Question 3 An economy is described by the following equations: Cd =100+0.5(YT)5000r Id = 800 - 50002. T: 400 Y: 2000 G = 600 where Y is real output, r is the real interest rate, T is a lumpsum tax, Cd is desired consumption, Id is desired investment, and G is government spending. A) Derive an expression for savings as a function of the real interest rate (r), taxes (T), and government spending (G). Then find the optimal real interest rate (r) as a function of taxes (T) and government spending (G). B) Now suppose G=T=500. Calculate the equilibrium level of national savings, consumption, and the real rate of interest. Double-check your answer by calculating the level of investment. C) The government decides to reduce taxes to 400 but government spending remains fixed at 500. What is the effect on the equilibrium savings, investment, consumption and real rate of interest. Assume output is fixed. Does Ricardian Equivalence hold in this example? D) Assume this economy is now a small open economy, and the world real rate of interest is 4%. Also suppose taxes (T) are back to the same level as part b) (T=500). Find the equilibrium values of saving, investment and consumption. Did these increase or decrease? Is the current account positive or negative