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(5) Suppose that a firm has Cobb-Douglas production technology f(L, K) = ALKB, where (L.K) E R? are the factor inputs, and A > 0, a > 0, and 3 > 0 are constants. Recall that a production function exhibits constant returns to scale if f(AL, AK) = Af(L, K) for any > > 1. It has decreasing returns if f(AL, AK) Af( L, K). (a) For what values of o and 3 does f (L, K) have constant or decreasing returns? (b) Show that f ( L, K ) is concave if it has constant or decreasing returns to scale. (c) Show that f( L, K) is quasiconcave regardless of its returns to scale. (Hint: any monotonic transformation of a concave function is quasiconcave.)Exercise 10.1 Explain carefully why a central bank does not operate to make a profit but a com- mercial bank does. What is the central bank's operating objective? What unique power does a central bank have that allows it to pursue its operating objective? Exercise 10.2 Explain carefully why a central bank's power to conduct monetary policy is based on its unique position as supplier of the monetary base. Exercise 10.3 Why would a change in the monetary base AMB cause a change in the money supply? (a) Suppose a central bank buys $10 million on the open market. What effect does this have on the monetary base and the reserve position of the commercial banks? (b) If the banks hold reserves equal to 2.5 percent of their deposit liabilities, and the public holds a constant amount of cash, calculate the effect of this open-market transaction on: i. The money supply. ii. The banks' reserve balances. Exercise 10.4 Suppose the central bank decides to use its power to set interest rates. Use a money market diagram to show and explain what happens to the real money supply if real output increases (AY > 0) and the central bank maintains a constant interest rate. Exercise 10.5 In terms of a monetary policy rule (a) What is the Bank of Canada's monetary policy target? (b) What monetary policy instrument does the Bank use to pursue this target? (c) What do the Bank's procedures for implementing policy mean for its control over money supply? Exercise 10.6 Use a diagram to show circumstances in the market for overnight funds that might lead the Bank of Canada to make an SRA. Why would the Bank use an SRA in this case rather than an open market operation? Exercise 10.7 Suppose a central bank decides to conduct monetary policy according to a rule for interest rates. (a) How does it choose the basic setting for the interest rate within the rule? 268 Central banking and monetary policy (b) How would it respond to a rise in the output gap (Y - Yp)? (c) How would the bank react to an inflation rate higher than its target inflation rate? (d) Why would the bank decide to change the basic setting of its interest rate?Exercise 11.1 Use a diagram to illustrate an economy at the equilibrium inflation rate. In this diagram, show how a permanent increase in exports would affect the equilibrium inflation rate and the equilibrium level of GDP if the central bank did not react and change its monetary policy. Exercise 11.2 Suppose the central bank reacted to defend its inflation target from the effect of the increase in exports in Exercise 11.1. Use an ADx/ASa diagram to show the change in the equilibrium interest rate setting and real GDP you would observe. Exercise 11.3 Suppose opportunities for investing in high tech applications boost aggregate de- mand in the short run, and aggregate supply in the long run. Using ASa and ADa curves with equilibrium at potential output, show why output might rise in the long run without much of an increase in inflation. Exercise 11.4 Suppose a new round of labour negotiations results in a higher average rate of increase in money wage rates for the next three years. Illustrate and explain how this would affect short-run aggregate supply conditions and the ASa curve. Exercise 11.5 Draw an aggregate supply and demand curve diagram to show an economy in short- run equilibrium at potential output. Suppose a wide-spread recession reduces incomes in foreign countries, leading to reduced demand for exports. Illustrate and explain how this would affect the short-run equilibrium Y' and it in your diagram. Exercise 11.6 Suppose central banks have reduced their policy interest rates to the lower bound to fight a deep and prolonged recession. Use a diagram to show how either a reduction in the inflation rate, or deflation, would change the slope of the ADI curve. Would cuts in nominal money wage rates and further reductions in the inflation rate reduce the recessionary gap when the central bank is constrained by the lower bound on its interest rate? Exercise 11.7 In the two years before 2008 the Canadian federal government reduced the GST from 7 percent to 5 percent. Use an ADA/ASa/Y'p diagram to illustrate and explain the effects of this tax change on equilibrium output and inflation. If the economy was in equilibrium at Y'p and the target inflation rate at* before the tax cut, what monetary policy action, if any, would the central bank make to maintain those equilibrium conditions after the tax cut? What short-run net benefit, if any, would households and businesses realize as a result of the cut in the GST? Exercise 11.8 Define the 'public debt' and explain why and how it might increase from one year to the next. 302 _ Inflation, real GDP, monetary policy & fiscal policy Exercise 11.9 Would it be possible for the ratio of the public debt to GDP (PD/Y) to fall even if the government's primary budget is in deficit? Explain your answer. Exercise 11.10 Would it be possible for the ratio of public debt to GDP (PD/Y ) to rise even if the government's primary budget balance is in surplus? Explain your answer. Exercise 11.11 Optional: Suppose the central bank's monetary policy sets the interest rate accord- ing to the function: i= 3.0 +2.0(x - x") with a* =4.0, and aggregate expenditure is the sum of: C = 200+0.75Y 1 = 85 - 21 G = 100 X - IM = 50-0.15Y - 3i (a) What is the equation for the ADx curve? (b) Plot the ADa curve in a diagram, not necessarily to scale, that shows the horizontal intercept and slope of the curve
