Answer to Question #212837 in Macroeconomics for gulsekilicc

Question

Let: C = consumption I = investment spending G = government spending Tx = tax revenue Yd = after-tax income MS = money supply MD = money demand r = interest rate Assume for a given closed economy: (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. a) What is the total money supply? b) What is the equilibrium interest rate? c) What is the equilibrium level of national income?

Answer 1

Money market attains its equilibrium point when the money supply is equal to the amount of money demand. Graphically, it is at the intersection point of money demand curve and money supply line. The money demand curve is negatively sloped as it is inversely associated with market interest rate. On the other hand, money supply is a vertical line parallel to the interest rate-axis due to no relationship between interest rate and the amount of money supplied.

a) 

Money supply is the ratio of total reserves divided by the reserve ratio. Using this:

$MS=\frac{Total\space Reserves}{Reserve\space ratio}\\=\frac{150}{0.20}\\=750$

Hence, total money supply amounts to 750 billion dollars.

b)

The equilibrium interest rate is established at the equality of money supply and money demand. Using this:

$MS=MD\\750=850-1000r\\1000r=850-750\\1000r=100\\r=0.1\\=10\%$

Hence, the equilibrium interest rate is 10 percent.

c)

The equilibrium level of income is one where the production level (as given by Y) matches with the level of aggregate spending. Using this:

$Y=C + G + I + NX$

 putting the given values

$Y=(200+0.8(Y−T) ) + 250 + (500 −2000r) +0 \\Y=950 + 0.8(Y−250) −2000×0.1 \\Y=950+0.8Y −200−200 \\0.2Y=550 \\Y=2750$

Hence, the equilibrium national income is 2750 billion dollars.