Microeconomics Consumer Theory Dr Hamish Low

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MicroeconomicsConsumer TheoryDr Hamish Low

• Lecture 3

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Key Issues

• What determines the demand curve? What are
  consumers doing?
• What are the welfare costs associated with
  comparative statics?
• Is the equilibrium unique? Will the economy move
  toward the equilibrium?

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The Economic Model of Behaviour

• Individuals act.
• Incentives determine behaviour.
• Incentives are produced by preferences and
  constraints.
• Preferences and constraints are strictly
  distinguished.
• Individuals pursue their own interests.

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Three questions

• How do we describe what the consumer can afford
  to consume?
• How do we describe what the consumer likes to
  consume?
• How do we describe what the consumer actually
  ends up consuming?

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A model of consumer choice
Step 1 Preferences (what consumers want to do)
Step 2 Budget Constraint (what consumers can do)
Step 3 The decision (what consumers actually do)
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Basic assumptions about behaviour

• The consumer selects from the set of affordable
  options, the option that maximises his or her
  objectives.
• The consumer selects the bundle of goods which
  gives him or her the most satisfaction subject to
  what he or she can afford to buy.

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The budget constraint

• One (representative) consumer.
• Two types of goods x and y.
• A bundle of goods (x,y).
• The consumer has a given income m.
• The consumer takes the prices, px and py, of the
  two goods as being out of their control.

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The budget line
Expenditure on good x
Expenditure on good y
Assume that the consumer wants to spend all
income.
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Objective terms of trade
Relative price
Real income
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y
The budget line
m/py
1
-px/py
The budget set.
x
m/px
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Comparative statics

• Increase in consumer income, m
• Increase in the price of good x
• Increase in the price of good y

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An increase in income
y
New budget line (m1)
m1/py
Old budget line (m0)
m0/py
x
m1/px
m0/px
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An increase in the price of good x
y
New budget line
m/py
Old budget line
x
Q
m/p0x
m/p1x
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An increase in the price of good y
y
New budget line
m/p0y
Old budget line
m/p1y
Q
x
m/px
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Question

• Suppose prices of the two goods are 1.
• You can choose between getting
• 10 in addition income
• 10 units of good x for free
• Which option would you choose?

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y
New budget line (m1)
m1
Old budget line (m0)
10
m0
New budget line (m1)
x
m1
m0
10
10
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Summary

• Comparative statics as shifts in demand and
  supply curves
• Beyond demand and supply curves need
  preferences and constraints to determine
  behaviour
• Comparative statics as changes in the budget
  constraints individuals face.

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Preference theory

• The objective is to describe the consumers taste
  or, as economists say, the consumers preference
• and to deduce from that what kind of consumption
  choices she would like to make.

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Ranking

• For every (relevant) pair of bundles, the
  consumer makes a comparison and conclusions
• Strict preference
• X strictly preferred to Y.
• Weak preference
• X weakly preferred to Y.
• Indifference
• X is as good as Y.

Ranking of the alternative bundles of goods
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Outline

• Utility functions.
• Marginal rate of substitution.
• Optimal consumer choice.

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Preferences Taste
Ranking of alternatives
Utility function
Indifference curve
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Definition
A utility function, u(.), assigns a number to
every possible bundle of goods according to the
following rules

• If the consumer strictly prefers bundle X to
  bundle Y, then u(X)gtu(Y).
• If the consumer weakly prefers bundle X to bundle
  Y, then u(X)?u(Y).
• If the consumer is indifferent between bundle X
  and bundle Y, then u(X)u(Y).

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The utility function

• The utility function provides a RANKING of
  bundles of goods
• and the actual difference between the numbers
  assigned has NO significance.
• Furthermore, many different utility functions can
  represent the same preferences.

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Suppose that,
then we can use any of the following three
utility functions to represent these preferences
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Two types of utility functions

• Ordinal utility functions only the ranking
  matters.
• Cardinal utility functions the absolute
  difference between the utility numbers matters.

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Utility functions and indifference curves.
An indifference curve is combinations of bundles
of goods that provide the consumer with the same
level of utility.
Fixed Level of Utility
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Indifference curves
y
Increasing utility
u12
u01
x
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The Marginal Rate of Substitution (MRS)
MRS measures the rate at which the consumer is
willing to substitute good y for good x
MRS is also called the subjective terms of trade.
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Example
If the MRS of apples for oranges is 2, then
the consumer is willing to sacrifice two apples
to get one more orange.
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MRS is the absolute value of the slope of an
indifference curve
y
MRS
1
y0
x
xo
Diminishing MRS
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Marginal utility
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Moving along the indifference curve...
y
u
x
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A little algebra
MRS
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Where are we?
Budget constraint
Preferences Utility
Optimal consumption decision