1. This question examines the effect of a reduction in the effective tax rate on capital. Assume that prices adjust slowly. [Note: This question should be answered in considerable detail.]

a. Using a diagram with MPK^f and the tax-adjusted user cost of capital, illustrate how a reduction in the effective tax rate on capital changes the level of desired capital stock. [5 points]
b. Explain how changes in the level of desired capital stock impact desired investment. (Hint: use relationship on p. 129) [5 points]
c. Using the investment and savings diagram, illustrate the changes in the goods market equilibrium. [3 points] Derive the new IS curve. [3 points]
d. If prices adjust slowly, illustrate the short-run equilibrium in the IS-LM-FE framework. [5 points]
e. Why is the equilibrium in (d) not sustainable in the long run? [5 points]
f. In the long run, prices will change. Demonstrate how prices change by drawing the asset market. [3 points] Derive the new LM curve. [3 points]
g. Examine the final IS-LM-FE equilibrium. How did the general equilibrium values of the real wage, employment, output, the real interest rate, consumption, investment, and the price level change? [7 points]
 

2. Define monetary neutrality. Show that, after prices adjust completely, money is neutral in the IS-LM model. What are the classical and Keynesian views about whether money is neutral in the short run? In the long run? (A complete answer should include detailed diagrams showing both the asset market equilibrium and the general equilibrium conditions.) [20 points]

3. Money demand in an economy in which no interest is paid on money is

        {M^d / P} = 750 + 0.4Y - 800i

a. You know that P = 80, Y = 900, and i = 0.08. Find real money demand, nominal money demand, and velocity. [3 points]
b. The price level doubles from P = 80 to P = 160. Find real money demand, nominal money demand, and velocity. [3 points]
c. Starting from the values of the variables given in part (a) and assuming that the money demand function as written holds, determine how velocity is affected by an increase in real income. [3 points] By an increase in the nominal interest rate. [3 points] By an increase in the price level. [3 points]

4. Consider a closed economy described by the following equations:

    C^d = 400 + 0.8(Y-T) - 100r
    I^d = 200 - 300r
    G = T = 400
    Y^f = 3500                                   (full-employment level of output)
    Expected Inflation = 0.05
    L = 0.5Y - 200i                         (money demand function)
    M = 1730                                   (nominal money supply)

a. Derive the IS curve and the LM curve. Graph both of these curves. [6 points]
b. Find the equilibrium values of the real interest rate, the nominal inte rest rate, and the price level. What is the level of savings in this economy? [5 points]
c. Suppose that the government doubles expenditures and doubles taxes (G=T =800). Find the new equilibrium values of the real interest rate, the nominal interest rate, and the price level. Will this economy be saving more or less than it was? [5 points]

5. The nominal exchange rate is 15 crowns per florin, the domestic price level is 6 florins/bottle, and the foreign price level is 2 crowns/bushel.

a. What is the real exchange rate? [3 points]
b. What is the real exchange rate in the foreign country? [3 points]
c. If the domestic price level rises to 8 florins/bottle, what must the nominal exchange rate become if the real exchange rate remains unchanged? [4 points]

Q1, Q2. The answers to these questions are largely graphical, but follow closely the discussion in the text. See Chapter 10 in general, and Figures 10.2 and 10.3 in particular, for the discussion of how IS shifts due to changes in the goods mar ket. For a discussion of monetary neutrality, consult pp. 341-42 and the explanation presented in Fig. 10.9.

Q3. For the given equation, M^d / P = 750 + 0.4Y - 800i,

a) Real money demand = 1046 ; Nominal money demand = 80* 1046 = 83680 ; Velocity = PY / M^d = 0.86

b) If price doubles to 160, real money demand (M / P) is unchanged. Nominal money demand is now 160*1046 = 167360. Since neither real income nor real money demand have changed, velocity is constant.

c) If real income rises, so does velocity (try Y=1000 in the above equation). If the nominal interest rate rises, so does velocity (try i = 0.1 above). If the price level changes (as in part b), there is no effect on velocity.

Q4.

a) First, find IS, where Y = C^d + I^d + G = 400 + 0.8 (Y - 400) - 100r + 200 - 300r + 400. Solving for Y (but solving for r would work as well), we get

Y = 3400 - 2000r

To find LS, use (M/P) = 0.5Y - 200i = 0.5Y -200(r + exp. Infl.) = 0.5Y - 200 (r + 0.05). Solving again for Y, we get

Y = 3460/P +400r + 20, with P unknown.

b) In a general equilibrium, it must be that Y =Y^fe . Thus, in IS, set Y = 3500 and solve for r = -0.05, the real interest rate. The nominal interest rate is (r + exp. Infl.) = 0 . The price level is then P = M / 0.5*Y^fe = 0.989 .

c) When the government increases taxes and spending proportionately, the IS curve shifts outwards. By substituting the new T and G into the IS derivation, IS becomes:

Y = 3800 - 2000r

LM doesn't change, since the asset market is not directly affected. Again, set Y=Y^fe for an equilibrium, and use the IS to find the real interest rate, r = 0.15. The nominal rate is 0.15 +0.05 =0.2. Then in LM (with Y=Y^fe), P = M /(0.5*Y^fe - 200*(0.15+0.05)) = 1.012 is the new price level.

Recall National Savings (S) in a closed economy are S = Y - C - G. With T = G = 400, S = 3500 - 2880 - 400 = 220. Now S = 3500 - 2560 - 800 = 140. So savings have gone down.

Q5. For all questions use e = e_nom* (P/P_for)

a) e = [15 crowns / 1 florin ]*[6 florins / 1 bottle]*[1 bushel / 2 crowns] = 45 bushels / 1 bottle

b) Now home becomes foreign, and vice versa. Then for the other country, e = 1 bottle / 45 bushels.

c) 45 bushels / 1 bottle = e_nom * [8 florins / 1 bottle] * [1 bushel / 2 crowns]

e_nom = 11.25 crowns / 1 florin