! Continued. Demand for labor. ! The firm tries to maximize its profits:

Transcription

1 Chapter 3: National Income: Where it Comes From and Where it Goes! Continued slide 0 Demand for labor! The firm tries to maximize its profits: Profit = Total Revenue Total Cost = P.Y W.L R.K Profit=P. F (K, L) W.L R.K! The competitive firm takes P, W, R as given and chooses L and K to maximize its profits! this is the basic force behind the demand function for the factors of production slide 1! A firm hires each unit of labor if the cost does not exceed the benefit.! cost = real wage! benefit = marginal product of labor slide 2 1

2 Marginal product of labor (MPL )! definition: The extra output the firm can produce using an additional unit of labor (holding other inputs fixed): MPL = F (K, L +1) F (K, L) slide 3 Y output MPL and the production function 1 MPL 1 MPL As more labor is added, MPL! 1 MPL Slope of the production function equals MPL L labor slide 4 Diminishing marginal returns! As a factor input is increased, its marginal product falls (other things equal).! Intuition: Suppose "L while holding K fixed # fewer machines per worker # lower worker productivity slide 5 2

3 Example! Suppose there is a firm with one computer, one Xerox machine, and one employee.! The worker s job is to answer and make photocopies.! When a second worker is hired, together they can produce more because while one is answering , the other can make copies.! They hire another worker. Now output still increases (because they can take breaks on rotation) but not as much as the case after 2nd worker.! Hence, holding the amount of capital fixed, as we increase the amount of labor, MPL decreases.! That is, output does increase for each additional unit of labor, but the change in output is smaller and smaller for each additional worker. slide 6! How does the firm use this analysis to decide on how many workers to hire? The firm checks the change in profits by hiring an additional worker:!profits =!Revenue -!Cost!Profits/!L =!Revenue/!L -!Cost/!L =! (P.Y)/!L -! (W.L)/!L = P (!Y/!L) W (!L/!L) = P.MPL W => The firm will hire more workers as long as!profits/!l > 0 P.MPL > W slide 7! As L increases, MPL decreases up to the point where P.MPL = W MPL=W/P! The firm hires additional workers until MPL is equal to the real wage ( i.e. the nominal wage as a ratio of the price level: W/P)! Note: price level= price of output slide 8 3

4 Exercise Suppose W/P = 6. d. If L = 3, should firm hire more or less labor? Why? e. If L = 7, should firm hire more or less labor? Why? L Y MPL 0 0 n.a slide 9 MPL and the demand for labor Units of output Real wage Each firm hires labor up to the point where MPL = W/P. Quantity of labor demanded MPL, Labor demand Units of labor, L slide 10 Notes! The firm takes the real wage as given and decides on how much labor to demand.! Real wage (measured in units of output) is located on the vertical axis.! The demand curve (MPL) is positive but decreasing (due to law of diminishing returns) slide 11 4

5 The equilibrium real wage Units of output Labor supply The real wage adjusts to equate labor demand with supply. equilibrium real wage MPL, Labor demand Units of labor, L slide 12 Determining the rental rate We have just seen that MPL = W/P. The same logic shows that MPK = R/P :! diminishing returns to capital: MPK! as K "! The MPK curve is the firm s demand curve for renting capital.! Firms maximize profits by choosing K such that MPK = R/P. slide 13 Notes! The marginal product of capital (MPK) is the amount of extra output the firm gets from an additional unit of capital, holding the amount of labor constant. MPK = F (K + 1, L) F (K, L)! What s the increase in profits due to the additional unit of capital?!profits/!k = (!Revenue/!K) (!Cost/!K) = (! (P. Y)/!K) (! (R.K)/!K) = (P (!Y/!K)) (R (!K/!K)) = P.MPK R To maximize profits, the firm rents more capital until P.MPK = R MPK = R/P slide 14 5

6 The equilibrium real rental rate Units of output Supply of capital The real rental rate adjusts to equate demand for capital with supply. equilibrium R/P MPK, demand for capital Units of capital, K slide 15 The Neoclassical Theory of Distribution! states that each factor input is paid its marginal product! is accepted by most economists slide 16 How income is distributed: total labor income = total capital income = If production function has constant returns to scale, then (we will see the proof later) national income labor income capital income slide 17 6

7 ! Assuming fixed amounts of L and K (and full employment), we determine the relative shares of these factors based on marginal products.! Looking at the actual data, one observes that the shares of labor and capital income are relatively constant over time. slide 18 The ratio of labor income to total income in the U.S. Labor s share of total income Labor s share of income is approximately constant over time. (Hence, capital s share is, too.) slide 19 Question! What type of a production function generates constant factor shares under our regular assumptions of perfect competition and profit maximization?! That is:! Capital income: MPK. K = "Y! Labor income: MPL.L = (1-") Y! " determines the relative shares of factors. slide 20 7

8 The Cobb-Douglas Production Function! The Cobb-Douglas production function has constant factor shares:! = capital s share of total income: capital income = MPK x K =! Y labor income = MPL x L = (1! )Y! The Cobb-Douglas production function is: where A represents the level of technology. slide 21! MPL =!Y/!L = #F (K, L)/#L = A (1- ") K " L -"! As K increases, MPL increases As L increases, MPL decreases As A increases, MPL increases slide 22! MPK =!Y/!K = #F (K, L)/#K = A " K "-1 L 1-"! As L increases, MPK increases As K increases, MPK decreases As A increases, MPK increases slide 23 8

9 ! We can write the marginal product of labor as:! MPL = A (1- ") K " L " = A (1- ") K " L " (L/L) =[A (1- ") K " L 1-" ]/L = (1- ") [A K " L 1-" ]/L MPL= (1-") Y/L slide 24! We can write the marginal product of capital as:! MPK = A " K "-1 L 1-" = " A K " L 1-" K -1 = (A " K " L 1-" )/K = " (A K " L 1-" )/K MPK= " (Y/K) slide 25 The Cobb-Douglas Production Function! Each factor s marginal product is proportional to its average product: slide 26 9

10 ! Total labor income: MPL.L = [(1-") Y/L] L = (1-") Y! Total capital income: MPK. K = [" Y/K] K = " Y " Ratio: (1-") Y/ " Y = (1-")/ " (a constant) " Y = MPL. L + MPK. K = (1-") Y + " Y = Y slide 27 10