Assignment:
1. Say that real money demand, which is Md / P, is 1000 + .6Y - 100i.
a. Do income, prices, and nominal interest rates have the same positive or negative impact on real money demand that we described in class? That is, if income, etc. increases, does real money demand increase or decrease as we described?
b. If Y was 100 and i = .05, what would the real demand for money be?
c. Given the values in b, what would the nominal demand for money be if P = 100?
d. Given the above description for the demand for money, if income rose, what would happen to the demand for non-money assets?
e. Is this form of money demand consistent with money demand in the Quantity Theory that we did in class and in previous homeworks? Why or why not?
2. Say that the face value on a one-year maturity Treasury Bill is $1,000 and its interest rate was 2%.
a. What would its price be?
b. Now, say that its interest rate rises to 4%. Consider the face value and price of this bond - how many of these two things would change and what would be the new value or values?
3. Consider this part of the Quantity Theory: M V = P Y. Say that V is fixed, that Y is at full employment, and that M is controlled by this country's central bank.
a. What does the above equation now describe?
4. Let's start this question with no currency in the economy, the reserve to deposit ratio ("res") is fixed at .1, and banks have $100 billion on deposit at the Fed.
a. Say that the Fed wished to increase M1 by $10 billion. What would they do to achieve this goal?
b. Now let's add currency to the economy; say that the public holds $50 billion and banks hold $20 billion. All other values are as there were in the previous question. Finally, assume that the currency to deposit ratio ("cu") is .2. Now, say that the Fed wished to increase M1 by the same $10 billion as above. What would it do in this case?
5. Say that Cd = 300 - 300r + .2Y, I = 500 - 500r and G = 40.
a. Find the equation for the IS curve. That is, the combination of r and Y where the goods market is in equilibrium. To be a bit more specific, you'll need an equation of the form r = ... and this equation includes the concept of equilibrium in the goods market (i.e. S = I or Y = C + I + G).
b. What would happen to the IS curve if G increased from the above value of 40 to 60? That is, what happens to the equation for the IS curve and how is the curve placed compared to the previous question?
6. Now, consider the money market. The Fed has set the nominal money supply to 15,000 and the price level is 3. Next, real money demand is 5000 + .7Y - 10,000i and πe = .02.
a. Find the LM curve. That is, find an equation for r = ... when the money market is in equilibrium. Hint: be careful about the distinction between real and nominal interest rates.
b. What happens to the LM equation and curve if the nominal money supply increases by 10% from its initial value of 15,000?
7. Now, consider the IS and LM curves generated in the last two questions (specifically, from 5a and 6a).
a. What values of r and Y solve both the IS and LM curve? That is, what combination of r and Y put both the money market and goods market in equilibrium?
b. Please graph the IS and LM curves as well as your answer.
c. Starting from the initial equilibrium (from 7a), what would be the new values of r and Y if G rose from the initial 40 to 60?
d. Please graph the new IS and LM curves as well as your answer.
e. Starting again from the initial equilibrium (from 7a), what would happen to r and Y if the money supply rose by 10%?
f. Please graph the new IS and LM curves as well as your answer.