Worth: Mankiw Economics 5e 48 PART 11 Classical Theory: The Economy in the Long Ru che good the firm produces Y Costs include both labor costs and capital costs. Labor costs equal WX L, the wage W times the amount of labor L Capital costs equal r x K, the rental price of capital R times the amount of capital K. We can Profit= Revenue- Labor Costs-Capital Costs WL RK To see how profit depends on the factors of production, we use the production function Y= F(K, L)to substitute for Y to obtain Profit= PF(K, L)-WL-RK This equation shows that profit depends on the product price P, the factor prices W and R, and the factor quantities L and K. The competitive firm takes the product price and the factor prices as given and chooses the amounts of labor and capital that maximize profit The Firm's Demand for Factors We now know that our firm will hire labor and rent capital in the quantities that maximize profit. But what are those profit-maximizing quantities? To answer this question, we first consider the quantity of labor and then the quantity of capital The Marginal Product of Labor The more labor the firm employs, the more output it produces. The marginal product of labor(MPL) is the extra amount of output the firm gets from one extra unit of labor, holding the amount of capital fixed. We can express this using the production function MPL= F(K, L+1)-F(K, L) m first term on the right-hand side is the amount of output produced with K of capital and L+ 1 units of labor; the second term is the amount of output oduced with K units of capital and L units of labor. This equation states that the marginal product of labor is the difference between the amount of output produced with L+ 1 units of labor and the amount produced with only L units of labor Most production functions have the property of diminishing marginal product: holding the amount of capital fixed, the marginal product of labor de creases as the amount of labor increases. Consider again the production of bread at a bakery. As a bakery hires more labor, it produces more bread. The MPL is the amount of extra bread produced when an extra unit of labor is hired. As more labor is added to a fixed amount of capital, however, the MPL falls. Fewer addi- tional loaves are produced because workers are less productive when the kitchen is more crowded. In other words, holding the size of the kitchen fixed, each ad ditional worker adds fewer loaves of bread to the bakery's output Figure 3-3 graphs the production function. It illustrates what happens to the amount of output when we hold the amount of capital constant and vary the User JoENA: Job EFFo1419: 6264_ch03: Pg 48: 24984#/eps at 1004 mI wed,Feb13,20028:564MUser JOEWA:Job EFF01419:6264_ch03:Pg 48:24984#/eps at 100% *24984* Wed, Feb 13, 2002 8:56 AM the good the firm produces Y. Costs include both labor costs and capital costs. Labor costs equal W × L, the wage W times the amount of labor L. Capital costs equal R × K, the rental price of capital R times the amount of capital K.We can write Profit = Revenue − Labor Costs − Capital Costs = PY − WL − RK. To see how profit depends on the factors of production, we use the production function Y = F(K, L) to substitute for Y to obtain Profit = PF(K, L) − WL − RK. This equation shows that profit depends on the product price P, the factor prices W and R, and the factor quantities L and K. The competitive firm takes the product price and the factor prices as given and chooses the amounts of labor and capital that maximize profit. The Firm’s Demand for Factors We now know that our firm will hire labor and rent capital in the quantities that maximize profit. But what are those profit-maximizing quantities? To answer this question, we first consider the quantity of labor and then the quantity of capital. The Marginal Product of Labor The more labor the firm employs, the more output it produces. The marginal product of labor (MPL) is the extra amount of output the firm gets from one extra unit of labor, holding the amount of capital fixed.We can express this using the production function: MPL = F(K, L + 1) − F(K, L). The first term on the right-hand side is the amount of output produced with K units of capital and L + 1 units of labor; the second term is the amount of output produced with K units of capital and L units of labor.This equation states that the marginal product of labor is the difference between the amount of output produced with L + 1 units of labor and the amount produced with only L units of labor. Most production functions have the property of diminishing marginal product: holding the amount of capital fixed, the marginal product of labor de￾creases as the amount of labor increases. Consider again the production of bread at a bakery. As a bakery hires more labor, it produces more bread.The MPL is the amount of extra bread produced when an extra unit of labor is hired. As more labor is added to a fixed amount of capital, however, the MPL falls. Fewer addi￾tional loaves are produced because workers are less productive when the kitchen is more crowded. In other words, holding the size of the kitchen fixed, each ad￾ditional worker adds fewer loaves of bread to the bakery’s output. Figure 3-3 graphs the production function. It illustrates what happens to the amount of output when we hold the amount of capital constant and vary the 48 | PART II Classical Theory: The Economy in the Long Run