Solve the following questions:
5. Consider a closed economy. Assume that nominal wages are sticky and that firms determine the level of employment in the short run. Use an AD/AS diagram to model the goods market, a labor demand/supply diagram to model the labor market, and the loanable funds diagram to model the financial market. Assume that aggregate consumption depends on current and expected future disposable income as well as on the real interest rate. Speculate what would happen in the current time period to equilibrium output, prices, real interest rates, savings (and consumption) and investment expenditures, real wages and employment as a result of: a. (5 points) Money supply increases. b. (5 points) A temporary increase in productivity that results in a substantial increase in output but does not change the marginal products of labor or capital. 6. Consider an open economy. Assume that all prices are flexible and there is complete information. Assume that aggregate consumption depends on current and expected future disposable income as well as on the real interest rate. Speculate on what would happen to the real exchange rate, the nominal exchange rate, net exports, the domestic real interest rate. domestic output, domestic investment, domestic nominal and real wages, and employment if: a. (5 points) The US men's soccer team wins the World Cup and delirious fans take off from work for the month of August to celebrate the team's victory. b. (5 points) Permanent increase in productivity increases marginal products of inputs as well as increasing output for the same level of inputs. 7. Consider an open economy. Assume that nominal wages are sticky and that firms determine the level of employment in the short run. Speculate on what would happen to the real exchange rate, the nominal exchange rate, net exports, the domestic real interest rate, domestic output, and domestic investment, domestic nominal and real wages, and labor if: a. (5 points) A tax cut is enacted but there is no change in government spending. Assume that people do realize that current government deficits imply increases in future taxes. Furthermore, household consumption (and saving) depends on current and future disposable income. b. (5 points) Tariffs on imported goods rises. Assume other taxes fall so that total tax revenue is unchanged.5. Convolution is associative (as we proved), so [(5 a: C) a: C = gab a: (C a: C). This convolution is a function that you know. The point of this problem is to nd out what it is by using one side of the equality and to give a second justication by using the other side. (a). (12 points.) Use a result in the notes to identify d: a: C as a familiar function (you can cite the result by the number in the notes), and, with that in hand, identify (d: 1: if) 1: C as a familiar function. Replace this with your answer. (I1). (6 points.) Identify C x: C; as a familiar function. Replace this with your answer. (c). (12points.) (i) Use parts (a) and (b) to deduce an equality that relates three familiar number-theoretic functions. (ii) Prove this equality a second way by citing a desirable property that both sides have, checking the identity at integers of a special form, and deducing the result in general from that. Replace this with your answer to (i). Replace this with your answer to (ii). 2) Consider the following demand and supply functions: Qi =24-4P, demand Q;=-6+2E, _, P, supply and expectations generator E, P, = P._ a) Calculate the long run price and quantity in this market. Justify your answer. b) Is this system a stable or unstable Cobweb model? Justify your answer. c) Beginning at P, =4 and Q, =8, calculate three years of prices and quantities in this market. Suppose instead that the demand and supply functions are: Q: =24-2P, demand Q;=-6+4E,_P, supply d) Repeat questions a) through c) where in c) part you begin with P, =4 and Of =16
