Question

The marginal product of capital for the next period (MPKf) is given by: MPKf =102−K2t+1

where MPKf is the expected future marginal product of capital, and Kt+1 is the desired capital stock in the next period. Assume that: corporate taxes (τ) are 70% of firms’ revenues, the capital depreciation rate (d) is 25% and the price of capital (Pk) is 2.

(a) Find the real rate of interest r that would imply a desired stock of capital of 10. Now assume that the interest rate is r = 0 (and it cannot be changed) and corporate taxes (τ) are still 70%. By how much would the depreciation rate have to change to still get a desired stock of capital equal to 10?

(b) Given an initial level of capital (Kt) of 10, derive the formula for gross investment (I) in terms of just the real interest rate (and other constants), assuming that corporate taxes (τ) are 50% of firms’ revenues, capital depreciates at 50% per period and the price of capital (Pk) is 10.

(c) Assume that output Y = 100, total taxes paid by households are T = 20, and public expenditure G is set at 20% of GDP: is the government’s budget balanced? Derive an expression for the desired level of saving (Sd) for this economy using the following desired consumption (Cd) function:

C =40−√ r+0.5(Y−T)

Answer 1