The Interdisciplinary Center Herzliya The Macroeconomic Environment Problem Set # 4: The IS-MP Model and short run equilibrium Submission: Wednesday, May 4" by noon. 1. Assume that: The Private consumption function is: C=50+0.6Y Y- national income (in million NIS), C- private consumption (in million NIS). The Investment function is: I=500-30r. r- real interest rate (the interest rate is measured by complete numbers, not decimals). G = 110 million NIS. A. Build the IS curve. B. Assume that the response function of the central bank is: r = 2+0.5(n - x) -50 (Y - Y) Y Full e Full = expected inflation, * = inflation target and Y = full employment output Assume that that the central bank determines the interest rate according to the function above. Assume that you =1,500 , n =2 -1 a =n' . Plug these numbers in the equation above and find the equation that defines the relation between r and Y. Notice that this is the MP curve. C. Use the IS curve and MP curve that you found above to find the equilibrium Y and r and show it in the diagram. Hint: in equilibrium the IS and MP cross each other, which means that r and Y is the same for both.2. For each one of the following changes (separately), analyze what will happen to the IS or MP curves and show what will happen to the output and the interest rate. i. The consumers are more pessimists with respect to the future. ii. A Permanent decrease in taxes. iii. An increase in government spending. iv. A Rise in investor's optimism. v. * 1 (notice that when the a f, according to the Taylor rule, for the same output level, the central bank will choose a higher real interest rate). 3. An economy is in short run equilibrium. The demand for private consumption increased and as a result there is an increase in the national product. Mainting the monetary policy according to the Taylor rule implies an increase in the interest rate and the central bank informed the proper increase. After a while it was found that the interest rate remained unchanged. What can the central bank do in order to change the interest rate as planned