24. Suppose the annual rate of return to capital is 10% (r = 0.10) and the annua
ID: 1123832 • Letter: 2
Question
24. Suppose the annual rate of return to capital is 10% (r = 0.10) and the annual economic depreciation rate of capital is 12% ( = 0.12) and the cost of buying a unit of capital is $1. In the absence of taxation, what is the annual marginal cost of capital? What is the user cost of capital? Illustrate both on a graph. Introduce a corporate income tax with a rate of 35% and with deductibility of interest on funds borrowed to finance the capital good as well as depreciation. a. What is the economic marginal cost per dollar of machinery investment (MC) if firms can expense capital for corporate tax purposes but not deduct the interest on funds borrowed to finance the capital good? Note the marginal cost of capital is given by the formula below MC = (@t ) * (1-TZ) where T is the tax rate, Z is the present value of the depreciation allowance. What is the user cost of capital? (Note that the after-tax demand for capital is (1-T) * MP b. What is the effective tax rate under the above conditions? Note the effective tax rate formula is: C. Retain the 35% tax rate and immediate expensing for depreciation. Add deducibility of interest (i) on borrowed funds to finance the capital good. A firm borrows some fraction of the cost of the capital good-denote the fraction with , what is the marginal cost of annual capital (MC) if a firm borrows ½ of the cost of capital ( = ½). The formula for the MC of capital is: MC = (p + )" (1-12-TAI)Explanation / Answer
The firm's profit will be maximised at a level where MR=MC. Thus 3500-0.02Q = 100+0.0126Q which gives Q= 104294 units (approx.) and P = 2457 (approx.) Maximum profit = 17076812.
Another way of maximising a firm's profit is to minimise its costs. This is done by setting up the lagrange function and minimizing the total cost subject to the total revenue function. The rationale behind this is that profit's of a firm can be maximized only at the point where its costs are minimized. If a firm's costs are not at its minimal level, then there is scope for cost reduction and profit increment.
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