Glossary
The following terms are arranged by subject group and provide a
basic understanding of elasticities and related economic
concepts.
Demand Elasticities
• Price Elasticity of
Demand
• Own-Price Elasticity
• Cross-Price Elasticity
• Income Elasticity of
Demand
• Expenditure Elasticity
of Demand
Demand Functions
• Hicksian or Compensated
Demand
• Marshallian,
Ordinary, or
Uncompensated
Demand
• Conditional Demand
• Unconditional Demand
Demand Properties (relationships
among elasticities)
• Additivity
• Homogeneity
• Negativity
• Symmetry
Commodity Elasticity
Models
• Double-Log
• Translog
• Rotterdam Model
• Linear Expenditure
System
• Almost Ideal Demand System
Type of Data Used
• Time Series Data
• Cross Sectional Data
• Panel Data
Resources
Demand
Elasticities
A measure of how demand change in response to changes in prices
or income. Since elasticity is a relative measure, it is
independent of scale and, thus, provides a useful measure of
comparison across all ranges and quantities.
Price Elasticity of Demand
A measure of the responsiveness of demand to a change in
price.
Own-Price Elasticity. A
measure of the responsiveness of demand for a good to a change in
price of that good. Represented by the ratio between percentage
change in quantity demanded and percentage change in price:
If the percent change in the quantity demanded is greater than
the percent change in the price of a good, demand is said to be
price elastic or more responsive to price changes. (Example: A
1-percent change in price induces a change in quantity demanded by
more than 1 percent.) If the percent change in the quantity
demanded is less than the percent change in the price of a good,
demand is said to be price inelastic, or less responsive to price
changes. (Example: A 1-percent change in price induces a change in
quantity demanded by less than 1 percent.) If the response is
exactly equal to 1 percent, the demand is said to be unitary, where
a 1-percent decrease in price results in a 1-percent increase in
demand. The higher the price elasticity, the more sensitive
consumer demand is to price changes.
Cross-Price Elasticity. A
measure of responsiveness of demand for one good to a change in the
price of another good. Represented by the ratio of the percent
change in the quantity demanded of good X to a percent change in
the price of some other good Y:
If the percent change in the quantity demanded of good X is
greater than the percent change in the price of good Y, the demand
for good X is said to be cross-price elastic with respect to good
Y, or responsive to changes in the price of good Y. (Example: A
1-percent change in cross price induces a change in quantity
demanded by more than 1 percent.) If the percent change in the
quantity demanded of good X is less than the percent change in the
price of good Y, the demand for good X is said to be cross-price
inelastic with respect to good Y, or not responsive to changes in
the price of good Y. (Example: A 1-percent change in cross price
induces a change in the quantity demanded by less than 1 percent.)
Cross-price elasticities can be complements or substitutes. If the
cross-price elasticity of demand is positive, the goods X and Y are
substitutes. If the cross-price elasticity of demand is negative,
the goods X and Y are complements.
Income Elasticity of
Demand
A measure of the responsiveness of demand to changes in income.
Shows how the quantity purchased changes (how sensitive it is) in
response to a change in the consumer's income. Represented by the
ratio between percentage change in quantity demanded and percentage
change in income:
If the percent change in the quantity demanded is greater than
the percent change in consumer income, the demand is said to be
income elastic, or responsive to changes in consumer income.
(Example: A 1-percent change in income induces a change in quantity
demanded by more than 1 percent.) If the percent change in the
quantity demanded is less than the percent change in consumer
income, the demand is said to be income inelastic, or not
responsive to changes in consumer income. (Example: A 1-percent
change in income induces a change in quantity demanded by less than
1 percent.) The higher the income elasticity, the more sensitive
consumer demand is to income changes.
Assumption: If the income elasticity of demand is positive, the
good is a normal good, and if the income elasticity of demand is
negative, the good must be an inferior good. Negative income
elasticity is common with staple foods in developing countries,
generally considered inferior goods. As income increases, consumers
substitute traditional staple foods (such as rice, cassava, corn,
wheat, and potatoes) for higher value foods such as meats, fruits,
and processed products.
Expenditure Elasticity of
Demand
A measure of the responsiveness of demand to changes in
expenditure on a bundle of similar goods. Shows how the quantity
purchased changes (how sensitive it is) in response to a change in
the consumer's expenditure, which is a proxy for income. The
expenditure is from a bundle of similar goods that can be separated
from other goods. Some demand models, such as the Almost Ideal Demand System (AIDS), use budget
shares or expenditure on goods and not household income in
estimating the demand system. Represented by the ratio between
percentage change in quantity demanded and percentage change in
expenditure:
If the percent change in the quantity demanded is greater than
the percent change in consumer expenditure, the demand is said to
be expenditure elastic, or responsive to changes in consumer
expenditure. (Example: A 1-percent change in expenditure induces a
change in quantity demanded by more than 1 percent.) If the percent
change in the quantity demanded is less than the percent change in
consumer expenditure, the demand is said to be expenditure
inelastic, or not responsive to changes in consumer expenditure.
(Example: A 1-percent change in expenditure induces a change in
quantity demanded by less than 1 percent.) The higher the
expenditure elasticity, the more sensitive consumer demand is to
expenditure changes.
The AIDS demand system provides expenditure elasticities of
demand. Modeling demand as commodity groups with budget shares and
expenditures uses the composite commodity theorem, separability of
commodities, and two-stage budgeting. For reference on these
topics, see Deaton and Muellbauer,Economics and Consumer Behavior,
Cambridge University Press, Cambridge, MA, 1980, chapter 5, pp.
117-142.
Demand
Functions
Economists use mathematical equations (functions) to model
consumer demand. The causal relationship is between quantity
demanded by the consumer, which is the dependent variable, and the
price of a good and consumer income, which are the independent
variables.
Hicksian or Compensated Demand
The Hicksian demand function (after British economist Sir John
R. Hicks) shows the relationship between the price of a good, P1,
and the quantity purchased on the assumption that other prices, P2,
and utility, U0, are held constant. This consumer demand function
is obtained by minimizing the consumer's expenditures subject to
the constraint that his/her utility (the satisfaction a consumer
derives from a particular market basket) is fixed at level U0.
Hicksian and Compensated Demand functions are the same and are
represented by the following equation: h1(P1, P2, U0).
Marshallian,
Ordinary, or Uncompensated Demand
The Marshallian demand function (after British economist Alfred
Marshall) shows the relationship between the price of a good, P1,
and the quantity purchased, Q1, on the assumption that other
prices, P2, and the consumer's budget (or income), Y0, is held
constant. The demand function is obtained by maximizing the
consumer's utility subject to the constraint that the customer's
budget is fixed at the level Y0 and so are other prices.
Marshallian, Ordinary, and Uncompensated Demand functions are the
same and are represented by the following equation: Q1= f (P1, P2,
Y0).
Conditional Demand
Conditional demand is derived from using a subset of the
consumer's total budget. An example would be estimating food demand
using the budget only for food. The demand is conditional upon the
food budget and not the entire budget.
Unconditional Demand
Unconditional demand is a demand system that uses the consumer's
entire budget.
Demand
Properties (relationships among elasticities)
Marshallian and Hicksian demand functions exhibit specific
theoretical properties based on the assumptions used to derive the
functions. Marshallian demand properties include additivity and
homogeneity. Hicksian demand properties include additivity,
homogeneity, negativity, and symmetry.
Additivity
For both Marshallian and Hicksian demand functions, the budget
constraint is satisfied for the given prices and income. The total
expenditure is equal to the sum of individual expenditures on
different commodities and goods. Additivity (or adding up) ensures
that the income effects add up.
Homogeneity
Marshallian demand functions are homogeneous of degree zero in
both prices and income. Hicksian demand functions are homogenous of
degree zero in prices only. If both prices and income double, then
Marshallian demand does not change. In Hicksian demand functions,
if all prices double with a given level of utility, then demand
does not change. If price and income increase by the same
percentage, there is no change in demand.
Negativity
The negativity-of-own-substitution effect is the law of the
downward-sloping Hicksian demand curve. If the own-price increases
and expenditure is adjusted to keep utility constant, then demand
for the good will decrease. This is a property of the Hicksian
demand function only, not of the Marshallian demand function.
Symmetry
The cross price elasticities of a Hicksian demand function are
symmetric because of Slutsky symmetry conditions. Assuming there is
no income effect of a price change, the cross-substitution effect
between good X and Y must be the same as the cross-substitution
effect between Y and X. This relationship can be used to predict
the change in demand for good X if the price of good Y
increases.
Commodity Elasticity
Models
An equation or set of equations with defined parameters used to
measure the elasticity of demand.
Double-Log
The double-log demand equation is obtained by taking logs of
both sides of a multiplicative demand equation. The convenient
property of double-log demand is that the parameters directly
measure the price elasticity of demand.
Translog
This modeling system is known as a flexible functional form. The
indirect translog model approximates the indirect utility function
by quadratic form in the logarithms of the price-to-expenditure
ratios. These demand equations are homogenous of degree zero. A
limitation in this model is the large number of parameters to be
estimated. For reference, see Christensen, Jorgenson, and Lau,
"Transcendental Logarithmic Utility Function,"American Economic
Review, Vol. 70, 1975, pp. 422-432.
Rotterdam
Model
This demand system/model was developed by Theil and Barten and
has been used frequently to test economic theory. The model is not
in logarithms but works in differentials. Theoretical restrictions
are applied directly to the parameters. For references, see A.P.
Barten, Theorie en empirie van een volledig stelsel van
fraagvergelijkingen, doctoral dissertation, 1966, University of
Rotterdam, Rotterdam, the Netherlands; and Theil, "The Information
Approach to Demand Analysis,"Econometrica, Vol. 33, 1965, pp.
67-87.
Linear Expenditure System
(LES)
The LES demand system is derived from the Stone-Geary utility
function and is a general linear formulation of demand and
algebraically imposed theoretical restrictions of additivity,
homogeneity, and symmetry. The LES is best used to estimate demand
for goods with independent marginal utilities such as large baskets
of goods or large categories of expenditures such as clothing,
housing, food, and durables. For reference, see J.R.N. Stone,
"Linear Expenditure System and Demand Analysis: An Application to
the Pattern of British Demand,"Economic Journal, Vol. 64, 1954, pp.
511-527.
Almost Ideal Demand System
(AIDS)
The AIDS demand system is derived from a utility function
specified as a second-order approximation to any utility function.
Demand is expressed in budget shares and uses the Stone geometric
price index. Theoretical restrictions are applied directly to the
parameters. This model allows testing of homogeneity and symmetry
in estimating demand. For reference, see Deaton and Muellbauer, "An
Almost Ideal Demand System," Econometrica, Vol. 70, 1980,
pp. 312-336.
Type of Data Used
The timeframe or specific range and coverage of data to be used
in estimating the model/demand system.
Time Series
Data
A series of observations made over time for the same variable,
such as prices or income. The frequency-such as days, weeks,
months, or years-is usually evenly spaced over the timeframe.
(Example: A data series of weekly retail prices for the same type
of head lettuce in the same city for the past 10 years.)
Cross
Sectional Data
Observations made at the same time for the same variable but
over a number of units. (Example: A data series of retail prices
for the same type of head lettuce in different cities across the
country for the same week.)
Panel Data
The combination of time series and cross sectional data.
(Example: A data series of weekly retail prices for the same type
of head lettuce in different cities across the country for the past
10 years.)
Resources
For more information on these definitions and demand estimation,
see:
- Angus Deaton and John Muellbauer, Economics and Consumer
Behavior, Cambridge University Press, 1980.
- Stanley R. Johnson, Zuhair A. Hassan, and Richard D. Green,
Demand Systems Estimation: Methods and Applications, Iowa
State University Press, 1984.
- Louis Phlips, Applied Consumption Analysis, Elsevier
Science Publisher, 1982.
- A. Robert Pollak and Terence J. Wailes, Demand System
Specification and Estimation, Oxford University Press,
1995.
- Robert Raunikar and Chung-Liang Huang, Food Demand
Analysis: Problems, Issues, and Empirical Evidence, Iowa State
University Press, 1987.
- Frederick Waugh, Demand and Price Analysis: Some Examples
from Agriculture, U.S. Department of Agriculture, Economic
Research Service, 1964.