IS-ML.

(32 points) This problem asks you to analyze the IS-LM model algebraically, so please provide steps for your calculation. Suppose consumption is a. linear function of disposable income: C(YT)=a+b(YT), where a > 0 and D 0 and d > 0. The parameter d! measures the sensitivity of investment to the interest rate, and the parameter c is a constant sometimes called autonomous investment. a. (4 points) Solve for 1' as a function of r, the exogenous variables 0' and T, and model's parameters a, b , c, and d. b. (4 points) How does the slope of the IS curve depend on the parameter d , the interest sensitivity of investment? Refer to your answer to part (a). c. (4 points) Which will cause a bigger horizontal shill: in the IS curve , a. 8100 tax cut or a. 3100 increase in government spending? Refer to your answer to part (a). Now suppose demand for real money balanc- is a linear function of income and the interest rate L(r,Y) = eY fr, where e > 0 and f > D. The parameter s measures the sensitivity of money demand to income , while the parameter f measures the sensitivity of money demand to the interest rate. d. (4 points) Solve for r as a function of Y, M , and P and the parameters 2 and f. e. (4 points) Using your answer to part (d), determine whether the LM curve is steeper for large or small values of F. f. (4 points) Use your answers to parts (a) and (d) to derive an expression for the aggregate demand curve. Your expression should show Y as a function of P, erogenous policy variables M, G, and T, and the model's parameters. This expremion should not contain 1'. g. (4 points) Use your answer to part (f) to prove that the aggregate demand curve has a negative slope. h. (4 points) Use your answer to part (f) to prove that increases in GandM and decrease inT shift the aggregate demand curve to the right. How does this result change if the parameter 1", the inter-at intensity of money demand, equals zero