::Solutions:: Practice Problem Set: Labor Markets

Transcription

1 ::Solutions:: Practice Problem Set: Labor Markets This is an ungraded assignment. Do not hand in. 1. As background to a consulting assignment, you have been asked to work through an analytical example to illustrate the impact of minimum wage legislation and payroll taxes on employment and unemployment. You decide to adapt the framework of your Global Economy class notes. The supply of labor rises with the wage, w, L S (w) = w 2. The labor demand function is L D (w) = ( 3 2 w) 3. a. Describe, first, how the labor market works in this economy if the market is unregulated. What is the wage? How much labor is employed? What is the unemployment rate? In a supply and demand diagram, sketch the labor supply and demand curves and label the equilibrium wage and level of employment with the values you computed. Setting labor demand equal to labor supply we have ( 2 3w ) 3 = w 2. Solving this for the wage yields w = After we substitute the value of the wage into either the supply or the demand equation we find that total employment is (The units don t mean anything in this example.) There is no unemployment in this economy, as labor demanded at this wage is equal to labor supplied, so the unemployment rate is 0%. w w = D S L = 0.61 L

2 Now consider the effect of introducing a minimum wage, w m. b. Suppose w m = 1. How much labor is employed? What is the unemployment rate? On your graph from part a., label the minimum wage, the amount of labor supplied at the minimum wage and the amount of labor demand at the minimum wage. Labor demand: L D (w = 1) = ( 2 3) 3 = and labor supply is L S (w = 1) = 1 2 = 1, so the amount of labor employed is The unemployed are = 0.704, so the unemployment rate is 70.4%. w = 1.0 w w = D S c. Suppose w m = 0.5. How much labor is employed? What is the unemployment rate? A minimum wage of 0.5 is lower than the equilibrium wage, so the minimum wage is nonbinding units of labor are employed and the unemployment rate is 0%. L page 2 of 5

3 2. With the supply and demand analysis settled, now consider the dynamic effects of labor market regulations on unemployment. As derived in the class notes, the change in the unemployment rate can be written as u t+1 = s(1 u t ) au t where s is the constant separation rate and a is the constant accession rate. The steady-state unemployment rate in this model is u ss = s/(s + a). a. If a = 0.28 and s = 0.013, what is the steady state level of unemployment in this economy? u ss = s a + s = A large spike in gasoline prices has severely decreased the demand for SUVs. This, in turn, has cost many people in the auto industry their jobs, raising the unemployment rate at time zero to u 0 = b. Compute the unemployment rate for the next 4 periods, u 1, u 2, u 3, u 4. It might be more efficient to compute these in Excel and report a neat table of numbers. The following table comes from the repeated application of u t+1 = s(1 u t ) au t, or equivalently, u t+1 = u t + s(1 u t ) au t, which is, after substituting for s and a, u t+1 = u t (1 u t ) 0.28 u t Time Unemployment Rate c. Compute the growth rate (it will be negative) between the unemployment rate in period 4 and period 0. ln ( ) = 12.03% page 3 of 5

4 3. Suppose that in a different country, a = 0.15 and s = What is the steady state level of unemployment in this economy? u ss = s a + s = 0.14 The growing popularity of low-carbohydrate diets has severely decreased the demand for bread and pasta. This, in turn, has cost many people in the flour milling industry their jobs, raising the unemployment rate at time zero to u 0 = a. Compute the unemployment rate for the next 4 periods, u 1, u 2, u 3, u 4. It might be more efficient to compute these in Excel and report a neat table of numbers. Using the same methods as in 2b, but with the different parameters. Time Unemployment Rate b. Compute the growth rate (it will be negative) between the unemployment rate in period 4 and period 0. ln ( ) = 7.84% In your analysis of labor markets in questions 2 and 3, the key factors were the separation and accession rates. Give two examples of policies that would affect the separation and/or the accession rates. For each example explain in a sentence or two how they affect the separation and/or accession rates. Any of the examples we talked about in class would work here, laws restricting work week length, firing costs, laws that give unions more power, unemployment benefits, or minimum wages to name a few. All these will tend to lower accession rates. page 4 of 5

5 5. There are 9,064,900 employed people in the New York City metro area and 538,2000 unemployed people (data are from December, 2014). The working age population is approximately 15 million. What is the labor force? What is the unemployment rate? What is the participation rate? labor force = 9, 064, , 200 = 9, 603, 400 unemployment rate = participation rate = 538, = 5.6% 9, 603, 400 9, 603, = 64.0% 15, 000, 000 If you would like to see how NYC employment statistics compare to other metro regions in the United States, you can find the data at metro.nr0.htm. page 5 of 5