Chapter 4 Consumer and Firm Behaviour: The Work-Leisure Decision and Profit Maximization Copyright © 2010 Pearson Education Canada
Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 5-2 Chapter 4 Topics Behavior of the representative consumer Behavior of the representative firm Copyright © 2010 Pearson Education Canada
The Representative Consumer We will consider the behaviour of a single representative consumer, who will act as a stand-in for all consumers in the economy. Consumer’s preferences over the available goods in the economy Consumer’s budget constraint How does the consumer behave (optimize) given market prices?
Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 5-4 The Representative Consumer 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 © 2010 Pearson Education Canada
The Representative Consumer’s Preferences Suppose that there are two goods that consumer desire. The first good is called the consumption good. This is a physical good, which we can think of as an aggregate of all consumer goods in the economy, or measured aggregate consumption. The second good is leisure, which is any time spent not working in the market. Thus in terms of this definition, leisure could include recreational activities, sleep, and work at home (cooking, yard work, housecleaning).
The Representative Consumer’s Preferences For macroeconomic purposes, it proves convenient to suppose that all consumers in the economy are identical. If all consumers are identical, the economy will behave as if there were only one consumer, and it is therefore convenient to write down the model as having only a single representative consumer.
The Representative Consumer’s Preferences We can capture the preferences of the representative consumer over leisure and consumption goods by a utility function, written as U(C,l) where U is the utility function, C is the quantity of consumption, and l is the quantity of leisure.
Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 5-8 Representative Consumer’s Indifference Curves An indifference curve slopes downward (more is preferred to less). An indifference curve is convex (the consumer has a preference for diversity in his or her consumption bundle). Copyright © 2010 Pearson Education Canada
Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 5-9 Indifference Curves Copyright © 2010 Pearson Education Canada
Copyright © 2008 Pearson Addison-Wesley. All rights reserved Properties of Indifference Curves Copyright © 2010 Pearson Education Canada
Copyright © 2008 Pearson Addison-Wesley. All rights reserved The consumer’s time constraint Copyright © 2010 Pearson Education Canada
Copyright © 2008 Pearson Addison-Wesley. All rights reserved The consumer’s budget constraint Copyright © 2010 Pearson Education Canada
Copyright © 2008 Pearson Addison-Wesley. All rights reserved The Consumer’s Budget Constraint Consumption is equal to total wage income, plus dividend income, minus taxes. Copyright © 2010 Pearson Education Canada
Copyright © 2008 Pearson Addison-Wesley. All rights reserved Budget constraint accounting for time constraint. Copyright © 2010 Pearson Education Canada
Copyright © 2008 Pearson Addison-Wesley. All rights reserved Rewriting the Budget Constraint Copyright © 2010 Pearson Education Canada
Copyright © 2008 Pearson Addison-Wesley. All rights reserved Rewriting the Budget Constraint Again Copyright © 2010 Pearson Education Canada
Copyright © 2008 Pearson Addison-Wesley. All rights reserved Representative Consumer’s Budget Constraint (T > π) Copyright © 2010 Pearson Education Canada
Copyright © 2008 Pearson Addison-Wesley. All rights reserved Representative Consumer’s Budget Constraint (T < π) Copyright © 2010 Pearson Education Canada
Copyright © 2008 Pearson Addison-Wesley. All rights reserved Consumer Optimization The consumer chooses the consumption bundle that is on his or her highest indifference curve, while satisfying his or her budget constraint. Copyright © 2010 Pearson Education Canada
Copyright © 2008 Pearson Addison-Wesley. All rights reserved Consumer Optimization Copyright © 2010 Pearson Education Canada
Copyright © 2008 Pearson Addison-Wesley. All rights reserved Consumer Optimization Copyright © 2010 Pearson Education Canada
Copyright © 2008 Pearson Addison-Wesley. All rights reserved Optimization Implies: The marginal rate of substitution of leisure for consumption equals the real wage. Copyright © 2010 Pearson Education Canada
Copyright © 2008 Pearson Addison-Wesley. All rights reserved The Representative Consumer Chooses Not to Work Copyright © 2010 Pearson Education Canada
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 © 2010 Pearson Education Canada
Copyright © 2008 Pearson Addison-Wesley. All rights reserved An Increase in π − T for the Consumer. Copyright © 2010 Pearson Education Canada
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 © 2010 Pearson Education Canada
Copyright © 2008 Pearson Addison-Wesley. All rights reserved Increase in the Real Wage Rate— Income and Substitution Effects Copyright © 2010 Pearson Education Canada
Copyright © 2008 Pearson Addison-Wesley. All rights reserved Labor Supply Curve Copyright © 2010 Pearson Education Canada
Copyright © 2008 Pearson Addison-Wesley. All rights reserved Effect of an Increase in Dividend Income or a Decrease in Taxes Copyright © 2010 Pearson Education Canada
Copyright © 2008 Pearson Addison-Wesley. All rights reserved Perfect Complements Copyright © 2010 Pearson Education Canada
Copyright © 2008 Pearson Addison-Wesley. All rights reserved The Representative Firm In our model economy, consumers and firms come together to exchange labour for consumption goods. The representative consumer supplies labour and demands consumption goods. On the other hand, firms demand labour and supply consumption good. The choices of the firms are determined by the available production technology and by profit maximization. Copyright © 2010 Pearson Education Canada
The Representative Firm As with consumer behaviour, we will ultimately focus here on the choices of a single, representative firm. The firms in this economy owns productive capital (plant and equipment), and it hires labour to produce consumption goods. We can describe the production technology available to each firm by a production function, which describes the technological possibilities for converting factor inputs into outputs.
The Firm’s Production Function We can express this relationship between inputs and outputs in algebraic terms as where z is total factor productivity, Y is output of consumption goods, K is the quantity of capital input in the production process, N d is the quantity of labour input measured as total hours worked by employees of the firm, and F is a function.
The Firm’s Production Function Since this is a one-period or static ( as opposed to dynamic) model, we treat K as being a fixed input to production, and N d as a variable factor of production. Total factor productivity z captures the degree of sophistication of the production process. An increase in z will make both factors of production, K and N d, more productive, in that, given factor inputs, higher z implies that more output can be produced.
The Firm’s Production Function The marginal product of a factor of production is the additional output that can be produced with one additional unit of that factor input, holding constant the quantities of the other factor inputs. Figure 4.12 shows a graph of the production function, fixing the quantity of capital at some arbitrary value, K *, and allowing the labour input, N d, to vary.
The Firm’s Production Function In Figure 4.12, the marginal product of labour, given the quantity of labour N *, is the slope of the production function at point A. This is because the slope of the production function is the additional output produced from an additional unit of the labour input when the quantity of labour is N * and the quantity of capital is K *. We will let MP N denote the marginal product of labour.
Copyright © 2008 Pearson Addison-Wesley. All rights reserved Production Function, Fixing the Quantity of Capital and Varying the Quantity of Labour (Figure 4.12) Copyright © 2010 Pearson Education Canada
The Firm’s Production Function Figure 4.13 shows a graph of the production function, fixing the quantity of labour at some arbitrary value, N *, and allowing the capital input, K, to vary. In Figure 4.13, the marginal product of labour, given the quantity of capital K *, is the slope of the production function at point A. This is because the slope of the production function is the additional output produced from an additional unit of the capital input when the quantity of labour is N * and the quantity of capital is K *. We will let MP K denote the marginal product of capital.
Copyright © 2008 Pearson Addison-Wesley. All rights reserved Production Function, Fixing the Quantity of Labor and Varying the Quantity of Capital (Figure 4.13) Copyright © 2010 Pearson Education Canada
Properties of the Firm’s Production Function 1.The production function exhibits constant returns to scale (CRTS). The alternative to constant returns to scale in production are increasing returns to scale and decreasing returns to scale. Given a CRTS production function, the economy will behave in exactly the same way if there were many small firms producing consumption goods as it would if there were a few large firms, provided all firms behave competitively ( they are price- takers in product and factor markets).
Properties of the Firm’s Production Function Given this, it is most convenient to suppose that there is only one firm in the economy, a single, representative firm.
Properties of the Firm’s Production Function 2.Output increases with increases in either the labor input or the capital input. 3.The marginal product of labor decreases as the labor input increases. 4.The marginal product of capital decreases as the capital input increases. 5.The marginal product of labor increases as the quantity of the capital input increases.
Copyright © 2008 Pearson Addison-Wesley. All rights reserved Marginal Product of Labor Schedule for the Representative Firm Copyright © 2010 Pearson Education Canada
Copyright © 2008 Pearson Addison-Wesley. All rights reserved Adding Capital Increases the Marginal Product of Labor Copyright © 2010 Pearson Education Canada
Copyright © 2008 Pearson Addison-Wesley. All rights reserved Total Factor Productivity Increases Copyright © 2010 Pearson Education Canada
Copyright © 2008 Pearson Addison-Wesley. All rights reserved Effect of an Increase in Total Factor Productivity on the Marginal Product of Labour Copyright © 2010 Pearson Education Canada
Specific Production Function A very common production function used in theory and empirical work is the Cobb-Douglas Production function. This function takes the form Y = zK a (N d ) 1-a, where a is a parameter, with 0<a<1. CRTS (because a+1-a =1) a is the share of share of income that capital receives ( in our model, the profit of firms) 1-a is the share that labour receives (wage income before taxes) in equilibrium.
Specific Production Function A good approximation to the actual Canadian aggregate production function is Y = zK 0.3 (N d ) 0.7 Y, K and N d all can measured directly. Total factor productivity can be measured only indirectly.
Solow Residual Using the aggregate production function, we can express total factor productivity or Solow Residual as, z = Y/(K 0.3 (N d ) 0.7 ).
Copyright © 2008 Pearson Addison-Wesley. All rights reserved The Solow Residual For Canada Copyright © 2010 Pearson Education Canada
Copyright © 2008 Pearson Addison-Wesley. All rights reserved Profit Maximization When the firm maximizes profits, the marginal product of labor equals the real wage. Copyright © 2010 Pearson Education Canada
Copyright © 2008 Pearson Addison-Wesley. All rights reserved Revenue, Variable Costs, and Profit Maximization Copyright © 2010 Pearson Education Canada
Copyright © 2008 Pearson Addison-Wesley. All rights reserved The Marginal Product of Labor Curve Is the Labor Demand Curve of the Profit-Maximizing Firm (Figure 4.20) Copyright © 2010 Pearson Education Canada
The Marginal Product of Labor Curve Is the Labor Demand Curve of the Profit-Maximizing Firm This is because the firm maximizes profits for the quantity of labour input that implies MP N = w. Therefore, given a real wage, w, the marginal product of labour schedule tells us how much labour the firm needs to hire such that MP N = w and so the marginal product of labour schedule and the firm’s demand curve for labour are the same thing.