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Midterm Exam
October 17, 2014
You must answer all the following questions. Some of them have bonus points. To manage your time, it is suggested that you focus on the bonus parts after completing the rest of the questions.
Part I
Empirical Observations
Question 1. Empirical Observations on Labor Supply
(15 Points) Answer the following questions:
(a) How did labor force participation evolve for men over the period 1900–2010? Which subgroup of this population experienced the greatest change?
(b) How did labor force participation evolve for women over the period 1900–2010? Which subgroup of this population experienced the greatest change?
(c) How did average weekly hours of work evolve over the period 1900–2010?
Part II
Theory and Economic Intuition
Question 2. Labor Supply
(30 points + 10 Bonus points) Let Franco’s utility function be U(C, L) = α log(C)+ β log(L). Let T denote the time available to split between leisure and work, w denotes the wage rate, and V ≥ 0 denote non-labor income (as in class).
(a) Derive his optimal choice as a function of w, T, and V .
(b) Calculate the first derivative of his optimal leisure choice with respect to w. Does the substitution effect dominate the income effect? Is this also true if V = 0?
(c) What is Franco’s reservation wage as a function of w, T, and V ? Is it increasing, decreasing, or constant in V ? Why?
(d) Now assume that Maria’s utility function is U(C, L) = C
2+L
2
. Derive her optimal choice as a function of w, T, and V. (Hint: Be careful, the non-labor income is not necessarily 0. You should take that into consideration when calculating the utility of each choice).
(e) (Bonus: 5 points) Explain graphically what is the difference between the optimal solution of Franco and Maria (interior vs. corner solution). Give the economic intuition of their optimal choice based on the type of their preferences.
(f) (Bonus: 5 points) Calculate Franco’s labor supply elasticity.
Question 3. Labor Demand
(35 points + 5 bonus points) In this problem, you can assume all solutions are interior. Suppose the hourly wage is $20 and the price of each unit of capital is $20.
The price of output is constant at $60 per unit. The production function is:
F(E, K) = E
1/4K1/8
(a) If the current capital stock is fixed at 256 units, how much labor should the firm use in the short run? How much profit will the firm earn?
(b) How much labor and capital should the firm use in the long run? How much profit will the firm earn?
(c) Now, assume w = 40. Repeat (b).
(d) Consider the increase in wage from part (b) to part (c). Create a graph without numbers to qualitatively show how the scale and substitution effect work.
(e) Qualitatively explain the economic intuition of the scale and substitution effect.
(f) (Bonus: 5 points) Find substitution and scale effects from (b) to (c). Include a table like the one provided. Not just with the signs but the actual values of substitution and scale effects! Create the graph as in part (d), with the actual values of capital, and employment. Are the substitution and scale effects that you found consistent with the theory? Why?.
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E |
K |
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Substitution Effect |
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Scale Effect |
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Total Effect |
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Part III
Scientific Methodology
Question 4. Minimum Wage Policy Application
(20 Points + 10 Bonus Points) Consider the scientific question: ”What is the effect of minimum wage on employment?”
Based on this question, answer the following:
(a) Explain graphically the testable prediction of the standard theory of (upward sloping) labor supply and (downward-sloping) labor demand that addresses the question under consideration.
(b) Does the result of the New Jersey–Pennsylvania minimum wage empirical study reject or fail to reject the theory? Explain by specifying the policy change, the control and treatment groups, the empirical methodology, and the study’s findings.
(c) (Bonus: 5 points) What version of the theory of supply and demand is consistent with the empirical results of the New Jersey–Pennsylvania empirical study?
(d) (Bonus: 5 Points) What are the methodological problems that could invalidate the this empirical study?