Question

12. 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 a unit of capital is $1. a. In the absence of taxation, what is the annual marginal cost of capital? What is the user cost of capital (MPk)? {Note equilibrium condition is MPk = MCk.} Illustrate both MPk and MCk on a graph. b. Introduce an income tax with a tax rate of 25% and with expensing of capital equipment purchases. What is the after-tax marginal cost of capital? Show the after-tax marginal cost supply curve. c. Show the after-tax demand curve or line for capital on a graph. d. What is the user cost of capital in this case? {Note: User cost is the MPk at the equilibrium quantity of capital.} e. What is the marginal effective tax rate under the tax system? Note the marginal effective tax rate formula is: f. Retain the 25% tax rate and expensing of capital for depreciation (Z=1). Add deductibility of interest (i = interest rate) on borrowed funds to finance the capital good. A firm borrows some fraction of the cost of the capital good – denote the fraction with λ. Calculate the marginal cost of annual capital (MC) if a firm borrows ½ of the cost of capital (λ = ½). The formula for the MC of capital is now: MC = (ρ + δ) * (1-τZ-τλi) g. Calculate the marginal effective tax rate for the tax regime in part f. (Assume interest rate (i) = 0.10. Note the marginal effective tax rate formula is: Will the equilibrium amount of capital increase or decrease after the tax is introduced relative to the equilibrium amount of capital before the tax is introduced?

Answer 1

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.