Econ 3710.02, Advanced Microeconomics, FALL 2002, ASSIGNMENT 2

Hand in your answers to all 3 questions at the BEGINNING of class on Wednesday November 13. This assignment is worth 10% of your final mark.

1. This question is based on an article by a Harvard Economics Professor, Michael Kremer “The O-ring theory of economic development.” Quarterly Journal of Economics, 1993, 108: 551- 575.

Consider the following production function:

Q = 3z1z2z3.

where Q is final output, zi (i =1, 2, 3) is the skill level of the worker performing the i-th task and is measured as the probability that a worker will perform his task perfectly (i.e., with no mistakes). Note that output is higher the higher is the skill of the workers. Assume that the price of output is fixed.

(i) Does this production function exhibit decreasing, increasing, or constant returns to scale. Prove your answer.

Suppose the output Q is produced by combining the skills of a computer engineer, a computer programmer, and an electrical engineer. These correspond to the tasks, 1, 2, and 3. Consider two firms. Call them X and Z. Suppose firm X has a computer engineer and a computer programmer each with a skill level of 0.8 and assume that firm Z also has these two workers but each with a skill level of 0.5. Assume that both firms are competing for an electrical engineer. Suppose there are only two electrical engineers available; one with a skill level of 0.8 (engineer A) and the other with a skill level of 0.6 (engineer B). Obviously each firm prefers carpenter A to B. Each firm is guaranteed B if it is unable to get A.

(ii) What is the maximum that firm X will pay to get A?

(iii) What is the maximum that firm Z will pay to get A?

(iv) Suppose A will work for the firm which is willingly to pay more money. Which of these firms will attract A?

(v) Sports teams, universities, law firms, etc with high-ability workers attract other high-ability workers compared to firms with low-ability workers. It is as if those who begin with some head-start advantage keep getting better. Harvard University continues to attract top academics relative to a young university (e.g., Joe Blow University). Can you verify this result based on your answers above? Explain.

(vi) In the National Basketball Association (NBA) and other North American Leagues, there are caps on the salaries of the players. This is partly to ensure that all the best players do not play for a few top teams. Can you use this salary cap mechanism to possibly change your answer in (iv)? Explain how you will do this.

2. Firm 1 has a contract with firm 2 to supply some quantity of a good at a price, p. The production for firm 1 is q = K0.25L0.25, where q is quantity, K is capital, and L is labor. The price of labor is $1 per unit and capital also costs $1 per unit. Firm 2 has agreed to buy any quantity from firm 1, so long as the price, p £ $10. (i) How many units will firm 2 buy from firm 1? (ii) How many units will firm 2 buy from firm 1 if K = 1 (i.e., capital is fixed)? (iii) Suppose firm 1 pays a tax of t dollars for every unit of output produced. Find how many units firm 2 will buy from firm 1 as a function of t, if K = 1?

3. In class we argued or proved that profit maximization necessarily implies cost minimization. Is the converse of this statement true? That is, does cost minimization necessarily imply profit maximization? Explain in NO more than eight sentences.

J. Atsu Amegashie

Department of Economics

University of Guelph

November 4, 2002