MO6.5( 100,000 650,000 AVC-1,700,000/100,000-$17 C-6.5+17a AC-C/Q- 6.5Q+17 4. 12

Question

MO6.5( 100,000 650,000 AVC-1,700,000/100,000-$17 C-6.5+17a AC-C/Q- 6.5Q+17 4. 120 pts] A high-tech firm produces a data processing service according to the production function a.) If the cost per hour of labor (L) and of machine time (K) is the same, what is the least-cost way to complete 100 data processing jobs? Will the firm ever use both inputs to complete processing MPL-1 MPK 2 Since MPK is higher then the firm will use strictly capital inputs to complete 100 data processing jobs. This is because capital helps complete a job twice as much as one unit of labor and it costs the same. Total cost--100/2-$s0- Price of capital b.) What if the cost per hour of labor is twice as much as the cost of machine time, then what is the least-cost way to complete 100 data processing jobs? 5. [10 pts] The annual expenditures of a small tax accounting firm are: Rent ($13,000), Secretary's Salary ($33,000), and Other Expenses (57,000)- The estimated number of tax returns per year is 850 Average processing cost per return is $140, and the average price charged per return is $300 The head of the firm has launched his solo practice after resigning from his $75,000-a year job. Estimate the economic and accounting profit of the new enterprise and comment on the decision. Accounting Profit Revenue: 850(300 2SS000 Processing coste 14018501 119,0oo Rent- 13,000 Salary- 33,000 Other sp807. NM

Explanation / Answer

a) Q=2K+L

MPK = dQ/dK = 2

MPL = dQ/dL = 1

To produce a given level of output less K is required as compared to L. Thus to minimize cost the firm should use only K. To complete Q = 100, if only K is used then K = 50 is required while if only Labor is used then L = 100 is required. The two goods are perfect substitutes. Thus to use K = 50 is the cost minimizing level of input. The firm will never use the two goods together.

b) The firm make decision based on the marginal product. Since the marginal product of Labour is less than the marginal product of capital. Therefore the firm will continue to employ only capital.

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