Consumer and Firm Behaviour
Chapter 4
Topics in Macroeconomics 2
Economics Division
University of Southampton
February 2010
Chapter 4
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Topics in Macroeconomics
Representative Consumers
The Representative Firm
Introduction
◮
One-period model
◮
Consumers and firms make static decisions (no dynamics)
◮
There are many consumers and firms, but we assume that
all firms are identical and all consumers are identical
◮
We will study a representative consumer and a
representative firm
◮
Consumers face a tradeoff between consuming and
working (work/leisure)
◮
Firms maximize profits given the state of technology
◮
Next Chapter: Market clearing
Chapter 4
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Topics in Macroeconomics
Representative Consumers
The Representative Firm
Preferences
Budget Constraint
Optimization
Consumers Care about Two Goods
1. Good 1: Physical good
◮
◮
You can think of this ‘good’ as an aggregation of all
consumer goods (composite consumption good)
Measurement: aggregate consumption
2. Good 2: Leisure
◮
◮
◮
Time spent not working in the market
Includes: recreational activities, sleep, and work at home
Measurement: total number of hours available minus total
working hours
3. Note: Representative consumer
Chapter 4
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Topics in Macroeconomics
Representative Consumers
The Representative Firm
Preferences
Budget Constraint
Optimization
Preference Representation
◮
Preferences can be represented by a utility function
◮
Individuals get utility from a consumption bundle (C, ℓ)
◮
The utility derived from C1 units of consumption goods and
ℓ1 quantity of leisure is
U(C1 , ℓ1 )
◮
The utility function is meant to measure a happiness index:
how happy you are to consume particular bundles of goods
Chapter 4
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Topics in Macroeconomics
Representative Consumers
The Representative Firm
Preferences
Budget Constraint
Optimization
Preference Representation
◮
The bundle (C1 , ℓ1 ) is strictly preferred to bundle (C2 , ℓ2 ) if
U(C1 , ℓ1 ) > U(C2 , ℓ2 )
◮
The bundle (C2 , ℓ2 ) is strictly preferred to bundle (C1 , ℓ1 ) if
U(C1 , ℓ1 ) < U(C2 , ℓ2 )
◮
The consumer is indifferent between bundle (C1 , ℓ1 ) and
bundle (C2 , ℓ2 ) if
U(C1 , ℓ1 ) = U(C2 , ℓ2 )
◮
NOTE: Utility levels are irrelevant—what matters is the
level of utility from one bundle relative to the level of utility
of another bundle
Chapter 4
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Topics in Macroeconomics
Representative Consumers
The Representative Firm
Preferences
Budget Constraint
Optimization
Assumptions on Preference
1. More is always preferred to less
◮
◮
Keeping leisure constant, more consumption is preferred to
less, and vice versa
We won’t worry about over eating and/or drinking
2. Diversity is a good thing
◮
If two consumption bundles give the same level of utility,
then a mixture of the two bundles will be preferred to either
bundle alone
3. Consumption goods and leisure are normal goods
◮
◮
◮
As their income increases, consumers want to consume
more of both goods
For eg., after winning the lottery you want to consume more
goods and take more vacation time (leisure)
This behaviour seems to be supported by the data
Chapter 4
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Topics in Macroeconomics
Representative Consumers
The Representative Firm
Preferences
Budget Constraint
Optimization
Indifference Curves
Indifference Curve
An indifference curve connects a set of points, with these points
representing bundles among which the consumer is indifferent
Chapter 4
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Topics in Macroeconomics
Representative Consumers
The Representative Firm
Preferences
Budget Constraint
Optimization
Property 1: Indifference Curves slope downward
This is because more is preferred to less
Chapter 4
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Topics in Macroeconomics
Representative Consumers
The Representative Firm
Preferences
Budget Constraint
Optimization
Property 2: Indifference Curves are convex
This is because diversity is a good thing
Chapter 4
10/41
Topics in Macroeconomics
Representative Consumers
The Representative Firm
Preferences
Budget Constraint
Optimization
Marginal Rate of Substitution
Marginal Rate of Substitution
The marginal rate of substitution of leisure for consumption
(MRSℓ,C ) is the rate at which the consumer is just willing to
substitute leisure for consumption goods
(the negative of the slope of an indifference curve)
Chapter 4
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Topics in Macroeconomics
Representative Consumers
The Representative Firm
Preferences
Budget Constraint
Optimization
Representative Consumer’s Budget Constraint
◮
The time constraint:
ℓ + Ns = h
h Total amount of time available
N s Amount of time spent working
ℓ Leisure time
◮
The budget constraint:
C = wN s + π − T
w
π
T
real wage rate per unit of time (in terms of C)
Firm profits redistributed to consumers (dividend income)
Lump-sum tax
Chapter 4
13/41
Topics in Macroeconomics
Representative Consumers
The Representative Firm
Preferences
Budget Constraint
Optimization
Alternative Representations of the Budget Constraint
◮
Replace the time constraint (ℓ + N s = h) into the budget
constraint
C = wN s + π − T
C = w (h − ℓ) + π − T
◮
Add w ℓ on both sides
C
=
| +
{zw }ℓ
Implicit expenditures
◮
wh
| +{zπ − T}
Implicit real disposable income
To graph the budget constraint, it is more convenient to
write
C = |{z}
−w ℓ + wh
| +{zπ − T}
Intercept
Slope
Chapter 4
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Topics in Macroeconomics
Preferences
Budget Constraint
Optimization
Representative Consumers
The Representative Firm
Representative Consumer’s Budget Constraint (T > π)
Chapter 4
15/41
◮
The horizontal intercept is found
by setting C = 0 and solving the
equation
−w ℓ + wh + π − T = C = 0
for ℓ
◮
The solution is ℓ = h + (π − T )/w
◮
If T > π, then
π − T < 0 and
h + (π − T )/w < h
Topics in Macroeconomics
Preferences
Budget Constraint
Optimization
Representative Consumers
The Representative Firm
Representative Consumer’s Budget Constraint (T < π)
Chapter 4
16/41
◮
The horizontal intercept was
ℓ = h + (π − T )/w
◮
If T < π, then
π − T > 0 and
h + (π − T )/w > h
◮
But you cannot consume more
leisure than your endowment of
time
◮
Point along BD all involve
working zero hours
◮
Points below B involve throwing
away income
Topics in Macroeconomics
Preferences
Budget Constraint
Optimization
Representative Consumers
The Representative Firm
Consumer Optimization
Chapter 4
18/41
◮
The consumer will choose the
best bundle that is budget
feasible
◮
Points below the budget line
(e.g. J) would never be chosen
(more is preferred to less)
◮
B is preferred to all points along
BD
Topics in Macroeconomics
Preferences
Budget Constraint
Optimization
Representative Consumers
The Representative Firm
Consumer Optimization
Chapter 4
19/41
◮
The market pays w consumption
goods for each unit of leisure you
give up
◮
Point F : MRSℓ,C > w : willing to
give up more than w
consumption goods for an extra
unit of leisure
◮
Point E : MRSℓ,C < w : willing to
give up less than w consumption
goods for an extra unit of leisure
◮
Point H: MRSℓ,C = w
Topics in Macroeconomics
Representative Consumers
The Representative Firm
Preferences
Budget Constraint
Optimization
Why is point H optimal
◮
The optimal bundle is at a point where the indifference
curve is tangent to budget line AB
◮
At point H the rate at which the consumer is willing to trade
leisure for consumption (MRSℓ,C ) is the same as the rate at
which leisure trades for consumption on the market (w )
◮
The marginal rate of substitution of leisure for consumption
equals the relative price of leisure in terms of consumption
goods
◮
More generally:
Consumer optimization in competitive markets will imply
that the consumer sets the marginal rate of substitution of
any good x for any good y equal to the relative price of x in
terms of y
Chapter 4
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Topics in Macroeconomics
Preferences
Budget Constraint
Optimization
Representative Consumers
The Representative Firm
The Representative Consumer Chooses not to Work
Chapter 4
21/41
◮
The consumer could, in principle,
choose not to work at all (point B)
◮
This will not be possible when
consumers and firms interact:
There would be no production
and so no consumption
◮
Points like A and B will be ruled
out by assuming that the
consumer wishes to consume
some of both goods
Topics in Macroeconomics
Representative Consumers
The Representative Firm
Preferences
Budget Constraint
Optimization
Using the Model: 2 Experiments
1. Increase in after-tax dividend income (π − T )
◮
◮
Holding wage rate (w) constant
As such, produces a pure income effect on the consumer’s
choices
2. Increase in the real wage rate (w )
◮
◮
Produces an income effect: the consumer is richer
Produces a substitution effect: the price of leisure in terms
of consumption goods is higher
Chapter 4
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Topics in Macroeconomics
Preferences
Budget Constraint
Optimization
Representative Consumers
The Representative Firm
Experiment 1: Increase in Dividend Income
Chapter 4
23/41
◮
The experiment is to increase
π−T
◮
ABD was the original budget
constraint (H was optimal)
◮
FJD is the new budget constraint
(higher intercept)
New optimum is K
◮
Both C and ℓ increase because
both are normal goods
Topics in Macroeconomics
Preferences
Budget Constraint
Optimization
Representative Consumers
The Representative Firm
Experiment 2: Increase in Real Wage Rate
Chapter 4
24/41
◮
ABD was the original budget
constraint (F was optimal)
◮
EBD is the new budget constraint
(higher intercept and higher
slope)
New optimum is H
◮
We know that C will increase
(you are richer)
◮
However, ℓ may increase,
decrease, or remain the same
◮
This is because there are two
opposing effects
Topics in Macroeconomics
Representative Consumers
The Representative Firm
Preferences
Budget Constraint
Optimization
The Substitution Effect
Chapter 4
◮
From the new budget constraint,
lower dividend income until the
consumer’s optimal choice is on
the same indifference curve as
the original bundle
◮
i.e. with the budget constraint
JKD the consumer chooses
point O which gives him the same
level of utility as point F
◮
Since leisure is now more
expensive, bundle O features less
leisure and more consumption
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Topics in Macroeconomics
Preferences
Budget Constraint
Optimization
Representative Consumers
The Representative Firm
The Income Effect
Chapter 4
26/41
◮
The movement from O to H is a
pure income effect
◮
As before, both C and ℓ will
increase since they are normal
goods
◮
Net effect on C must be positive
◮
Net effect on ℓ is unclear:
In this examples, both effects
cancel each other out
Topics in Macroeconomics
Preferences
Budget Constraint
Optimization
Representative Consumers
The Representative Firm
The Labor Supply Curve
Chapter 4
27/41
◮
The labour supply curve is
obtained by finding the optimal
bundle under many different real
wage rates: C(w ), ℓ(w )
◮
For any given w the labour
supply is N s (w ) = h − ℓ(w )
◮
This labour supply curve
assumes that the substitution
effect dominates the income
effect:
The labour supply curve is
upward sloping
Topics in Macroeconomics
Preferences
Budget Constraint
Optimization
Representative Consumers
The Representative Firm
Increase in Dividend Income
Chapter 4
28/41
◮
We know that an increase in
(π − T ) increases leisure (pure
income effect)
◮
It follows that the labour supply at
any wage rate is lower following
an increase in (π − T )
◮
The labour supply shifts to the left
following an increase in (π − T )
Topics in Macroeconomics
Representative Consumers
The Representative Firm
Technology
Profit Maximization
Firm Behaviour
◮
The firm demands labour and supplies consumption goods
◮
We will assume that the firm owns some capital (K ) which
is fixed in this static model
◮
The firm uses its capital and hires labour to produce
consumption goods
◮
The choice of the firm is determined by the available
technology and profit maximization
Chapter 4
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Topics in Macroeconomics
Representative Consumers
The Representative Firm
Technology
Profit Maximization
Technology and the Production Function
Y = zF (K , N d )
◮
The production function tells us how much output will be
produced for given quantities of capital and labour
◮
◮
◮
◮
◮
Y is total output produced
F is the production function
z represents total factor productivity
K is capital
N d is the labour input, measured as total hours worked by
employees of the firm
Chapter 4
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Topics in Macroeconomics
Representative Consumers
The Representative Firm
Technology
Profit Maximization
The Marginal Product of Labour
Chapter 4
32/41
◮
The marginal product of labour
(MPN ) is the additional output
that can be produced with one
additional unit of labour holding
capital constant
◮
It is equal to the slope of the
production function (holding
capital fixed at K ∗ )
Topics in Macroeconomics
Representative Consumers
The Representative Firm
Technology
Profit Maximization
The Marginal Product of Capital
Chapter 4
33/41
◮
The marginal product of Capital
(MPK ) is the additional output
that can be produced with one
additional unit of capital holding
labour constant
◮
It is equal to the slope of the
production function (holding
labour fixed at N ∗ )
Topics in Macroeconomics
Representative Consumers
The Representative Firm
Technology
Profit Maximization
Properties of the Production Function
1. Exhibits constant returns to scale (CRS)
◮
◮
◮
If you double the inputs, output doubles as well
The size of firms is irrelevant: One big firm is equivalent to
many small ones
With CRS, all we need is a representative firm
2. Output increases with inputs
◮
◮
You can do more with more inputs
Alternatively, marginal products are positive
( MPN > 0 and MPK > 0 )
Chapter 4
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Topics in Macroeconomics
Representative Consumers
The Representative Firm
Technology
Profit Maximization
Properties of the Production Function
3. The marginal product of labour decreases as the quantity
of labour increases
◮
The slope of the production function (MPN ) decreases as
N d increases
4. The marginal product of capital decreases as the quantity
of capital increases
◮
The slope of the production function (MPK ) decreases as K
increases
5. The marginal product of labour increases as the quantity of
capital increases (shown on the next slide )
Chapter 4
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Topics in Macroeconomics
Representative Consumers
The Representative Firm
Technology
Profit Maximization
Adding Capital Increases the Marginal Product of
Labor
Chapter 4
36/41
◮
The curve labeled MPN1
corresponds to a level of
capital K = K 1
◮
The curve labeled MPN2
corresponds to a level of
capital K = K 2 > K 1
Topics in Macroeconomics
Representative Consumers
The Representative Firm
Technology
Profit Maximization
Effects of an increase in TFP
Shifts the production function
up because more output is
produced with the same inputs
Chapter 4
37/41
Increases the marginal product
of labour (given a level of
capital)
Topics in Macroeconomics
Representative Consumers
The Representative Firm
Technology
Profit Maximization
Revenue, Variable Costs, and Profit Maximization
Chapter 4
39/41
◮
Profits are equal to production
minus the cost of labour (K is
fixed)
π = Y − wN d
π = zF (K , N d ) − wN d
◮
The profit maximizing quantity of
labour is such that the slope of
the production function is equal
to the slope of the labour cost
curve (w )
◮
⇒ MPN = w
◮
π ∗ is the distance AB
Topics in Macroeconomics
Representative Consumers
The Representative Firm
Technology
Profit Maximization
Why is N ∗ Optimal?
Chapter 4
40/41
◮
To the left of N ∗ , MPN > w , so
one more unit of labour at w
produces more than w units of
consumption goods
◮
To the right of N ∗ , MPN < w , so
one fewer unit of labour would
save w but would lower output by
less than w
◮
Eventually the firm will set
N d = N ∗ , where MPN = w
Topics in Macroeconomics
Representative Consumers
The Representative Firm
Technology
Profit Maximization
Labor Demand Curve of the Profit-Maximizing Firm
Chapter 4
41/41
◮
The labour demand curve is
obtained by finding the optimal
level of labour under many
different real wage rates
◮
But firms always set N such that
MPN = w
◮
So the marginal product of labour
curve is the labour demand curve
Topics in Macroeconomics