Chapter6 - Chapter 6 Firms Labor Demand Investment Demand...

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© Sanjay K. Chugh 75 Spring 2008 Chapter 6 Firms: Labor Demand, Investment Demand, and Aggregate Supply We have studied in depth the consumers’ side of the macroeconomy. We now turn to a study of the firms’ side of the macroeconomy. Continuing with our representative agent paradigm, we suppose there is a single “representative firm” in the economy. This firm must use labor and capital (machines) in order to produce the output good (“all stuff”) that consumers demand. Condensing all of the inputs that a firm uses into the two categories “labor” and “capital” is a useful simplification. 35 In studying firms, we again adopt the two-period idea from the consumption-savings model. f(n,k) n f(n,k) k Figure 24. The production function f(k, n) displays diminishing marginal returns to both labor and capital. The left panel shows that as capital is held constant, increases in labor increase output at an ever-decreasing rate. The right panel shows that as labor is held constant, increases in capital increase output at an ever- decreasing rate. 35 Indeed, if you think about it, there really is only one thing that is not readily categorized as either labor or capital – land. Thus, we abstract from land.
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© Sanjay K. Chugh 76 Spring 2008 Aggregate Production Function We assume a standard production function ( , ) f k n , where n denotes the number of hours of labor the firm hires (from consumers) and k denotes the number of machines (capital) the firm uses. As should be familiar from basic microeconomics, we assume this production function displays diminishing marginal returns to both labor and capital. Specifically, holding the amount of labor fixed, increases in capital increase total output at an ever-decreasing rate, and holding the amount of capital fixed, increases in labor increase total output at an ever-decreasing rate, as shown in Figure 24. Profit Maximization – The Firm’s Labor Hiring Decision Again as familiar from basic microeconomics, the goal of a firm is to maximize profit, which equals total revenue minus total cost. Let 1 P be the period-1 price of the output good (again, the same “all stuff”) in terms of dollars and 1 W the period-1 hourly wage rate in terms of dollars. Total revenue for the firm in period 1 is then simply 1 1 1 ( , ) P f k n , and the total labor cost of the firm is 1 1 W n . The “1” subscript in all of the preceding indicates the time-period we are considering, namely period 1 of the two- period model. Similarly, in period 2 total revenue for the firm is 2 2 2 ( , ) P f k n and the total labor cost is 2 2 W n . Because the firm exists for both periods of the two-period world, the goal of the firm is to maximize lifetime profits, which is the sum of profits in each of the two periods. The timing of events for the firm in the two-period model is depicted in Figure 25. It begins period 1 with some initial amount of capital 1 k , which it cannot alter during period 1. That is, the initial amount of capital is what it must use in production in period 1 – in
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