Question

5. 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 /2 hour of computer time and 5 hours of clerical time. a. Sketch the isoquant that shows all the 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 раyroll?

Answer 1

A. The isoquant is show below

4 2

Since K and L can be substituted for each other (perfect substitutes), its a linear isoquant. The production function is Q=10000K+1000L.

B. For optimal inputs, the ratio of isocost line is given by w/r. In our case, this becomes -7.5/5=-1.5. Since this is more steep than the isoquant, which is the current inputs, it means that the firm should employ only computer time to minimize cost. So the combination that would minimize costs would K-1, L=0. The cost will be $5 if the firm is processing 10000 payrolls since it will take one computer 1 hour to do that.

C. The firm will start employing clerical time when the ratio of marginal productivity of labor to its wage would be higher than or equal to to the ratio of marginal productivity of capital to its rent. In other worlds, when

MPL/w>=MPK/r

Putting values in, we get

.1/7.5=1/r, where r is the new rent rate of capital (here, computers)

we get r>=75.