hi please help me with this qn thank you

14. Suppose GDP Y is determined by aggregate demand Y = C + 1+ G. Consumption is given by the Keynesian consumption function G = Co + C(Y T). where Y T is disposable income, c is the marginal propensity to consume (0 0). Investment is l = in br. where r is the real interest rate, b is the sensitivity of investment to the interest rate (b } D), and in is autonomous investment expenditure (in 5 0). Assume initially that government expenditure G and tax revenue T are xed at exogenous levels G = Go and T = To. Assume the central bank uses monetary policy to set the interest rate r at some xed level. (a) [4 marks] Derive the demand-determined level of GDP Y in terms of Co. in, Go. To, r, and b and c. (b) [2 marks] Suppose there is a decline in either autonomous investment in or autonomous consumption Cu. 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 deciines in rms' condence (affecting lg), or consumer condence (affecting Cu), or a mixture of both. The debate focuses on the household saving rate, de- ned as s = (Y T C)/(Y T), which is observed to rise in recessions. (c) [2 marks] Assuming that autonomous investment in declines without any change in CD, what is the effect on the household saving rate 5 as GDP falls? (d) [2 marks] Assuming that autonomous consumption Cu declines without any change in in, 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