Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Chapter 4 Consumer and Firm Behavior: The Work-Leisure Decision and Profit Maximization

Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 4-2 Chapter 4 Topics Behavior of the representative consumer Behavior of the representative firm

Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 4-3 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

Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 4-4 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?

Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 4-5 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(C 1, l 1 ) >U(C 2, l 2 ) –Indifferent: U(C 1, l 1 ) = _ U(C 2, l 2 )

Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 4-6 Assumptions for Preference More is better than less. Diversity is needed in consumption bundle. C and l are both normal goods.

Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 4-7 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.

Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 4-8 Figure 4.1 Indifference Curves I-Curve: connects a set of points, with these points representing consumption bundles among which a consumer is indifferent.

Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 4-9 Figure 4.2 Properties of Indifference Curves 1.Downward-sloping (more is better than less) 2.Convex (Diversification is desired)

Copyright © 2008 Pearson Addison-Wesley. All rights reserved Equation 4.1: The consumer’s time endowment

Copyright © 2008 Pearson Addison-Wesley. All rights reserved Equation 4.2: The consumer’s budget constraint 1.Work and receive real wage in terms of consumption goods. 2.Own production units (firms) and receive real dividend income. 3.Pay lump-sum tax in terms of goods to government.

Copyright © 2008 Pearson Addison-Wesley. All rights reserved 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.

Copyright © 2008 Pearson Addison-Wesley. All rights reserved Equation 4.4: Rewriting the Budget Constraint Trade off between C and l w: relative price of l to C

Copyright © 2008 Pearson Addison-Wesley. All rights reserved 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.

Copyright © 2008 Pearson Addison-Wesley. All rights reserved 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.

Copyright © 2008 Pearson Addison-Wesley. All rights reserved 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.

Copyright © 2008 Pearson Addison-Wesley. All rights reserved Figure 4.5 Consumer Optimization

Copyright © 2008 Pearson Addison-Wesley. All rights reserved 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).

Copyright © 2008 Pearson Addison-Wesley. All rights reserved 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).

Copyright © 2008 Pearson Addison-Wesley. All rights reserved Figure 4.7 An Increase in π − T for the Consumer. 1.BC shifts out and parallels to original one since relative price of l to C is unchanged. 2.Both C and l increase. (income effect, normal goods) 3.Labor supply drops, labor income declines. 4.Overall income increases.

Copyright © 2008 Pearson Addison-Wesley. All rights reserved 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.

Copyright © 2008 Pearson Addison-Wesley. All rights reserved Figure 4.8 Increase in the Real Wage Rate—Income and Substitution Effects F→O: substitution effect O→H: income effect

Copyright © 2008 Pearson Addison-Wesley. All rights reserved Figure 4.9 Labor Supply Curve N s (w) = h – l (w)

Copyright © 2008 Pearson Addison-Wesley. All rights reserved Figure 4.10 Effect of an Increase in Dividend Income or a Decrease in Taxes

Copyright © 2008 Pearson Addison-Wesley. All rights reserved The Representative Firm The production function. Profit maximization and labor demand.

Copyright © 2008 Pearson Addison-Wesley. All rights reserved 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. N d : amount of labor inputs, measured as total hours worked. Y: outputs of consumption goods. F: the function that maps inputs into outputs.

Copyright © 2008 Pearson Addison-Wesley. All rights reserved Properties of the Firm’s Production Function Constant returns to scale. Output increases with increases in either the labor input or the capital input.

Copyright © 2008 Pearson Addison-Wesley. All rights reserved Figure 4.12 Production Function, Fixing the Quantity of Capital and Varying the Quantity of Labor MP N: additional output produced by additional one unit of labor input, keeping K unchanged. The marginal product of labor decreases as the labor input increases.

Copyright © 2008 Pearson Addison-Wesley. All rights reserved Figure 4.13 Production Function, Fixing the Quantity of Labor and Varying the Quantity of Capital MP K : additional output produced by additional one unit of capital input, keeping N d unchanged. The marginal product of capital decreases as the capital input increases.

Copyright © 2008 Pearson Addison-Wesley. All rights reserved Figure 4.14 Marginal Product of Labor Schedule for the Representative Firm

Copyright © 2008 Pearson Addison-Wesley. All rights reserved 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.

Copyright © 2008 Pearson Addison-Wesley. All rights reserved Figure 4.16 Total Factor Productivity Increases

Copyright © 2008 Pearson Addison-Wesley. All rights reserved Figure 4.17 Effect of an Increase in Total Factor Productivity on the Marginal Product of Labor

Copyright © 2008 Pearson Addison-Wesley. All rights reserved Equation 4.10: Specific Production Function

Copyright © 2008 Pearson Addison-Wesley. All rights reserved Equation 4.11: Solow Residual

Copyright © 2008 Pearson Addison-Wesley. All rights reserved Figure 4.18 The Solow Residual for the United States

Copyright © 2008 Pearson Addison-Wesley. All rights reserved 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.

Copyright © 2008 Pearson Addison-Wesley. All rights reserved Equation 4.12: Profit Maximization When the firm maximizes profits, the marginal product of labor equals the real wage. MP N : marginal benefits from hiring one additional unit of labor. w: marginal costs from hiring one additional unit of labor.

Copyright © 2008 Pearson Addison-Wesley. All rights reserved Figure 4.19 Revenue, Variable Costs, and Profit Maximization

Copyright © 2008 Pearson Addison-Wesley. All rights reserved Figure 4.20 The Marginal Product of Labor Curve Is the Labor Demand Curve of the Profit-Maximizing Firm