The document provides an overview of two demand models: the Linear Expenditure System (LES) and the Almost Ideal Demand System (AIDS). It summarizes the key features of each model, including their basic structure and equations. The LES assumes a linear relationship between income and expenditures, while AIDS allows for more flexibility. AIDS also accounts for substitution effects between goods and can estimate price and income elasticities. The document compares the advantages and limitations of each approach.

1. Course code – AGECON-601
Course title- Advance Micro Economic Analysis
Submitted to
Submitted by
Dr. BC Jain Ankur
Jaiswal
Model – Linear expenditure system
and
Almost ideal demand system

2. Introduction
Demand Model:-
 Primary function of demand models is to predict the
future using time series related or other data we have in
hand. Demand modeling uses statistical methods and
business intelligence inputs to generate accurate
demand forecasts and effectively address demand
variability.
Demand Model
Linear
Expenditure
System (LES)
Almost Ideal
Demand System
(AIDS)

3. Linear Expenditure System (LES)
 Developed by- Stone (1954)
 The Linear Expenditure System (LES) is an economic
model used to analyze consumer behavior in terms of
their spending patterns.
 It is a simple and classical model that assumes a linear
relationship between a consumer's income and their
expenditure on various goods and services.
 The LES is often used in microeconomics and consumer
theory to understand how changes in income affect
consumption.

4. Linear Expenditure System (LES)
 The basic idea behind the Linear Expenditure System
can be summarized in the following equation:
 Where:
 Ei is the expenditure on a specific good or service.
 Y represents the consumer's income.
 ai is the expenditure coefficient, which indicates the
proportion of income spent on that particular good or
service.
 biis the intercept term, representing the minimum
expenditure on the good or service, even if the
Ei​= aiY+bi

5.  Expenditure on a specific good or service (Ei): This
represents how much a consumer spends on a particular
product or service. In the LES, it is assumed to depend on
the consumer's income (Y) and other constants specific to
that good or service.
 Income (Y): This is the total amount of money a consumer
has available to spend on goods and services.
 Expenditure Coefficient (ai): This coefficient reflects the
proportion of a consumer's income spent on a specific good
or service. In other words, it represents how sensitive the
consumer's spending on that particular item is to changes in
their income. If ai is 0.2, it means that for every $1 increase
in income, the consumer will spend 20 cents more on that
item.
 Intercept Term (bi): This term indicates the minimum
expenditure on the good or service, even if the consumer
has zero income. It captures the idea that some level of
consumption may occur even when income is very low or
zero. For example, b could represent the minimum amount

6.  The LES model assumes that the expenditure
coefficients ai and intercept terms bi remain constant
over a certain range of income. However, in reality,
consumer spending patterns may not always follow a
perfectly linear relationship, especially at very low or
high income levels.
 The LES can be used to make predictions about how
changes in income or prices of goods and services will
affect a consumer's spending behavior. It is a basic tool
for analyzing demand and can be helpful in estimating
the effects of changes in government policies, such as
income taxes or subsidies, on consumer choices and
welfare.
Linear Expenditure System (LES)

7. ASSUMPTIONS
 Linearity
 Homogeneity
 Fixed Budget
 Stability
 No Time Dimension
 Perfect Information
 No External Influences
 Rational Behavior

8. Application of LES
 Demand Analysis: The LES is used to analyze and
predict consumer demand for specific goods and services.
By understanding how changes in income affect consumer
spending on different items, it helps businesses and
policymakers anticipate market behavior.
 Budgetary Planning: LES can be employed to estimate
how individuals or households allocate their income to
different categories of expenditure. This information is
crucial for financial planning, budgeting, and assessing the
impact of changes in income or expenses.
 Tax Policy Analysis: Economists and policymakers use
LES to evaluate the impact of tax policies on consumer
behavior. By understanding how consumers adjust their
spending in response to changes in income due to

9. Application of LES
 Economic Welfare Analysis: The model can be applied to
assess the welfare implications of economic policies. It helps
in understanding how changes in prices, income, or policies
affect the well-being of various income groups and can be
used to design policies that aim to reduce income inequality
and improve overall welfare.
 Market Research: LES is a useful tool for businesses to
forecast consumer behavior in response to changes in prices
or income. This information is invaluable for marketing,
product development, and pricing strategies.
 Government Subsidy Programs: It can help assess the
impact of subsidy programs on the consumption of specific
goods or services. Policymakers use LES to understand
whether subsidies effectively encourage the consumption of

10. Advantages of the Linear
Expenditure System (LES):
 Simplicity: The LES is a straightforward model that is
easy to understand and apply. It serves as a useful starting
point for teaching and learning about consumer behavior in
introductory economics courses.
 Analytical Tool: It provides a simple framework for
analyzing and predicting how changes in income or prices
affect consumer spending on specific goods and services.
This makes it a valuable tool for examining basic demand
relationships.
 Policy Analysis: The model can be used to evaluate the
impact of changes in government policies, such as income
taxes, subsidies, or welfare programs, on consumer
choices and overall welfare.
 Useful Benchmark: While the LES may be an
oversimplification of real-world consumer behavior, it can

11. Disadvantages of the Linear
Expenditure System (LES):
 Assumptions: The LES relies on several simplifying assumptions, such
as the linearity of expenditure coefficients and constant intercept terms,
which may not hold in reality. Consumer spending patterns are often
more complex and nonlinear.
 Limited Realism: The model does not capture the full range of factors
that influence consumer behavior, such as consumer preferences,
substitution effects, and complementarity between goods. It
oversimplifies the dynamics of real-world markets.
 Inflexibility: The LES assumes that the relationships between income
and spending on goods are fixed over a specific income range. In reality,
consumer behavior can change at different income levels, and spending
patterns may vary.
 Lack of Precision: The LES may not provide precise predictions of
consumer behavior because it doesn't consider many nuances and
factors that affect spending decisions.
 Not Suitable for All Goods: It may work well for certain categories of
goods and services that exhibit relatively stable consumption patterns
but may not be appropriate for goods with highly elastic or inelastic
demand.
 Limited Use for Long-Term Analysis: The LES is more suitable for

12. Almost ideal demand system
 The Almost Ideal Demand System (AIDS) is an
advanced economic model used to analyze consumer
behavior and demand for various goods and services. It
is an extension of the Linear Expenditure System (LES)
and offers more flexibility and realism in capturing how
consumers allocate their income among different goods.
 Developed by Angus Deaton and John Muellbauer in
the 1980s.

13. Key features and components of
the Almost Ideal Demand System:
 The Utility Function: The AIDS model is grounded in consumer utility
theory, which assumes that individuals seek to maximize their utility, a
measure of well-being or satisfaction, subject to budget constraints.
 Consumer Preferences: Unlike the LES, which assumes linear
relationships between income and spending, the AIDS model allows for
non-linear demand relationships. It captures consumer preferences more
accurately by considering the interdependence and substitution effects
between different goods. This means that as prices and incomes change,
consumers may shift their consumption patterns accordingly.
 Demands for Different Goods: The AIDS model typically includes a set
of demand equations, one for each good or category of goods that the
consumer purchases. These equations represent how consumers allocate
their income to different goods based on their preferences and the prices
of those goods.
 Price and Income Elasticities: The model provides estimates of price
and income elasticities for each good. These elasticities measure how the
quantity demanded of a good responds to changes in its price or the

14. Key features and components of
the Almost Ideal Demand System:
 Expenditure and Engel Curves: The AIDS model allows for
the estimation of expenditure and Engel curves, which
illustrate how the expenditure on a good or category of goods
changes with income. Engel curves provide insights into the
income elasticity of demand for different goods.
 Estimation Methods: To apply the AIDS model, econometric
techniques, such as Maximum Likelihood Estimation (MLE)
or Generalized Method of Moments (GMM), are often used to
estimate the parameters of the demand equations. This
involves using real-world data on prices, incomes, and
consumer choices.
 Versatility: The AIDS model is versatile and can be used to
analyze various aspects of consumer behavior, including
market demand, consumer welfare, the impact of tax policies,
and changes in consumer spending patterns over time.

15. Equation
 The Almost Ideal Demand System (AIDS) model
includes a set of demand equations, one for each good
or category of goods that consumers purchase. The
typical form of an AIDS equation is as follows:
Qi=αi+βi ln(pi​)+γi ln(Y)+ϵi

16. Equation
 Where:
 qi is the quantity demanded of the ith good.
 αi is the intercept term, which represents the baseline
demand for the ith good when prices and income are at
some reference level.
 βi is the price elasticity of demand for the ith good. It
measures how the quantity demanded of the good responds
to changes in its price.
 pi is the price of the ith good.
 γi is the income elasticity of demand for the ith good. It
measures how the quantity demanded of the good responds
to changes in consumer income (Y).
 Y is the consumer's income.
 ϵi is the error term, representing unexplained variations in
the quantity demanded. It captures factors other than price
and income that affect demand for the ith good.

17.  In the AIDS model, each equation represents the
demand for a specific good, and the parameters (α,
β, and γ) are estimated using econometric
techniques with real-world data on prices, incomes,
and quantities consumed. These estimated
parameters provide insights into how consumers
allocate their income among different goods and how
sensitive their consumption is to changes in prices
and income.
 It's important to note that the AIDS model allows for
non-linear relationships between prices, income, and
demand. This flexibility makes it a valuable tool for
analyzing consumer behavior and market dynamics
in a more realistic way compared to the simpler linear
models like the Linear Expenditure System (LES).

18. Structure
 1. Expenditure Share Equations:
 The expenditure share equations in the AIDS model
represent the share of the total expenditure allocated to
each individual good or commodity. These equations
account for how consumers distribute their budget
among various goods based on their preferences and
budget constraints.
 The expenditure share equations are typically estimated
as follows: For a given good i, the expenditure share
equation can be expressed as:

19.  si​
=
𝑒𝑖
𝐸
=
ai​
+∑nj=1 bij ln(Pj)+εi
𝐸
Where:
si represents the expenditure share of good i.
ei is the total expenditure on good i.
E is the total expenditure on all goods.
ai is a parameter representing the intercept for good i.
bij is a parameter representing the price elasticity of good i
with respect to the price of good j.
pj is the price of good j.
εi represents the error term for good i.
n is the total number of goods considered in the analysis.

20. 2. Price Elasticity Equations:
 The price elasticity equations in the AIDS model are
used to estimate the responsiveness of the quantity
demanded for each good to changes in its own price
and the prices of other goods.
 These elasticity equations are crucial for understanding
how consumers make substitution choices when prices
change. The price elasticity equations are typically
estimated as follows:
 For good i, the price elasticity equation can be
expressed as:
∂ln(xi​
)
∂ln(pj​
)
=
𝑏𝑖𝑗 .𝑥𝑖
𝑠𝑖

21.  Where:

∂ln(xi​
)
∂ln(pj​
)
represents the price elasticity of demand
for good i with respect to the price of good j.
 bij​​is​the​parameter​representing​the​price​
elasticity of good i with respect to the price of
good j.
 xi​​is​the​quantity​demanded​of​good​i.
 si​​is​the​expenditure​share​for​good​i.
The AIDS model's structure is designed to capture how
consumers allocate their budget among different goods and
how they respond to changes in prices, making it a valuable
tool for analyzing consumer preferences and market
dynamics for multiple goods.

22. Advantages
 Incorporation of Both Price and Income Effects:
AIDS simultaneously considers how changes in prices
and incomes affect consumer behavior.
 Flexibility for Analyzing Multiple Goods: It is
adaptable for analyzing consumer choices across
various goods.
 Estimation of Price and Income Elasticities: AIDS
calculates the responsiveness of demand to price and
income changes.
 Captures Substitution Effects: It quantifies how
consumers switch between goods when prices change.
 Realistic Representation of Consumer Behavior: It

23. Limitations
 Data and Computation Demands: AIDS requires
extensive data and computational resources, limiting its
use in smaller-scale studies.
 Complex Mathematical Structure: The model's
complexity can be a barrier to understanding and
application.
 Assumption of Utility Maximization: It relies on the
assumption of rational utility-maximizing consumers,
which may not always hold in reality.
 Sensitivity to Model Specification: Results can vary
based on specific assumptions and functional forms
chosen, introducing subjectivity.
 Limited Causality: AIDS provides correlations but
doesn't explain causation in consumer choices.

24. Diffrences in LES and AIDS
Aspect
Linear Expenditure System
(LES) Almost Ideal Demand System (AIDS)
Type of Model Simplified budget allocation model Comprehensive demand analysis model
Budget
Constraint
Linear Non-linear and more flexible
Price Elasticities Limited to one good Provides price elasticities for all goods
Income Effects Ignores income effects Incorporates income effects
Price Effects Considers only price effects
Simultaneously accounts for price and
income effects
Substitution
Effects
Minimal representation of
substitution effects
Captures substitution patterns among
goods
Complexity Simpler and less data-intensive More complex and data-intensive
Realism
May not accurately represent
consumer behavior
Aligns with economic theory and provides
a more realistic portrayal of consumer
choices
Applicability
Suitable for basic demand
analysis
Applicable to analyzing complex consumer
preferences and diverse goods
Policy Analysis
Limited in its ability to assess
policy impacts
Valuable for policy analysis, including tax
and subsidy effects on consumer choices
Data
Requires less extensive data
Demands more data for parameter