Answer to Question #212839 in Macroeconomics for gulsekilicc

Question

assume (i) Consumers spend $200 billion plus 80% of after-tax income, or C=200+0.8 Yd (ii) Investment demand varies inversely with the interest rate, such that I= 500-2000r (iii) Currently government spending and taxes are both $250 billion, or G=250 and Tx=250, (iv) The total money demand or liquidity preference schedule for this economy is an inverse function of the rate of interest and is given by the equation MD=850-1000r (v) The required reserve ratio for banks in this economy is 20%. No bank holds excess reserves, and everybody keeps their money in the bank. The total of reserves in the banks is $150 billion. Answer the following questions given the information above. d) The central bank wants national income to be $3000 billion. What must investment be for the equilibrium level of national income to be $3000 billion (if investment alone changes in response to the change in the interest rate)? e) At what interest rate is this level of investment (your answer to part (d)) achieved?

Answer 1

d)

Computing the level of investment:

We will use the equilibrium condition in goods market to derive the value of investment:

$Y =C +I + G + NX\\Y=(200 +0.8Yd) + I + 250 +0\\Y=450 + 0.8(Y−T) + I \\Y= 450 +0.8(Y−250)+I \\Y=450 +0.8Y −200 +I\\0.2Y=250 + I ,\\ putting Y = 3000\\0.2\times 300=250+I\\600=250 +I\\I=350$

So, investment must be equal to 350 billion dollars for the economy to attain the national income of 3000 billion dollars.

e)

Deriving the value of interest rate:

We will put the value of investment into the investment function to get the required interest rate:

$I = 500 −2000r\\350=500 −2000r\\ 2000r=150\\r=0.075\\r=7.5\%$

So, the interest rate amounts to 7.5 percent.