Provide solutions ,to the following this question is complete.

Question 5. [18 marks] (a) Consider a 2-player game with the following payoff matrix. Here, the row player's strategies are r1, T2, and T3 and the column player's strategies are c1, Cg, and c3. As usual, the row player's payoff is given rst and the column player's payoff is given second in each cell. [1,12] [0,1] [2, 3) r; [2,0] [1, 2] [2,1] r3 (0,1) [0,1] [1, 2] Does this game possess a pure Nash equilibrium? If so, list all pure Nash equilibria for this game. [4] (b) 'What does it mean for a 2-player game to be a zero-sum game? [3] Now, consider the following zero-sum game. The row player and the column player each simultaneously hold up 1 or 2 ngers. If the sum of the number of ngers both players hold up is even, the row player wins. If the sum is odd, the column player wins. The losing player pays the winning player an amount equal to the number of ngers the winner held up. (c) Give the payo\" matrix for this game from the perspective of the row player. [5] [d] Formulate a linear program that gives the row player's optimal mixed strategy for this game [you do not need to solve this program]. [6] Question 1: Fact I: Consider the following setup that follows the standard Solow model in Country A. There are N consumers, each endowed with one unit of available time. Consumers do not value leisure and they divide output between consumption and savings according to the following rule: a fraction s of output is saved, and the rest is consumed. There is a representative firm that has a Cobb- Douglas production technology of the form Y = zF(K,N), where K denotes capital, N denotes Labour, z is (Total Factor Productivity (TEP). Initially country A had 100 units of Capital, 144 units of labour and population growth rate was 0.01. Suppose you are given the fact that in this economy depreciation d is 0.09 and at steady state, the output per-capita could be expressed as y* = (k*15. Now, consider the unfortunate situation where a disease took several lives, reducing the number of labour force equal to 81 units. 1.1 Describe and explain changes/effect of this disease on country A's per-capita output, and per capita capital in the steady state, comparing these with the initial steady state that was prevailing before the disaster. (Note: you are supposed to describe and explain changes in detail, following Solow Model. The numbers are provided to give you more details about the economy, but you are not required to provide mathematical derivationsumbers for this question). 1.2 If you were illustrating the old and new steady state in a diagram, with per-capita capital in x-axis, describe how your graph would change before and after the disease. Would you expect the growth rate of output per worker in country A smaller or greater than it was before the disease? Question 2: Consider country B, where every citizen is identical (like clones of each other) and each individual has one unit of labour to supply. The country produces only one commodity, food. Current aggregate output of food, Y, is produced using current inputs of land, L. and current labour, N, that is Y = ZF(L,N). where z is total factor productivity (TFP). Future population is N, population grows at a rate n = 0.01, and depends on consumption per worker, c - CIN. There is no money; wage payment is provided solely in terms of foods. In equilibrium all foods produced in the economy are consumed and this is a closed economy without any government, net export or savings. Consider the Malthus model in the context of country B. Suppose the economy is currently at steady state. Now suppose considerable amount of land is destroyed due to an earthquake in country B. Describe and explain changes/effect of this incidence on steady state land per capita, and standard of living. Explain how wage would be determined in country B and how this process (of determining wage in Mathus model) is different compared to the competitive equilibrium models we studied in Chapter 4 and 5. Explain if you think wage would be higher or lower in country B after the earthquake. Question 3: Fact II. Assume the endogenous growth model (from Chapter 8) perfectly explain the growth situation in the country Econland, where a representative consumer starts the current period with H. units of human capital and does not use time for leisure. In each period, the consumer has one unit of time, which can be allocated between work and accumulating human capital. Let u denote the fraction of time devoted to working in each period. The consumer's quantity of human capital is the measure of the productivity of the consumer's time when he or she is working. For each efficiency unit of labour supplied, the consumer receives the current real wage w. The consumer cannot save, but they can trade off current consumption for future consumption by accumulating human capital. b is a parameter that captures the efficiency of the human capital accumulation technology, with b > 0. The representative firm produces output using only efficiency units of labour. The production function is given by Y- zuHe, where He is the units of labour in production. Sunnose the economy of Ecoaland was initially in a steady state with H.= Has He In the home of giving the economy a3.5 ** Consider the generalized externality problem. Assume the damage and cost functions are given by E- C(E) = E -a 2 D(E, v) = v- 2 - YEv. a. B. y> 0. (a) Determine the non-regulated level of E if the polluter has the right to pollute. (b) Determine the level of E under the polluter-pays principle. (c) Determine the efficient solution. (d) Determine the payoffs for both parties under no regulation and the polluter-pays principle for a=1, =2 and y=3. Assume now there are transaction costs of Tr=1/240. (e) Which contract will the household suggest to the polluter if the polluter has the right to pollute and the household has to pay the transaction costs? What are the final payoffs to both parties? (f) What will be different if the polluter has to bear the transaction costs? (g) Which contract would the polluter suggest to the household if the household has the right to a clean environment and polluter has to pay the transaction costs? What are the final payoffs to both parties