1. Consider a two-player game where player A chooses Up or Down and player B chooses Left, Center, or Right. Their payoffs are as follows: When player A chooses Up and player B chooses Left player A gets $5 while player B gets $5. When player A chooses Up and player B chooses Cenrer they get $6 and $1 correspondingly, while when player A chooses Up and player B chooses Right player A loses $2 while player B gets $4. Moreover, when player A chooses Down and player B chooses Left they get $6 and $1, while when player A chooses Down and player B chooses \"Center they both get $1. Finally, when player A chooses Down and player B chooses Right player A loses $1 and player B gets $2. Assume that the players decide simultaneously (or, in general, when one makes his decision doesn't know what the other player has chosen). a) b) c) d) Solve for the pure strategy Nash Equilibrium using normal form. Suppose player A chooses up with probability p and down with probability (/-p) and player B chooses lefi with probability and right with probability (/-g). Determine player A's best response to any choice of g by player B, and player B's best response to any choice of p by player A. What happened to Center? Find the mixed strategy Nash equilibrium. Show these best Response functions and all the possible equilibria on a graph. Now suppose that player B moves first, and Player A moves second. Show the game information in extensive form. What is the Nash equilibrium in this case? 2. Suppose Cheese (C') and Watches (W) in Switzerland are produced using only labor and the production functions are: =10/L, W =al, Lcand Ly represent labor devoted to the production of cheese and watches, respectively, and a>0is a constant. Suppose labor supply in the country is fixed at L = 400, and the utility function of the representative Swiss consumer is U(C,W ) = +/CW . Note that this utility function implies that the marginal utility of a Swiss consumer from one extra unit of watch consumption is higher if she has more cheese to consume, which is a natural assumption about Swiss preferences for Cheese and Watches. This study source was downloaded by 100000783486959 from CourseHero.com on (a-z(]-!()Z 07:43:10 GMT -05:00 hl:pA:ffwww.c:)urwhcm,c()m/hlciI8235'?383\"1%I-H%%&wm'ad Msallem (msallem.ahmed@gmail.com) a) b) c) d) Suppose o = 1. That is, one unit of labor can produce one watch. Derive and draw the Swiss production possibility frontier for watch and cheese production. If we now make no assumption about the value of . Suppose Switzerland didn't sell or buy any Cheese or Watches to other countries. What would be the equilibrium price ratio and equilibrium quantities of Cheese and Watches in the Swiss domestic market? [Note: Your answers will depend on o, which you should treat as an unknown for now. Of course, the solution will require finding the point of tangency between the PPF and the highest feasible indifference curve.| How do the equilibrium quantities change when o increases? How does the price ratio change? Notice that you can interpret o as a productivity parameter: when a rises, watchmakers get more watches with the same amount of L,.. In light of this interpretation of , explain the intuition behind your mathematical results. Assume now that Switzerland can trade with other countries specifically, France. Suppose the French price ratio is Pc /Pw = 1. Atthe French price ratio, how much would Swiss consumers want to consume and how much would Swiss producers want to produce of each good? Find consumption bundle (C,, W) and production bundle (Cp,, W,). In your solution assume o > 1/4. Can you find the values of a whereby Switzerland will want to export Cheese to France? How about Watches? 3. Suppose Amy and Bailey are consumers in a pure exchange economy, with two goods, tonkas and zeenas (this will be used as the numeraire and will be normalized to 1). Amy has 9 units of tonkas and lunit of zeenas. Bailey has 3 units of tonkas and 8 units of zeenas. Amy and Bailey have identical preferences given by the utility function Us(x.) = (x'4)"(x*0)** for Amy and Us(xs) = (x'5)**(x*s)'" for A= a) b) d) Amy and ;8 = Bailey. Suppose the price of zeenas, p2, is normalized to 1. In a perfectly competitive market, solve for the equilibrium price of tonkas, p; and the optimal allocation of consumption for both consumers Amy and Bailey. Calculate the utility for Amy and Bailey at the initial endowment allocation and the optimal allocation of consumption. Are Amy and Bailey made better off at the optimal allocation of consumption? Show in the Edgeworth box the initial allocation of endowment W, the optimal allocation of consumption M, the price line, and Amy and Bailey's indifference curves which go through the optimal allocation of consumption. State Walras law and use your findings above to verify it