Explain. the following questions as attached below.

a. Equating supply to demand gives 50w - 100 = 650 - 25w which solves for w = 10 and L = 400. b. A union maximising economic rent earned by workers acts as a firm- monopolist maximising its profit. Since union faces a downward sloping demand curve its marginal revenue is twice as steep as the demand curve. Since LD = 650 - 25w , w =- 650 25 25 LD = 26 - 0.04LD. It follows that MR = 26 - 0.08L. MC is the wage that workers are willing to work for: Ls = 50w - 100 => w = 2+= = 2 +0.02L = MC. Equating MR to MC gives 26 - 0.08L = 2 + 0.02L. It solves for L = 240. From the labour demand w = 26 - 0.04 . 240 = 16.4. c. Aggregate wages of all workers hired = wL. Given that the union faces downward-sloping demand curve wl = (26 - 0.04L) . L - max. Taking the derivative with respect to L and setting it equal to 0 gives: 26 - 0.08L = 0 = L = 325 From the labour demand w = 26 - 0.04 . 325 = 13. Maximising aggregate wages of all workers hired is equivalent to maximising "total revenue", which results in MR = 0, whereas maximising economic rent in part b is equivalent to maximising "profit", thus, MR = MC. So different objectives of the union have a significant effect on the wage and number of people employed (see the graph below). 26 L' = HC 16.4 13 10 2 MR 240 325 4001. Consider a competitive exchange economy with two consumers and two goods. Suppose that consumer i has initial endowments wi = (wj, w2), where w; > 0, i = 1, 2 and j = 1, 2. His preferences are given by the following utility function: U' = aln(x;) + (1 -a) In(x2), where 0 a(s), where a(s) = e- At any t, there is a T(t) > 0 such that a(s, t) = a(s) = es for all s T(t). There is learning by doing of the form a(s, t) - So bl(v, t) du if a(s, t) > a(s) a(s, t) 0 if a(s, t) = a(s) Here a(s, t) denotes the partial derivative of a(s, t) with respect to t and b > 0. There is no storage/saving. (a) Provide motivations for assumptions of the production technology de- scribed above. (b) Define an equilibrium for this economy. Characterize (solve) the equilib rium as much as possible. (c) Consider now a two country world in which the two countries are identi- cal except in their labor endowments and their initial technology levels. In particular, 71(0) > 72(0). Define an equilibrium for this economy. (d) Illustrate and explain the five different possibilities for patterns of pro- duction and consumption in the model of part (c).Question 2 Suppose that uncovered interest parity holds all the time (both in the short run and in the long run), while the purchasing power parity holds only in the long run, because prices are sticky in the short run. Consider an economy characterized by a demand for money of the form: L(Y, R) = 3r 10R The variable Y denotes output and R is the domestic interest rate. Assume Y = 2 and R = 0.1 (Le 10%). Domestic money supply, M5, is 20. The foreign interest rate is R' = 0.05 (Le 5%). The exchange rate of domestic country [domestic currency per foreign currency) is 1} 2. (3.) Calculate the long run domestic price level P and the foreign price level P\". (b) Now suppose the domestic central bank temporarily increases its money supply to '22 for one period. What's the corresponding domestic interest rate, nominal exchange rate, and real exchange rate? Graph this change in the domestic money market and the foreign exchange. (c) Now suppose the domestic central bank permanently increases its money supply to 22. Assume that in the long run the domestic price level full adjusts so that real money demand is the same as before this increase in the money supply. What are the long-run levels of the domestic interest rate, price level, nominal exchange rate1 and expected nominal exchange rate, as well as the real exchange rate? (d) Same as in (c), the domestic central bank permanently increases its money supply to 22. Assume that in the short run prices are sticky and do not change. What are the short-run levels of the domestic interest rate, price level, nominal exchange rate, and real exchange rate? (e) Graph the time paths of money supply, price level, interest rate, nominal exchange rate, and real exchange rate for the domestic economy after the permanent increase in money supply. (f) Explain how overshooting applies to this situation