Suppose the annual rate of return to capital is 10% (r = 0.10) and the annual economic depreciation rate of capital is 12% (ρ = 0.12) and the cost of buying a unit of capital is $1. Further questions are in the picture.

24-. Suppose the annual rate of return to capital is 10% [r = 0.10] and the annual economic depreciation rate of capital is 12% [p = 0.12] and the cost of buyinga 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 asdepreciation. a. What is the economic marginal cost per dollar of machinery investment [MC] if firms can expense capital for corporate tax purposes but notdeduct the interest on funds borrowed to finance the capital good? Note the marginal cost of capital is given by the formula below.MC = [p + 6) * [1-12] where 1: is the tax rate, Z is the present value of the depreciation allowance. What is the user cost of capital? [Note that the after-taxdemand for capital is [1-1:] * w b. What is the effective tax rate under the above conditions? Note theeffective tax rate formula is: (f-tz)(l-tz) c. Retain the 35% tax rate and immediate expensing for depreciation. Add deducibility of interest [1} on borrowed funds to finance the capital good.A firm borrows some fraction of the cost of the capital good — denote the fraction with 1. What is the marginal cost of annual capital [M C] ifa ﬁrmborrows 1:12 of the cost of capital [1 = 5‘2]. The formula for the MC ofcapital is: MC = [p + a) * [1-12-111] What is the user cost of capital [gross of tax price of capital or marginal product of capital] under the above conditions?For the tax regime in part c ofthis question, will capital investment increase or decrease relative to investment in part a of this question? :1. What is the effective tax rate for the tax regime in part c? Note theeffective tax rate formula is: (r—az—rﬁi)(l—zz—oh’)

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