# Agenda. Productivity, Output, and Employment, Part 1. The Production Function. The Production Function. The Production Function. The Demand for Labor

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1 Agenda Productivity, Output, and Employment, Part A production function shows how businesses transform factors of production into output of goods and services through the applications of technology. Factors of production: Capital (K) Labor () Other (raw materials, land, energy, etc.) The productivity of factors depends on technology and management (A)

2 The economy s production function is: = AF(K, ) Shows how much output () can be produced from a given amount of capital (K) and labor () and a given level of technology (A). The parameter A is total factor productivity or the effectiveness with which K and are used. A more specific production function that works well in macroeconomics is the Cobb- Douglas production function. = AK α (1-α) For the U.S. economy it would be: = AK : Output and Capital : Output & Capital Shows how depends on K for a given and A. K

3 : Output and Capital Two main properties of this production function: Exhibits increasing returns to capital. Slopes upward because more K produces more. Exhibit diminishing marginal product of capital. Slope becomes flatter because each additional increment of K produces less additional. : Output and Capital Marginal product of capital, MPK = / K. Equals the slope of production function graph ( vs. K). MPK is always positive. MPK declines as K increases The Marginal Product of Capital The Marginal Product of Capital = A 0 F(K, 0 ) MPK K 3-11 K

4 : Output & Capital : Output and Capital What happens if or A changes? = A 0 F(K, 0 ) K : Output and Labor : Output & Labor Shows how depends on for a given K and A

5 : Output and Labor Two main properties of this production function: Exhibits increasing returns to labor. Slopes upward because more produces more. Exhibit diminishing marginal product of labor. Slope becomes flatter because each additional increment of produces less additional. : Output and Labor Marginal product of labor, MP = /. Equals the slope of production function graph ( vs. ). MP is always positive. MP declines as increases The Marginal Product of Labor = A 0 F(K 0, ) The Marginal Product of Labor MP

6 : Output & Labor : Output and Labor What happens if K or A changes? = A 0 F(K 0, ) Productivity is calculated as a residual: A = K Productivity growth is calculated as: Observations about productivity growth: Productivity moves sharply from year to year. Productivity grew strongly from the mid-1950 s through 1973, very slowly from 1973 through 1995, and more quickly again since %ΔA = ΔA/A *

7 Supply shocks: Supply shocks affect the amount of output that can be produced for a given amount of inputs. Also called productivity shocks. Supply shocks: Supply shocks shift the production function. egative or adverse shock: A decline in A usually causes the slope of production function to decrease at each level of input. Positive or beneficial shock: An increase in A usually causes the slope of production function to increase at each level of input Effects of an Adverse Supply Shock = A 0 F(K 0, ) The demand for labor is determined by individual business firms. The aggregate demand for labor is the sum of all the business firms demand for labor. The demand for labor depends on the costs and benefits of hiring additional workers

8 How much labor do firms want to use? Assumptions: The capital stock fixed, i.e., a short-run analysis. Workers are homogeneous. The labor market is competitive. What is the cost of hiring one more worker? The marginal cost of hiring one more worker is the cost of that worker to the firm, i.e., the nominal wage: W Firms maximize profits What is the benefit of hiring one more worker? The benefit of hiring one more worker is the additional income that the worker generates, i.e., the marginal revenue product of labor: MRP = P * MP How much labor do firms want to use? A profit-maximizing firm will hire additional workers up to the point where the marginal revenue product of labor equals the nominal wage: W = MRP = P * MP

9 How much labor do firms want to use? Marginal Cost of Hiring an Extra Worker w This equilibrium condition: W = MRP = P * MP can be re-written as: w = MP because w= W/P and MRP = P * MP Marginal Benefit of Hiring an Extra Worker MP The Determination of Labor Demand w, MP

10 How much labor do firms want to use? Costs and benefits of hiring one extra worker. If w > MP, profits rise if number of workers declines. How much labor do firms want to use? The labor demand curve shows the relationship between the real wage rate (w) and the quantity of labor demanded (). If w < MP, profits rise if number of workers increases. When w = MP, profits are maximized Determination of the Labor Demand Curve w, MP The Labor Demand Curve, D. w 0 w 0 Changing the real wage rate: An increase in the real wage rate means w > MP unless is reduced so the MP increases. MP A decrease in the real wage rate means w < MP unless is increased so the MP decreases

11 The Labor Demand Curve, D. The (Aggregate) Labor Demand Curve w, MP The labor demand curve is downward sloping. The higher the real wage, the less labor firms will hire. Because w = MP in equilibrium (regardless of what w is), the D curve is the same as the MP curve Factors that shift the labor demand curve: Effect of an Increase in K or A w, MP Changes in the capital stock, ΔK. Increases in K raise MP and shift the labor demand curve to the right. Supply shocks, ΔA. Beneficial supply shocks raise MP and shift the labor demand curve to the right. D

12 Key Diagram #1: Key Diagram #2a: Demand for Labor = A 0 F(K 0, ) w, MP D Key Diagrams #1 & #2a. Factors that Shift the Production Function and the Demand for Labor: Increases in the capital stock, K, shift the production function higher, increase the MP and the demand for labor. Increases in productivity, A, shift the production function higher, increase the MP and the demand for labor

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