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Consider a closed economy with the following set of characteristics:
Consumption function is Cd =100 + 0.95Y – 200r, where Y is real output and r is real interest rate
Government purchases G=200
Labor supply line is vertical (perfectly inelastic), and given by the equation N=100.
The production function is given by Y = 40K – 0.01K2 + 4N – 0.01N2 . Marginal product of labor, MPN = 4 – 0.02N; Future marginal product of capital is MPKf = 40 – .02Kf , where Kf is future capital stock.
The depreciation rate of capital d=20% per period, while revenue taxes that firms have to pay are equal to 50% of revenues; Suppose that the current capital stock K is 900 units.
The economy is closed, and so both NX as well as NFP equal 0. The price of a unit of capital is pK =1 unit of output.
a. What is the level of current output Y in this economy?
b. Drive the equation describing the demand for investment Id as a function of real interest rate, r.
c. Derive the equation describing the level of savings in the current period as a function of Y and r
d. Use the equilibrium in the market loanable funds (Sd = Id ) to derive the equilibrium real interest rate r, level of investment demand Id and savings Sd . Use the level of current output to perform the calculations.
e. Compute the level of future capital, Kf and consumption, Cd .
f. Verify that all output is sold in this economy.
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