# Econ 100B: Macroeconomic Analysis Fall Problem Set #3 ANSWERS (Due September 15-16, 2008)

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1 Econ 100B: Macroeconomic Analysis Fall 2008 Problem Set #3 ANSWERS (Due September 15-16, 2008)

2 A. On one side of a single sheet of paper: 1. Clearly and accurately draw and label a diagram of the Production Function relating economic activity to employment. Y Y = A 0 * F( N, K 0 ) 2. Provide an economic explanation of the shape of the curve(s) in your diagram in #1. The production function shows the positive relationship between economic output, Y, and employment, N, for a given level of technology, A, and the capital stock, K. The production function slopes upward because there are increasing returns to labor, i.e., as employment increases, economic output also increases. The slope of the production function decreases as employment increases because of the diminishing marginal product of labor, i.e., as employment increases, economic output also increases but by progressively smaller and smaller amounts. 3. List the endogenous and exogenous variables in this model. Endogenous variables: Economic output, Y, and employment, N. Exogenous variables: Technology (or productivity), A, and the capital stock, K. 4. List the variables (and the direction of their change) that would shift the Production Function higher. Also provide an economic explanation for why each of these variables would shift the Production Function. An increase in technology from A 0 to A 1 would shift the production function higher. At every level of employment and the capital stock, greater technology would allow greater economic output. An increase in the capital stock from K 0 to K 1 would shift the production function higher. At every level of employment and technology, a larger capital stock would allow greater economic output. N

3 B. On one side of a single sheet of paper: 1. Clearly and accurately draw and label a diagram of the Labor Market. w Ns w 0 Nd N 0 N 2. Provide an economic explanation of the shape of the curve(s) in your diagram in #1. The labor demand curve is the inverse relationship between the current real wage and employment. It is downward sloping because profit-maximizing businesses will only hire additional workers up to the point where the real wages equals the marginal product of labor. Because the marginal product of labor diminishes as the level of employment rises, the labor demand curve slopes downward. The labor supply curve is the positive relationship between the current real wage and employment. It is upward sloping because a higher real wage will induce some workers to work more hours and some people who are out of the labor force to enter the labor force and seek employment this is the substitution effect of a higher current real wage. However, a higher current real wage also allows workers to buy more leisure and offer less work this is the income effect of a higher current real wage. Because the substitution effect is greater than the income effect in the short-run, the labor supply curve is upward sloping. The intersection of the labor demand and labor supply curves generate the equilibrium real wage, w 0, where the quantity of labor demanded by businesses is exactly equal to the quantity of labor supplied by individuals. The level of employment associated with the equilibrium real wages is equilibrium employment, N List the endogenous and exogenous variables in this model. Endogenous: the real wage, w, and employment, N. Exogenous: Technology (or productivity), the capital stock, wealth, expected future real wage, the working age population, and the labor force participation rate. 4. List the variables (and the direction of their change) that would shift the demand for labor function to the right. Also provide an economic explanation for why each of these variables would shift the Demand for Labor Function. An increase in either technology (or productivity) and/or the capital stock would shift the production function higher, increasing the marginal product of labor. This increases the demand for labor and shifts the labor demand curve to the right.

4 5. List the variables (and the direction of their change) that would shift the supply of labor function to the right. Also provide an economic explanation for why each of these variables would shift the Supply of Labor Function. A decrease in wealth, a decrease in the expected future real wage, an increase in the working age population, and/or an increase in the labor force participation rate would shift the labor supply curve to the right. A decrease in wealth and/or decrease in the expected future real wage has a negative income effect that induces people to buy less leisure and consequently to supply more labor to the labor market at every real wage rate. An increase in the working age population and/or and increase in the labor force participation rate increases the supply of labor at every real wage rate. 6. Assume that the labor market starts in equilibrium. Suppose now that the supply of labor increases. Describe the adjustment process that moves the labor market from its initial equilibrium to its final equilibrium. When the supply of labor increases, the labor supply curve shifts to the right. At the initial equilibrium real wage, the quantity of labor supplied exceeds the quantity of labor demanded. Therefore, the real wage begins to decline. As the real wage declines, the quantity of labor demanded increases along the labor demand curve and the quantity of labor supplied decreases along the new labor supply curve. The real wage will continue to decline until equilibrium is restored when the quantity of labor demanded exactly equals the quantity of labor supplied. The equilibrium real wage is lower and the equilibrium level of employment is higher.

5 C. On one side of a single sheet of paper: 1. Clearly and accurately draw and label a diagram of Okun s Law. Y/Y 0 OL 2. Provide an explanation of the shape of the curve(s) that you have drawn in your diagram in #1. Okun s Law shows the inverse relationship between deviations in economic output from its fullemployment level and changes in the unemployment rate. For the U.S., empirical evidence indicates that the trade-off is for every 2 percentage point decline in economic output relative to fullemployment output, the unemployment rate rises by 1 percentage points. In the U.S. the growth rate of full-employment output is approximately 3%. Consequently, when the economy grows by 3%, there should be no change in the unemployment rate. When the economy grows slower than 3%, the unemployment rate should rise and when the economy grows slower than 3%, the unemployment rate should fall. 3. Provide an economic explanation of Okun s Law u Okun s Law follows directly from the production function relating economic output to employment. Increases in economic output (relative to its full-employment level) requires greater employment so that the unemployment rate will fall and vise-versa.

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