Question 1

The processing of payroll for the 10,000 workers in a large firm can either be done using 1 hour of computer time (denoted by K) and no clerks or with 10 hours of clerical time (denoted by L) and no computer time. Computers and clerks are perfect substitutes; for example, the firm could also process its payroll using 1/2 hour of computer time and 5 hours of clerical time.

(a) Sketch the isoquant that shows all combinations of clerical time and computer time that allows the firm to process the payroll for 10,000 workers. (b) Suppose computer time costs $5 per hour and clerical time costs $7.50 per hour. What are the cost-minimizing choices of L and K? What is the minimized total cost of processing the payroll?

(c) Suppose the price of clerical time remains at $7.50 per hour. How high would the price of an hour of computer time have to be before the firm would find it worthwhile to use only clerks to process the payroll?

Question 2

A firm operates with the production function Q = K2L. Q is the number of units of output per day when the firm rents K units of capital and employs L workers each day. The manager has been given a production target: Produce 8, 000 units per day. She knows that the daily rental price of capital is r = $400 per unit. The wage rate paid to each worker is w = $200 day.

(a) Currently the firm employs at 80 workers per day. What is the firm's daily total cost if it rents just enough capital to produce at its target? (b) Compare the marginal product per euro spent on K and on L when the firm operates at the input choice in part (a). What does this suggest about the way the firm might change its choice of K and L if it wants to reduce the total cost in meeting its target?

(c) In the long run, how much K and L should the firm choose if it wants to minimize the

cost of producing 8,000 units of output day? What will the total daily cost of production be?

For questions 3, select your answer and motivate it with a short comment.

Question 3

Consider the function Q = KL. By only computing the marginal rate of technical substitution we can argue that the isoquants are decreasing in the space LxK even though the function does not have diminishing marginal productivities of products of capital and labor.