Chapter 4
Consumer and
Firm Behavior:
The Work-Leisure
Decision and Profit
Maximization
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Chapter 4 Topics
• Behavior of the representative consumer
• Behavior of the representative firm
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Features of Model
• Representative
– Agents are identical in all respects. The whole economy
behaves as if there is only one consumer or one firm.
• Static
– Last one period, no saving decision.
– Dynamic model: last more than one period, need to decide
how much to spend today and how much to save for
tomorrow.
• Microfoundation
– Optimizing consumers and firms
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Representative Consumer
• Consumer’s preferences over consumption and leisure
as represented by indifference curves.
• Consumer’s budget constraint.
• Consumer’s optimization problem: making his or
herself as well off as possible given his or her budget
constraint.
• How does the consumer respond to: (i) an increase in
non-wage income; (ii) an increase in the market real
wage rate?
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Preference
• Utility function U(C , l)
– Representation of preference over C and l.
– Level of happiness, or utility
• (C , l) is called a consumption bundle, and the
utility function tells how consumers rank
different consumption bundles.
– Strictly preferred: U(C1, l1) >U(C2, l2)
– Indifferent: U(C1, l1) =_U(C2, l2)
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Assumptions for Preference
• More is better than less.
• Diversity is needed in consumption bundle.
• C and l are both normal goods.
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Representative Consumer’s
Indifference Curve
• Graphic representation of utility function.
• Def: connect a set of points, with these points
representing consumption bundles, among
which consumers are indifferent.
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Figure 4.1 Indifference Curves
I-Curve: connects a set of points,
with these points representing
consumption bundles among which
a consumer is indifferent.
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Figure 4.2 Properties of
Indifference Curves
1.
2.
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Downward-sloping
(more is better than less)
Convex
(Diversification is desired)
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Equation 4.1: The consumer’s
time endowment
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Equation 4.2: The consumer’s
budget constraint
1.
2.
3.
Work and receive real wage in terms of consumption goods.
Own production units (firms) and receive real dividend income.
Pay lump-sum tax in terms of goods to government.
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The Consumer’s Budget
Constraint
• One period game, spend up all income available.
• Consumption is equal to total wage income, plus
dividend income, minus taxes.
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Equation 4.4: Rewriting the
Budget Constraint
Trade off between C and l
w: relative price of l to C
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Figure 4.3 Representative
Consumer’s Budget Constraint (T > π)
At B, can not spend all time
on leisure, since need to work
to pay tax.
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Figure 4.4 Representative
Consumer’s Budget Constraint (T < π)
At point B,
spend all time on leisure,
and still enjoy positive C.
Because T< π.
That is, use nonwage income
to purchase C.
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Consumer Optimization
•
•
Rationality: representative consumer knows
his preference and budget constraint. And he
can evaluate which feasible consumption
bundle is best for him.
Optimal consumption bundle: the point
represents a consumption bundle that is
–
–
On the highest possible IC (largest utility).
On or inside the budget Constraint.
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Figure 4.5 Consumer
Optimization
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Equation 4.6: Holds when the
consumer is optimizing
The marginal rate of substitution of leisure for
consumption equals the real wage rate at the
optimal consumption bundle (the relative price
of l to C).
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Real dividends or taxes change
for the consumer
• Assume that consumption and leisure are both
normal goods.
• An increase in dividends or a decrease in taxes
will then cause the consumer to increase
consumption and reduce the quantity of labor
supplied (increase leisure).
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Figure 4.7 An Increase in π − T
for the Consumer.
1.
2.
3.
4.
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BC shifts out and parallels to original one
since relative price of l to C is unchanged.
Both C and l increase.
(income effect, normal goods)
Labor supply drops, labor income declines.
Overall income increases.
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An increase in the market real
wage rate
• This has income and substitution effects.
• Substitution effect: the price of leisure rises, so the
consumer substitutes from leisure to consumption.
• Income effect: the consumer is effectively more
wealthy and, since both goods are normal, consumption
increases and leisure increases.
• Conclusion: Consumption must rise, but leisure may
rise or fall.
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Figure 4.8 Increase in the Real Wage
Rate—Income and Substitution Effects
F→O: substitution effect
O→H: income effect
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Figure 4.9 Labor Supply
Curve
Ns (w) = h – l (w)
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Figure 4.10 Effect of an Increase in
Dividend Income or a Decrease in Taxes
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The Representative Firm
• The production function.
• Profit maximization and labor demand.
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Equation 4.9: The Firm’s
Production Function
Production function: describe the technological possibilities for
converting factor inputs Into outputs.
Z: total factor productivity, degree of sophistication of production process.
K: amount of capital inputs, fixed in one-period model.
Nd: amount of labor inputs, measured as total hours worked.
Y: outputs of consumption goods.
F: the function that maps inputs into outputs.
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Properties of the Firm’s
Production Function
• Constant returns to scale.
• Output increases with increases in either the
labor input or the capital input.
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Figure 4.12 Production Function, Fixing the
Quantity of Capital and Varying the Quantity
of Labor
MPN: additional output produced by additional
one unit of labor input, keeping K unchanged.
The marginal product of labor decreases as
the labor input increases.
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Figure 4.13 Production Function, Fixing
the Quantity of Labor and Varying the
Quantity of Capital
MPK: additional output produced by additional
one unit of capital input, keeping Nd unchanged.
The marginal product of capital decreases
as the capital input increases.
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Figure 4.14 Marginal Product of Labor
Schedule for the Representative Firm
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Figure 4.15 Adding Capital Increases
the Marginal Product of Labor
The marginal product of labor increases
as the quantity of the capital input increases.
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Figure 4.16 Total Factor
Productivity Increases
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Figure 4.17 Effect of an Increase in Total
Factor Productivity on the Marginal Product
of Labor
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Equation 4.10: Specific
Production Function
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Equation 4.11: Solow Residual
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Figure 4.18 The Solow Residual
for the United States
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Profit Maximization
• A representative firm takes market prices for
capital and labor as given, maximizes the profits
by choosing the number of labor employed in
production.
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Equation 4.12: Profit
Maximization
When the firm maximizes profits, the marginal
product of labor equals the real wage.
MPN: marginal benefits from hiring one additional unit of labor.
w: marginal costs from hiring one additional unit of labor.
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Figure 4.19 Revenue, Variable
Costs, and Profit Maximization
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Figure 4.20 The Marginal Product of
Labor Curve Is the Labor Demand Curve
of the Profit-Maximizing Firm
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