Question 12 Macroeconomics
12. Suppose GDP Y is determined by aggregate demand Y = C + /+ G. Consumption is given by the Keynesian consumption function C = Co + c(Y - T), where Y - T is disposable income, c is the marginal propensity to consume (0 0). Investment is / = /, - br, where r is the real interest rate, b is the sensitivity of investment to the interest rate (b > 0), and /o is autonomous investment expenditure (10 > 0). Assume initially that government expenditure G and tax revenue T are fixed at exogenous levels G = Go and T = To. Assume the central bank uses monetary policy to set the interest rate r at some fixed level. (a) [4 marks] Derive the demand-determined level of GDP Y in terms of Co. lo. Go. To, r, and b and c. (b) [2 marks] Suppose there is a decline in either autonomous investment / or autonomous consumption Co. Explain why GDP Y declines by more than the change in autonomous expenditure and give the economic intuition. Suppose there is a debate among economists on whether recessions are caused by declines in firms' confidence (affecting /o), or consumer confidence (affecting Co), or a mixture of both. The debate focuses on the household saving rate, de- fined as s = (Y - T - C)/(Y - T), which is observed to rise in recessions. (c) [2 marks] Assuming that autonomous investment /o declines without any change in Co. what is the effect on the household saving rate s as GDP falls? (d) [2 marks] Assuming that autonomous consumption Co declines without any change in /o, what is the effect on s? (e) [2 marks] What conclusions about the sources of recessions can you draw from your results given the observed behaviour of s? To reduce the severity of recessions, the government decides to adjust its expen- diture or the amount of tax it collects in response to changes in GDP. It is consid ering either G = Go - aY or T = To + aY, where a is a positive coefficient (in the case T = To + aY, the sensitivity of tax revenue to income arises naturally if tax rates were fixed). (f) [3 marks] Show mathematically that both of these policies are automatic sta- bilizers: they reduce the fall in GDP after a negative shock to Co or /p. (g) [2 marks] For the same value of a, which type of automatic stabilizer is most effective? Provide intuition for your answer. (h) [2 marks] Again for the same value of a, is the more effective policy in part (g) the one that raises the government's budget deficit D = G - T by more in a recession? (i) [1 mark] Suppose the government must run a balanced budget and sets G = Go + aY and T = Go + aY. Is a positive value of a still an automatic stabilizer
