1. Suppose that the real money demand function is
where Y is the real output, r is the real interest rate, and is the expected inflation rate. Real output is constant over time at Y=150. The real interest rate is fixed in the goods market at r=5% per year.
A) Suppose that the nominal money supply is growing at the rate of 10% per year and this growth rate is expected to persist forever. Currently, the nominal money supply is M=300. What are the values of the real money supply and the current price level? (Hint: For finding the expected inflation rate, use the equation which relates inflation rate to the growth rate of nominal money supply and the growth rate of output. Suppose people are rational and realize this relationship when they form their expectations.)
B) Now, suppose the real output is not constant over time, and that the real output is growing at the annual rate of 4% and this growth rate is expected to persist forever. As in part (A), M=300 and the nominal money supply is growing (and expected to be growing) at the rate of 10% per year. Moreover, the income elasticity of money demand equals 2/3. What are the values of the real money supply and the current price level? Compare your result to part (A) and provide your intuition.
C) Suppose that the money supply is M=300 and output is constant. The central bank announces that from now on the nominal money supply will grow at the rate of 5% per year. If everyone believes this announcement, and if all markets are in equilibrium, what are the values of the real money supply and the current price level? Compare your result to part (A). Explain the effects on the real money supply and the current price level of a slowdown in the rate of money growth.
2. How does each of the following factors affect the LM curve? Start your argument from the diagram of MD-MS and show how the associated change will affect LM curve.
- An increase in nominal money supply.
- An increase in the risk of non-monetary assets relative to the risk of holding money.
3. How does each of the following factors affect the IS curve? Start your argument from the diagram of Id-Sd and show how the associated change will affect IS curve.
- An increase in government purchases (when it does not affect the productivity).
- An increase in marginal productivity of capital.
4) The production function in an economy is Y = A(5N-0.0025N2), where A is productivity. Accordingly the marginal product of labor is MPN = 5A-0.005AN. Also, let A=2. The labor supply curve is Ns=55+10(1-t)w, where Ns is the amount of labor supplied, w is the real wage, and t is the tax rate on wage income, which equals 0.50.
Desired consumption and investment are: Cd = 300+0.8(Y-T)-200r; Id = 258.5-250r.
Taxes and government purchases are: T=20+0.5Y; G=50.
Money demand is Md/P = 0.5Y-250(r+). The expected rate of inflation is 0.02, and the nominal money supply M is 9150.
A) Find the general equilibrium levels of the real wage, employment, and output.
B) Find IS and LM. Then find the general equilibrium level of price, real rate of interest, consumption, and investment.
C) Suppose that the government purchases increase to G=72.5. What are the general equilibrium values of real wage, employment, output, real interest rate, consumption, investment, and price level?