Economics 222, Sections A, B, C
Assignment 4

  Due Monday, 22 Nov 1999, 4pm

  1. [10 points]
    The nominal exchange rate is 10 crowns per florin, the domestic price level is 5 florins/bottle, and the foreign price level is 2 crowns/bushel.
    a) What is the real exchange rate?
    b) What is the real exchange rate in the foreign country?
    c) If the domestic price level rises to 7 florins/bottle, what must the nominal exchange rate become if the real exchange rate remains unchanged?

  2. [10 points]
    When the real exchange rate rises, what happens to net exports in the short run? In the long run? What explains the difference between the short-run effect and the long-run effect?

  3. [10 points]
    What happens to the exchange rate and net exports in each of the following cases?
    a) The foreign real interest rate rises.
    b) Foreign output falls.
    c) Foreign demand for domestic goods falls.
    d) Domestic output falls
    e) The domestic real interest rate rises.

  4. [10 points]
    a) What happens to the fundamental value of a country's exchange rate when it raises its money supply in a fixed-exchange-rate system? Does this make the currency overvalued or undervalued if, originally, the official rate equaled the fundamental value?
    b) What happens to the fundamental value of a country's exchange rate when the foreign country raises its money supply? Does this make the currency overvalued or undervalued if originally the official rate equaled the fundamental value?
    c) So, if a country wants to maintain its official rate equal to its fundamental value, what must it do when the foreign country raises its money supply? What happens to inflation?

  5. [10 points]
    Consider the following Keynesian small open economy.

    Desired consumption: Cd = 20 + 0.75Y
    Desired investment: Id = 75 - 15r
    Net exports: NX = 80 - 0.1Y - e
    Real Exchange rate: e = 15 - 0.02Y + er*( r - rfor )
    Full-employment output: Yfe = 450

    Where we use a general coefficient "er" so that we may study several values.

    a) Graph NX and Id - Sd against the real interest rate, as in Figure 11.5 of the text.
    b) Derive the IS curve for arbitrary values of G, rfor, and er.
    c) What is the slope of the IS curve if er is very large?
    d) Suppose now that er is very large, so that r = rfor. Suppose also that rfor = 0.05, G = 15, the LM curve is

    M/P = Y - 100r

    and that initially the nominal money supply, Ms, = 495. What are the values of Y, e and P? Find the short-run and long-run effects on output Y, the price level P, and the real exchange rate e of an increase in the money supply to 525.

    6. IMPORTANT: THE FOLLOWING QUESTION NEED NOT BE COMPLETED FOR ASSIGNMENT 4

  6. [10 points]
    Consider the following misperceptions model of the economy:

    AD: Y = 600 + 10*(M/P)
    SRAS: Y = Yfe + P - Pe
    Okun's Law: ( Y - Yfe) / Yfe = -2*(u - ufe)

    Let Yfe = 750, ufe = 0.05, M = 600, and Pe=40.

    a) What is the price level?
    b) Suppose there is an unanticipated increase in the nominal money supply to 800. What is the short-run equilibrium level of output, the unemployment rate, and the price level?
    c) When price expectations adjust fully, what is the price level?

ANSWERS

  1. a) enom = ePfor P implies that the real exchange rate e = 25 bushels per bottle.

    b) Foreign exchange rate = 1/e = 0.04

    c) 25*2/7 = 7.1428

  2. In the short run, net exports rise, while in the long run net exports fall. The difference is the J-curve effect, because quantities are slower to adjust than prices.

  3. a) Exchange rate falls, net exports rise.
    b) Exhange rate falls, net exports fall.
    c) Exchange rate falls, net exports fall.
    d) Exchange rate rises, net exports rise.
    e) Exchange rate rises, net exports fall.

  4. a) The fundamental value falls below the official rate. The currency will be overvalued.
    b) The fundamental value increases above the official rate, so the currency becomes undervalued.
    c) The country must raise its money supply. This leads to inflation worldwide.

  5. a) Substitute into the equation for NX, along with the expression for e, to obtain the following relation between the levels of NX and the interest rate (r):

    r = 1/er (65 - 0.08Y + er rfor - NX).

    This is a downward sloping relationship between r and NX as illustrated in fig. 11.5.

    Now, desired savings are Sd = Y - Cd - G, so that using the expression given in the question for desired investment we may write:

    Id - Sd = 95 - 15r - 0.25Y + G

    an upward sloping relationship between r and Id - Sd as illustrated in figure 11.5.

    The equilibrium interest rate and NX = Id - Sd will be determined depending on the values of Y, G, etc.

    b) The IS curve is given by the goods market equilibrium condition Y = Cd + Id + G + NX or equivalently by NX = Id - Sd.

    Clearly, given the results from a) above, this is easiest to derive using the latter of these conditions:

    NX = Id - Sd ==> 65 - 0.08Y + er rfor - er r = 95 - 15r - 0.25Y + G.

    This is the IS curve for arbitrary values of G, rfor,, and er . (This may be rearranged and simplified of course.)

    c) If er becomes very large then the exchange rate becomes very sensitive to any deviation of the domestic interest rate from the foreign interest rate. Consequently, small changes in the domestic interest rate will have large effects on the exchange rate and these large exchange rate effects will have correspondingly large effects on NX. Finally, the effect of changes in the interest rate on NX (via the exchange rate) will impact the goods market equilibrium which implies that output (aggregate demand or income, Y) will also be sensitive to the interest rate. Thus, the IS curve will tend to be flatter, the larger is er (that is, the IS curve now reflects a strong relationship from interest rates to output (Y)).

    Alternatively, of course, this result can be derived by rewriting the IS curve above and observing the implications in the equation for large values of er.

    d) Now r = rfor so that the IS-curve is no longer applicable (or, alternatively it is viewed as absolutely flat).

    Start with goods market equilibrium: Y = C d+ Id + G + NX.

    Using r = rfor = 0.05, G = 15, and the expressions for Cd, Id, NX, and e, we can solve directly for Y = 522.75.

    From this we have e = 15 - 0.02Y = 4.545, and from the LM equation with Ms = 495 we can solve for P = 495/517.75= 0.95605.

    Now, Ms increases to 525. In the short-run prices will remain fixed at P = 1.04595. Since interest rates are also fixed by the foreign rate then the LM curve uniquely determines temporary equilibrium implications for Y. That is,

    525/0.95605 = Y - 100(0.05), ==>'s Y = 554.134

    With this expansion of output and no changes in the interest rate, net exports will fall and the exchange rate will also fall:

    e = 15 - 0.02*554.134 = 3.91

    In the Long-run, output returns to the full employment level, Yfe = 450, interest rates remain fixed at the foreign rate and the money supply is assumed to be unchanging at its new higher level Ms = 525. Thus, again, the LM curve will uniquely determine equilibrium adjustment, although here, the adjustment now takes place through movements in the price level.

    525/P = 450 - 100(0.05) ==>'s P = 1.17977

    The money supply increase(s) have lead to aggregate inflation in the long-run. The lower long-run level of output also has implications for the exchange rate,

    e = 15 - 0.02*450 = 6.00.

    END