[1] It is a price index determined by measuring the price of a standard group of goods meant to represent the typical market basket of a typical urban consumer.[2] Related, but different, terms are the United Kingdom's CPI, RPI, and RPIX. It is one of several price indices calculated by most national statistical agencies. The percent change in the CPI is a measure estimating inflation. The CPI can be used to index (i.e., adjust for the effect of inflation on the real value of money: the medium of exchange) wages, salaries, pensions, and regulated or contracted prices. The CPI is, along with the population census and the National Income and Product Accounts, one of the most closely watched national economic statistics.
introduction
Two basic types of data are needed to construct the CPI: price data and weighting data. The price data are collected for a sample of goods and services from a sample of sales outlets in a sample of locations for a sample of times. The weighting data are estimates of the shares of the different types of expenditure as fractions of the total expenditure covered by the index. These weights are usually based upon expenditure data obtained for sampled decades from a sample of households. Although some of the sampling is done using a sampling frame and probabilistic sampling methods, much is done in a commonsense way (purposive sampling) that does not permit estimation of confidence intervals. Therefore, the sampling variance is normally ignored, since a single estimate is required in most of the purposes for which the index is used. Stocks greatly affect this cause.
The index is usually computed yearly, or quarterly in some countries, as a weighted average of sub-indices for different components of consumer expenditure, such as food, housing, clothing, each of which is in turn a weighted average of sub-sub-indices. At the most detailed level, the elementary aggregate level, (for example, men's shirts sold in department stores in San Francisco), detailed weighting information is unavailable, so elementary aggregate indices are computed using an unweighted arithmetic or geometric mean of the prices of the sampled product offers. (However, the growing use of scanner data is gradually making weighting information available even at the most detailed level.) These indices compare prices each month with prices in the price-reference month. The weights used to combine them into the higher-level aggregates, and then into the overall index, relate to the estimated expenditures during a preceding whole year of the consumers covered by the index on the products within its scope in the area covered. Thus the index is a fixed-weight index, but rarely a true Laspeyres index, since the weight-reference period of a year and the price-reference period, usually a more recent single month, do not coincide. It takes time to assemble and process the information used for weighting which, in addition to household expenditure surveys, may include trade and tax data.
Ideally, the weights would relate to the composition of expenditure during the time between the price-reference month and the current month. There is a large technical economics literature on index formulae which would approximate this and which can be shown to approximate what economic theorists call a true cost of living index. Such an index would show how consumer expenditure would have to move to compensate for price changes so as to allow consumers to maintain a constant standard of living. Approximations can only be computed retrospectively, whereas the index has to appear monthly and, preferably, quite soon. Nevertheless, in some countries, notably in the United States and Sweden, the philosophy of the index is that it is inspired by and approximates the notion of a true cost of living (constant utility) index, whereas in most of Europe it is regarded more pragmatically.
The coverage of the index may be limited. Consumers' expenditure abroad is usually excluded; visitors' expenditure within the country may be excluded in principle if not in practice; the rural population may or may not be included; certain groups such as the very rich or the very poor may be excluded. Saving and investment are always excluded, though the prices paid for financial services provided by financial intermediaries may be included along with insurance.
The index reference period, usually called the base year, often differs both from the weight-reference period and the price reference period. This is just a matter of rescaling the whole time-series to make the value for the index reference-period equal to 100. Annually revised weights are a desirable but expensive feature of an index, for the older the weights the greater is the divergence between the current expenditure pattern and that of the weight reference-period.
Example: The prices of 95,000 items from 22,000 stores, and 35,000 rental units are added together and averaged. They are weighted this way: Housing: 41.4%, Food and Beverage: 17.4%, Transport: 17.0%, Medical Care: 6.9%, Other: 6.9%, Apparel: 6.0%, Entertainment: 4.4%. Taxes (43%) are not included in CPI computation
formula
CPI= (Productrep X Pricecurrent)/(Productrep X Price11987*)
Weighting
Weights and sub-indices
Weights can be expressed as fractions or ratios summing to one, as percentages summing to 100 or as per mille numbers summing to 1000.
In the European Union's Harmonised Index of Consumer Prices, for example, each country computes some 80 prescribed sub-indices, their weighted average constituting the national Harmonised Index. The weights for these sub-indices will consist of the sum of the weights of a number of component lower level indexes. The classification is according to use, developed in a national accounting context. This is not necessarily the kind of classification that is most appropriate for a Consumer Price Index. Grouping together of substitutes or of products whose prices tend to move in parallel might be more suitable.
For some of these lower level indexes detailed reweighing to make them be available, allowing computations where the individual price observations can all be weighted. This may be the case, for example, where all selling is in the hands of a single national organisation which makes its data available to the index compilers. For most lower level indexes, however, the weight will consist of the sum of the weights of a number of elementary aggregate indexes, each weight corresponding to its fraction of the total annual expenditure covered by the index. An 'elementary aggregate' is a lowest-level component of expenditure, one which has a weight but within which, weights of its sub-components are usually lacking. Thus, for example: Weighted averages of elementary aggregate indexes (e.g. for men’s shirts, raincoats, women’s dresses etc.) make up low level indexes (e.g. Outer garments),
Weighted averages of these in turn provide sub-indices at a higher, more aggregated level,(e.g. clothing) and weighted averages of the latter provide yet more aggregated sub-indices (e.g. Clothing and Footwear).
Some of the elementary aggregate indexes, and some of the sub-indexes can be defined simply in terms of the types of goods and/or services they cover, as in the case of such products as newspapers in some countries and postal services, which have nationally uniform prices. But where price movements do differ or might differ between regions or between outlet types, separate regional and/or outlet-type elementary aggregates are ideally required for each detailed category of goods and services, each with its own weight. An example might be an elementary aggregate for sliced bread sold in supermarkets in the Northern region.
Most elementary aggregate indexes are necessarily 'unweighted' averages for the sample of products within the sampled outlets. However in cases where it is possible to select the sample of outlets from which prices are collected so as to reflect the shares of sales to consumers of the different outlet types covered, self-weighted elementary aggregate indexes may be computed. Similarly, if the market shares of the different types of product represented by product types are known, even only approximately, the number of observed products to be priced for each of them can be made proportional to those shares.
Estimating weights
The outlet and regional dimensions noted above mean that the estimation of weights involves a lot more than just the breakdown of expenditure by types of goods and services, and the number of separately weighted indexes composing the overall index depends upon two factors:
The degree of detail to which available data permit breakdown of total consumption expenditure in the weight reference-period by type of expenditure, region and outlet type.
Whether there is reason to believe that price movements vary between these most detailed categories.
How the weights are calculated, and in how much detail, depends upon the availability of information and upon the scope of the index. In the UK the RPI does not relate to the whole of consumption, for the reference population is all private households with the exception of a) pensioner households that derive at least three-quarters of their total income from state pensions and benefits and b) “high income households” whose total household income lies within the top four per cent of all households. The result is that it is difficult to use data sources relating to total consumption by all population groups.
For products whose price movements can differ between regions and between different types of outlet:
The ideal, rarely realisable in practice, would consist of estimates of expenditure for each detailed consumption category, for each type of outlet, for each region.
At the opposite extreme, with no regional data on expenditure totals but only on population (e.g. 24% in the Northern region) and only national estimates for the shares of different outlet types for broad categories of consumption (e.g. 70% of food sold in supermarkets) the weight for sliced bread sold in supermarkets in the Northern region has to be estimated as the share of sliced bread in total consumption × 0.24 × 0.7.
The situation in most countries comes somewhere between these two extremes. The point is to make the best use of whatever data are available.
The nature of the data used for weighting
No firm rules can be suggested on this issue for the simple reason that the available statistical sources differ between countries. However, all countries conduct periodical Household Expenditure surveys and all produce breakdowns of Consumption Expenditure in their National Accounts. The expenditure classifications used there may however be different. In particular:
Household Expenditure surveys do not cover the expenditures of foreign visitors, though these may be within the scope of a Consumer Price Index.
National Accounts include imputed rents for owner-occupied dwellings which may not be within the scope of a Consumer Price Index.
Even with the necessary adjustments, the National Account estimates and Household Expenditure Surveys usually diverge.
The statistical sources required for regional and outlet-type breakdowns are usually weaker. Only a large-sample Household Expenditure survey can provide a regional breakdown. Regional population data are sometimes used for this purpose, but need adjustment to allow for regional differences in living standards and consumption patterns. Statistics of retail sales and market research reports can provide information for estimating outlet-type breakdowns, but the classifications they use rarely correspond to COICOP categories.
The increasingly widespread use of bar codes, scanners in shops has meant that detailed cash register printed receipts are provided by shops for an increasing share of retail purchases. This development makes possible improved Household Expenditure surveys, as Statistics Iceland has demonstrated. Survey respondents keeping a diary of their purchases need to record only the total of purchases when itemised receipts were given to them and keep these receipts in a special pocket in the diary. These receipts provide not only a detailed breakdown of purchases but also the name of the outlet. Thus response burden is markedly reduced, accuracy is increased, product description is more specific and point of purchase data are obtained, facilitating the estimation of outlet-type weights.
There are only two general principles for the estimation of weights: use all the available information and accept that rough estimates are better than no estimates.
Reweighing
Ideally, in computing an index, the weights would represent current annual expenditure patterns. In practice they necessarily reflect past expenditure patterns, using the most recent data available or, if they are not of high quality, some average of the data for more than one previous year. Some countries have used a three-year average in recognition of the fact that household survey estimates are of poor quality. In some cases some of the data sources used may not be available annually, in which case some of the weights for lower level aggregates within higher level aggregates are based on older data than the higher level weights.
Infrequent reweighing saves costs for the national statistical office but delays the introduction into the index of new types of expenditure. For example, subscriptions for Internet Service entered index compilation with a considerable time lag in some countries, and account could be taken of digital camera prices between re-weightings only by including some digital cameras in the same elementary aggregate as film cameras.
Re: linear programming
can anyone help with this problem
Julia is a senior at Tech, and she's investigating different ways to finance her final year at school. She is considering leasing a food booth outside the Tech stadium at home football games. Tech sells out every home game, and Julia knows, from attending the games herself, that everyone eats a lot of food. She has to pay $1,000 per game for a booth, and the booths are not very large. Vendors can sell either food or drinks on Tech property, but not both. Only the Tech athletic department concession stands can sell both inside the stadium. She thinks slices of cheese pizza, hot dogs, and barbecue sandwiches are the most popular food items among fans and so these are the items she would sell.
Most food items are sold during the hour before the game starts and during half time; thus it will not be possible for Julia to prepare the food while she is selling it. She must prepare the food ahead of time and then store it in a warming oven. For $600 she can lease a warming oven for the six-game home season. The oven has 16 shelves, and each shelf is 3 feet by 4 feet. She plans to fill the oven with the three food items before the game and then again before half time.
Julia has negotiated with a local pizza delivery company to deliver 14-inch cheese pizzas twice each game - 2 hours before the game and right after the opening kickoff. Each pizza will cost her $4.50 and will include 6 slices. She estimates it will cost her $0.50 for each hot dog and $1.00 for each barbecue sandwich if she makes the barbecue herself the night before. She measured a hot dog and found it takes up about 16 in2 of space, whereas a barbecue sandwich takes up about 25 in2. She plans to sell a piece of pizza for $1.50 and a hot dog for $1.60 each and a barbecue sandwich for $2.25. She has $1,500 in cash available to purchase and prepare the food items for the first home game; for the remaining five games she will purchase her ingredients with money she has made from the previous game.
Julia has talked to some students and vendors who have sold food at previous football games at Tech as well as at other universities. From this she has discovered that she can expect to sell at least as many slices of pizza as hot dogs and barbecue sandwiches combined. She also anticipates that she will probably sell at least twice as many hot dogs as barbecue sandwiches. She believes that she will sell everything she can stock and develop a customer base for the season if she follows these general guidelines for demand.
If Julia clears at least $1,000 in profit for each game after paying all her expenses, she believes it will be worth leasing the booth.
A. Formulate a linear programming model for Julia that will help you to advise her if she should lease the booth. Formulate the model for the first home game. Explain how you derived the profit function and constraints and show any calculations that allow you to arrive at those equations.
B. Solve the linear programming model using a computer for Julia that will help you advise her if she should lease the booth. In this solution, determine the number of pizza slices, hot dogs and barbecue sandwiches she should sell at each game. Also determine the revenues, cost and profit; and do an analysis of how much money she actually will make each game given the expenses of each game.
Do an analysis of the profit solution and what impact it has on Julia's ability to have sufficient funds for the next home game to purchase and prepare the food. What would you recommend to Julia?
C. If Julia were to borrow some money from a friend before the first game to purchase more ingredients, she feels she can increase her profits. What amount, if any, would you recommend to Julia to borrow?
can anyone help with this problem
Julia is a senior at Tech, and she's investigating different ways to finance her final year at school. She is considering leasing a food booth outside the Tech stadium at home football games. Tech sells out every home game, and Julia knows, from attending the games herself, that everyone eats a lot of food. She has to pay $1,000 per game for a booth, and the booths are not very large. Vendors can sell either food or drinks on Tech property, but not both. Only the Tech athletic department concession stands can sell both inside the stadium. She thinks slices of cheese pizza, hot dogs, and barbecue sandwiches are the most popular food items among fans and so these are the items she would sell.
Most food items are sold during the hour before the game starts and during half time; thus it will not be possible for Julia to prepare the food while she is selling it. She must prepare the food ahead of time and then store it in a warming oven. For $600 she can lease a warming oven for the six-game home season. The oven has 16 shelves, and each shelf is 3 feet by 4 feet. She plans to fill the oven with the three food items before the game and then again before half time.
Julia has negotiated with a local pizza delivery company to deliver 14-inch cheese pizzas twice each game - 2 hours before the game and right after the opening kickoff. Each pizza will cost her $4.50 and will include 6 slices. She estimates it will cost her $0.50 for each hot dog and $1.00 for each barbecue sandwich if she makes the barbecue herself the night before. She measured a hot dog and found it takes up about 16 in2 of space, whereas a barbecue sandwich takes up about 25 in2. She plans to sell a piece of pizza for $1.50 and a hot dog for $1.60 each and a barbecue sandwich for $2.25. She has $1,500 in cash available to purchase and prepare the food items for the first home game; for the remaining five games she will purchase her ingredients with money she has made from the previous game.
Julia has talked to some students and vendors who have sold food at previous football games at Tech as well as at other universities. From this she has discovered that she can expect to sell at least as many slices of pizza as hot dogs and barbecue sandwiches combined. She also anticipates that she will probably sell at least twice as many hot dogs as barbecue sandwiches. She believes that she will sell everything she can stock and develop a customer base for the season if she follows these general guidelines for demand.
If Julia clears at least $1,000 in profit for each game after paying all her expenses, she believes it will be worth leasing the booth.
A. Formulate a linear programming model for Julia that will help you to advise her if she should lease the booth. Formulate the model for the first home game. Explain how you derived the profit function and constraints and show any calculations that allow you to arrive at those equations.
B. Solve the linear programming model using a computer for Julia that will help you advise her if she should lease the booth. In this solution, determine the number of pizza slices, hot dogs and barbecue sandwiches she should sell at each game. Also determine the revenues, cost and profit; and do an analysis of how much money she actually will make each game given the expenses of each game.
Do an analysis of the profit solution and what impact it has on Julia's ability to have sufficient funds for the next home game to purchase and prepare the food. What would you recommend to Julia?
C. If Julia were to borrow some money from a friend before the first game to purchase more ingredients, she feels she can increase her profits. What amount, if any, would you recommend to Julia to borrow?
abhishreshthaa
Abhijeet S
Re: linear programming
hey friend, check this link the solution is here...
LPP SOLUTION
:thedevil1:
can anyone help with this problem
Julia is a senior at Tech, and she's investigating different ways to finance her final year at school. She is considering leasing a food booth outside the Tech stadium at home football games. Tech sells out every home game, and Julia knows, from attending the games herself, that everyone eats a lot of food. She has to pay $1,000 per game for a booth, and the booths are not very large. Vendors can sell either food or drinks on Tech property, but not both. Only the Tech athletic department concession stands can sell both inside the stadium. She thinks slices of cheese pizza, hot dogs, and barbecue sandwiches are the most popular food items among fans and so these are the items she would sell.
Most food items are sold during the hour before the game starts and during half time; thus it will not be possible for Julia to prepare the food while she is selling it. She must prepare the food ahead of time and then store it in a warming oven. For $600 she can lease a warming oven for the six-game home season. The oven has 16 shelves, and each shelf is 3 feet by 4 feet. She plans to fill the oven with the three food items before the game and then again before half time.
Julia has negotiated with a local pizza delivery company to deliver 14-inch cheese pizzas twice each game - 2 hours before the game and right after the opening kickoff. Each pizza will cost her $4.50 and will include 6 slices. She estimates it will cost her $0.50 for each hot dog and $1.00 for each barbecue sandwich if she makes the barbecue herself the night before. She measured a hot dog and found it takes up about 16 in2 of space, whereas a barbecue sandwich takes up about 25 in2. She plans to sell a piece of pizza for $1.50 and a hot dog for $1.60 each and a barbecue sandwich for $2.25. She has $1,500 in cash available to purchase and prepare the food items for the first home game; for the remaining five games she will purchase her ingredients with money she has made from the previous game.
Julia has talked to some students and vendors who have sold food at previous football games at Tech as well as at other universities. From this she has discovered that she can expect to sell at least as many slices of pizza as hot dogs and barbecue sandwiches combined. She also anticipates that she will probably sell at least twice as many hot dogs as barbecue sandwiches. She believes that she will sell everything she can stock and develop a customer base for the season if she follows these general guidelines for demand.
If Julia clears at least $1,000 in profit for each game after paying all her expenses, she believes it will be worth leasing the booth.
A. Formulate a linear programming model for Julia that will help you to advise her if she should lease the booth. Formulate the model for the first home game. Explain how you derived the profit function and constraints and show any calculations that allow you to arrive at those equations.
B. Solve the linear programming model using a computer for Julia that will help you advise her if she should lease the booth. In this solution, determine the number of pizza slices, hot dogs and barbecue sandwiches she should sell at each game. Also determine the revenues, cost and profit; and do an analysis of how much money she actually will make each game given the expenses of each game.
Do an analysis of the profit solution and what impact it has on Julia's ability to have sufficient funds for the next home game to purchase and prepare the food. What would you recommend to Julia?
C. If Julia were to borrow some money from a friend before the first game to purchase more ingredients, she feels she can increase her profits. What amount, if any, would you recommend to Julia to borrow?
hey friend, check this link the solution is here...
LPP SOLUTION
:thedevil1:
Jennyshine
Jenny Shine
lease help me can anybody guide me how to make project on "cost minimization in consumer price indices" ? if any ony have any project of linear programming shopping please mail me at [email protected]
Hey friend,
Here I am up-loading Study on Consumer Price Index Methodology, please check attachment below.