02 Jun Question Each student is to turn in their own assignment. It is to be han
Question
Each student is to turn in their own assignment. It is to be hand-written and it must be legible. To receive
credit you must show all work. Please “Box” your final answers.
1. Textbook, Chapter 3, Numerical Problem 1 (p 100), Part (a) only.
2. Suppose that the economy’s supply side can be described by the following:
Production function:
Y = A [(12)N – (1/4)N2]
where A = 10.
(a) Graph the production function for N = 5, 10, 15, 20, and 25. Does it have diminishing returns? Explain.
(b) Suppose that the firm can only hire in groups of 5 and must pay each worker a nominal wage of W = 20. If the price level is P = 2, calculate the real wage rate paid to each worker. How many workers should the firm hire to maximize profits?
Instead of groups, for the rest of this problem assume that firms can hire any amount of labor, even fractions (i.e. labor is perfectly divisible). The marginal product of labor is given by Marginal Product of Labor:
MPN = A [12 – (1/2)N]
(c) If the price level is P = 2 and the nominal wage W = 20, how much labor will firms demand (ND)? Suppose that the nominal wage increases to W = 70. Calculate what will happen to ND?
(d) What is the equation for the labor demand curve that expresses ND as a function of the real wage rate (?)? Illustrate the ND curve in a graph using the real wage rates from part (c).
The Labor Supply Equation is given by NS = 5 + 2?
(e) Compute the equilibrium quantity of labor ( N ) and real wage ( ? ). What is the full employment level of output ( Y )? Illustrate your answer in a clear diagram of the labor market and production function.
3. Given the labor market & production information in Problem 2, suppose that increases in the price of energy and oil adversely affects the manufacturing sector and lowers total productivity which reduces A to 2 (a negative productivity or supply shock).
(a) Graph the production function for N = 5, 10, 15, 20 and 25.
(b) Assume firms can hire any amount of divisible labor. What will be the new equation for the labor demand curve?
(c) Compute the new equilibrium quantity of labor, real wage, and full employment level of output. How has the supply shock affected the full employment level of output? On the same diagram as Problem 2 (e) illustrate your answer by indicating how each curve has shifted and in which direction.
4. The marginal product of labor in the economy is given by MPN = 200 – 0.5 N, while the supply of labor is NS = 100 + 4?
(a) Find the market equilibrium real wage rate and quantity of labor. Graph your answer.
(b) What happens if the government imposes a minimum wage of 40? Is there involuntary unemployment ? Graph your answer.
(c) What happens if the government imposes a minimum wage of 60? Is there involuntary unemployment ? Graph your answer.
5. Suppose that the population of a country is 200,000. There are 30,000 retired persons, 10,000 full time students, and another 150,000 have a full or part time job. All other persons are looking for work. Calculate the following:
(a) Number of unemployed, labor force, labor force participation rate, employment ratio, and unemployment rate.
Suppose 2,000 of the 10,000 students graduate: 1,000 of them find a job right away and 1,000 are still looking.
(b) Redo part (a). Are there more people working now than before? What has happened to the unemployment rate? Is the unemployment rate a good indicator of the level of employment
in this question?
6. For each year the following table contains information about actual real GDP (Y), the full employment level of GDP ( Y ), and the unemployment rate (u). Use the growth rate version of Okun’s Law to fill in the blanks:
YEAR
1
2
3
4
Y
1000
1050
1029
(c)
Y
1000
1030
(b)
1082.12
u
5%
(a)
6%
5%
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