Perpetual plastic plant makers cost $200 each. The number of plants that your firm expects to produce each year for each level of capital stock is as follows:
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The plants sell for $1 each and your firm faces no other costs. The real interest rate is 10% and the depreciation rate of capital is 15%. There is a 20% tax on your firm's revenues from selling these plants.
a. What is the firm's tax-adjusted user cost of capital?
b. What is the marginal product of capital for each number of machines (1, 2, 3, 4, and 5)?
c. How many machines should the firm buy? What is their production, pretax revenue, and profit after deducting taxes, interest, and depreciation?

Question

Perpetual plastic plant makers cost $200 each. The number of plants that your firm expects to produce each year for each level of capital stock is as follows:
?  
The plants sell for $1 each and your firm faces no other costs. The real interest rate is 10% and the depreciation rate of capital is 15%. There is a 20% tax on your firm's revenues from selling these plants.
a. What is the firm's tax-adjusted user cost of capital?
b. What is the marginal product of capital for each number of machines (1, 2, 3, 4, and 5)?
c. How many machines should the firm buy? What is their production, pretax revenue, and profit after deducting taxes, interest, and depreciation?

Quizplus · Accepted Answer

The Answer is a. Tax-adjusted user cost = (r + d)pK/1 - T) = (.10 + .15) × $200/(1 - 0.20) = $62.50
b. MPKs: one machine produces 250 plants × $1 each = $250; two produce 150 more plants × $1 each = $150; three:
100 × $1 = $100; four: 65 × $1 = $65; five: 35 × $1 = $35.
c. Four machines (MPK > uc); production = 565 plants, pretax revenue = $565, profit = $565 - $113 (taxes = $565 ×.20) - $80 (interest = $800 × .10) - $120 (depreciation = $800 × .15) = 252

Perpetual Plastic Plant Makers Cost $200 Each