Question 1 A closed economy is described by the following equations: Cct = 50 + 0.5(1 7)}! 1000r I\" = 350 1000: MN? = 10 + 0.5Y 20000 + x") where l" is real output, .P is the price level, r is the real interest rate, 11'" is inflation expectation, T is a lump-sum tax, C d is desired consumption, I d is desired investment, and M is the nominal supply of money which is set by the central bank. Derive an algebraic expression for the IS and LM curves with the real interest rate on the left hand side. e1 Derive two algebraic expressions for the AD curve. One with real output {Y} on the left hand side and one with the price level {P}. 0) Assume expected inflation, as", is 2%, nominal money supply, M, is 500, full employment output, Y, is 704, government spending, G, is 200 and the tax rate, r is 50%. Use your results from parts a] and b}, to find the price level, P, and the real interest rate, J". D) Now suppose business owners' confidence weakened. In other words, business owners are not optimitic about the future of the economy. This change in beliefs by business owners is represented by this new desired investment equation: I\" = 300 IOOOr (Note: The onii-r difference is a reduction of the cons rent by 50}. Find real output, 1'53 , and the real interest reai, r 53 , in the Keynesian short-run equilibrium. E) Find the values of parts c} and d} if the tax rate was zero [I = 0'}. F) Automatic stablizers are policies that are put in place to oset economic fluctuations without the direct intervention of the government. For exampleI during a recession people lose their jobs and they can use employment insurance {El}. El is therefore an automatic stabilizer. Unemployed people get some income and keep the Canadian demand higher than without El. Note that El was in place be'iore the recession {that's the automatic part). 0n the other hand, the Canada Emergency Response Benefit iCERB) is a policy that was put by the government right after the COVID crisis started. It is a stabilizer. as it helped to maintain demand, however, it is not an automatic stabilizer because it was put in place aftennrards. Do you think the tax rate is an automatic stabilizer? Explain using your answers from parts cl) and e). {Hint Look at the change in output with and without taxation. J G) The Central Bank is aware of this lack of optimism in the economy, via the Business Outlook Survey, and fear it will lead to a recession. They decide to act to keep output at its lull employment level, Y. i. Find the new level of nominal money supply [M] for the case in which 1 = 0.5. ii. Using a graph of the lS-LM-FE framework, show and explain the transition from the initial equilibrium [part c} to the short-run equilibrium (part d), and the return to the long run equilibrium [part 9) i.}. Make sure to label your axes and curves and indicate clearly the shift of the curves