Economics 222, Sections A, B, C
Assignment 3

  Due Friday, 5 Nov 1999, 4pm

     
  1. [10 points]
    (a) What is the relationship of fixed investment and the real interest rate to each other over the business cycle?
    (b) If firms maximize profits what can you say about the cyclical behaviour of the marginal product of capital, assuming that the price of capital goods does not change over the business cycle?

  2. [10 points] For each of the economic changes, determine the effects in the short run on the real interest rate and output. Then analyze the long run (general equilibrium) effects on the real wage, output, the real interest rate, consumption, investment and the price level.
    (a) An increase in consumer optimism that increases the desired consumption at each level of income and the interest rate.
    (b) As the financial crisis in Asia blows over, the volatility in the Canadian stock market is reduced.
    (c) An influx of working-age immigrants increases the labour supply.
    (d) Innovation increases the expected marginal product of capital.

  3. [10 points] Suppose the Bank of Canada's short-run response to any change in the economy is to change the money supply to maintain the existing real interest rate. What would happen to the money supply if there were a reduction in government purchases?

    Given the Bank's policy, what would happen in the very short run (before general equilibrium is restored) to output and the real interest rate? What must happen to the LM curve and the price level to restore general equilibrium?

  4. [15 points] A closed economy is described by the following relationships:

    Cd = 100 + 3/4 (Y - T) Desired Consumption
    Id = 0.1Y - 1,500r Desired Investment
    T = (1/3)Y Taxes (government revenue)
    G = 170 Government Spending
    M/P = Y - 10,000r Real money demand
    M = 250 Nominal money supply

    (a) Let P=2. Derive the IS and LM equations and show that the short-run equilibrium is characterized by r=4% and Y=525. What is the budget surplus or deficit?

    (b) Suppose the long run (full employment) output level is Yfe=800, describe (qualitatively or otherwise) how the economy can attain its long-run equilibrium without policy intervention. What happens to prices, wages and interest rates along the transition?

    (c) How can monetary policy be used to reach the full-employment output? How can fiscal policy be used to reach full-employment output?

    (d) If you were responsible for Economic Planning in this country, would you use fiscal or monetary policy to move the economy to its full-employment level of output? Why?

    IMPORTANT: The following question need not be done for Assignment #3.

  5. [15 points] Consider the following closed Keynesian economy.

    Desired consumption and investment are given by:

      Cd = 200 + 0.8(Y-T) - 500r
      Id = 200 - 500r

    Taxes and government expenditure are given by:

      T= 20 + 0.25Y
      G = 196

    The real money demand is:

      Md/P = 0.5Y - 250(r+pie)

    The money supply M = 9890 and the expected inflation pie = 0.10.

    (a) Derive the equations for the IS and LM curves and show them on a graph.
    (b) If the full-employment output is Yfe = 1000, what are the equilibrium values of r, P, C and I?
    (c) Suppose there is a surprise increase in M to 12,650, what will be the short run equilibrium values of Y, r, C and I? What will happen in the long-run? [Hint: Prices are sticky in the short run, since Keynesian].

ANSWERS

    1. Fixed investment is procyclical while the real interest rate is acyclical. Thus, fixed investment and the real interest rate does not have a relationship over the business cycle.

    2. Profit-mazimization by firms lead to

      MPK = (r+d) pK

      Since the price of capital goods is assumed not to change over the business cycle, MPK is acyclical since its behaviour over the business cycle depends on the beahviour of the real interest rate.

      However, if one contends that capital is "fixed" to some degree, its behaviour will exhibit certain cyclical tendencies. For example, if more labour is employed in a "boom", the MPK could rise (given fixed K) and so MPK could be seen to vary procyclically.

    1. Desired saving curve shifts to the left (to Sd1). This causes the IS curve to shift to the right (to IS1). In the short run (point F), r increases and Y increases. In the long run, the LM curve must shift to the left (to LM1) to intersect with the FE and the new IS curve. Hence, P and r rises, Y goes back to full-employment level. At the new general equilibrium (point G), C has increased, I has fallen and real wage, w, is unchanged.

      2.  

    2. The decline in the volatility of stocks causes the real money demand to decline. This causes the LM curve to shift to the right. In the short run, this increases r and Y. But in the long run, prices increase until the LM curve shifts back to its origial position. In the long run equilibrium, the real variables in the economy (r, w, Y, C, and I) are unchanged relative to the general equilibrium before the change. Only P is higher.

      3.  

    3. The increase in labour supply causes the FE line to shift to the right. In the long run, prices fall so that the LM curve shift to the right to intersect with the new FE line and the IS curve. In the new general equilibrium, R, w and P have fallen while Y, C and I have increased.

    4. The increase in MPKf causes desired investment to rise. The Id curve shifts up and to the right which causes the IS curve to shift to the right. In the short run (intersection of the new IS curve and the LM curve), r and Y increase. In the long run, prices must increase so that the LM curve shifts to the left to intersect the Fe line and the new IS curve. At the new general equilibrium, r, I and P have increased, Y and w are unchanged while C has fallen.

  3. When G falls, desired national saving rises. Thus, the Sd curve shifts to the right. This causes the IS curve to shift to the left (to IS1). To maintain interest rate, the Bank of Canada has to reduce money stock so that the LM shifts to the left (to LM1) so that it intersects with the new IS curve at the old interest rate.

    In the short run (point F), Y falls and the real interest rate is unchanged. In the long run, to restore general equilibrium (point G), prices will have to fall so that the LM curve shifts to the right (to LM2) until it intersects with the FE line and the new IS curve. So, prices have fallen by more than if the money supply had not changed, real interest rate has fallen, and output is back at the full-employment level.

    4.

    1. P=2

      The IS curve is given by equilibrium in the goods market:

      Sd = Y - Cd - G = 0.5Y - 270.

      Id = Sd implies 0.1Y - 1500r = 0.5Y - 270

      Hence,

      r = 9/50 - 13750Y

      is the equation for the IS curve.

      [Alternatively, you could use the AS=AD method : Y = Cd + Id + G . This gives the same equation for the IS curve as found using Id = Sd above.]

      The LM curve is found by equating real money supply with real money demand:

      M/P = 125 = Y - 10000r = Md/P

      Hence,

      r = 1/10000 Y - 1/80

      is the equation for the LM curve.

      The short run equilibrium is given by the intersection of the IS and LM curves. Equating r given by each of IS and LM, we get

      Y = 525 ; r = 0.04 = 4%

      The budget surplus is T - G = 5.

    2. Full employment output is 800, which is greater than the short run output. To get to long run equilibrium, prices have to fall so that the LM curve shifts to the right until it intersects the IS curve at Y = 800. In the general equilibrium, P and r have fallen while Y has risen. As well, C and I increase while the real wage, w, falls.

    3. Using monetary policy, the central bank can increase the money supply so that P does not fall by as much (or not at all). Using fiscal policy, the government can increase G and shift the IS curve to the right until it intersects the old LM curve at Y = 800 (again, so that P does not have to fall).

    4. Suppose that the objective of the policies is to maintain the price level. With monetary policy, the new general equilibrium involves a lower r and a higher I. With the fiscal policy, r increases and I falls. The increase in G crowds out private investment.

      One argument in favour of using monetary over fiscal policy to move the economy to full-employment output is that monetary policy favours investment, while fiscal policy does not (via the effect on r). Investment is important in determining a country's long run productive capacity.

      That being said, the question gives little indication as to why the economy has found itself at its original point. Determining this reason is important in choosing the best policy. For example, if IS shifted back due to a fall in consumer confidence, fiscal policy could be favoured. Note also that in restoring the economy to full employment by increasing the money supply, policy makers are implicitly choosing a NEGATIVE real interest rate. Because of the effects this might have on the asset market (ie. it raises the demand for money to extremely high levels), using monetary policy could be an unwise policy choice in the context of this economy.

    END