Question

Assume M = 4000, P = 2.0, πᵉ = 0.01, and Y = 5000. Mᵈ/P=1500+0.2Y-10,000(r+π⁶)

Note: we are holding P and Y constant in this problem until we get to case #2 below.

A) What is the market clearing real interest rate?

B) Please illustrate your results on a real money supply, real money demand diagram and label this initial equilibrium point as point A. Be sure to label your graph completely! Be sure to put relevant shift variables in parentheses next to the appropriate function.

C) Suppose Janet Yellen and the Fed were successful in their campaign to decrease inflationary expectations to 0.5% (.005). Why would they want to do this? Use the Fisher equation to support your argument.

D) Solve for the real interest rate that clears the money market given the change in inflationary expectations. Please show work and Label this new point as point B on your diagram above.

E) Explain how this strategy of decreasing inflationary expectations is supposed to pull back on the economy. Recall that output is equal to C + I + G! Be very specific. Hint: The price of current consumption in terms of future consumption and the user cost of capital most definitely need to be in your response.

Answer 1

The market-clearing real interest rate is initially -5%. Decreasing inflationary expectations to 0.5% leads to a new real interest rate of -4.5%, which encourages spending and investment. This strategy is designed to stimulate economic activity by reducing the real cost of holding money and the user cost of capital.

Step-by-step explanation:

We have to determine the market-clearing real interest rate given that M = 4000, P = 2.0, πᵢ = 0.01, and Y = 5000, and the real money demand function is given by Mᵤ/P = 1500 + 0.2Y - 10,000(r + π⁶).

A) To find the market-clearing interest rate, we equate real money supply (M/P) to real money demand (Mᵤ/P).

M/P = Mᵤ/P
2000 = 1500 + 0.2 × 5000 - 10,000(r + 0.01)
2000 = 1500 + 1000 - 10,000r - 100
500 = -10,000r
r = -0.05

So, the market-clearing real interest rate is -5%. This negative rate reflects the expectation of inflation (0.01 or 1%) in this scenario.

B) On a real money supply and demand diagram, the real money supply line is vertical (independent of the interest rate) and the real money demand line slopes downward. Point A indicates the initial equilibrium where these two lines intersect at the interest rate of -5%.

C) Janet Yellen and the Fed would want to decrease inflationary expectations to 0.5% (or π⁶ = 0.005) because, according to the Fisher equation, the real interest rate equals the nominal interest rate minus the inflation rate. Lowering inflationary expectations could cause the nominal interest rate to decline, potentially stimulating investment and consumption.

D) With the new inflationary expectations (πᵢ = 0.005), we substitute in the money demand equation.

2000 = 1500 + 0.2 × 5000 - 10,000(r + 0.005)
2000 = 1500 + 1000 - 10,000r - 50
450 = -10,000r
r = -0.045

The new real interest rate that clears the money market is -4.5%. This rate would be labeled as point B on our diagram.

E) The strategy of decreasing inflationary expectations pulls back on the economy by increasing the real cost of holding money, which encourages spending and investment over saving. Decreased inflation expectations can lower the price of current consumption in terms of future consumption, thus stimulating immediate demand. Simultaneously, it may reduce the user cost of capital, motivating businesses to invest more in capital, potentially leading to an increase in aggregate demand (C + I + G), and thereby stimulating the economy.