1. Chapter 4
Consumer and Firm Behavior: The Work-Leisure Decision and Profit Maximization

2. Chapter 4 Topics Behavior of the representative consumer
Behavior of the representative firm
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3. Features of Model Representative Static Microfoundation
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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4. 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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5. 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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6. 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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7. 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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8. 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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9. Figure 4.2 Properties of Indifference Curves
Downward-sloping
(more is better than less)
Convex
(Diversification is desired)
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10. Equation 4.1: The consumer’s time endowment
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11. Equation 4.2: The consumer’s budget constraint
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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12. 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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13. Equation 4.4: Rewriting the Budget Constraint
Trade off between C and l
w: relative price of l to C
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14. 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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15. 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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16. 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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17. Figure 4.5 Consumer Optimization
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18. 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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19. 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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20. Figure 4.7 An Increase in π − T for the Consumer.
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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21. 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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22. 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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23. Figure 4.9 Labor Supply Curve
Ns (w) = h – l (w)
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24. Figure 4.10 Effect of an Increase in Dividend Income or a Decrease in Taxes
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25. The Representative Firm
The production function.
Profit maximization and labor demand.
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26. 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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27. 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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28. 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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29. 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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30. Figure 4.14 Marginal Product of Labor Schedule for the Representative Firm
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31. 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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32. Figure 4.16 Total Factor Productivity Increases
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33. Figure 4.17 Effect of an Increase in Total Factor Productivity on the Marginal Product of Labor
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34. Equation 4.10: Specific Production Function
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35. Equation 4.11: Solow Residual
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36. Figure 4.18 The Solow Residual for the United States
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37. 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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38. 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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39. Figure 4.19 Revenue, Variable Costs, and Profit Maximization
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40. Figure The Marginal Product of Labor Curve Is the Labor Demand Curve of the Profit-Maximizing Firm
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