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In the long run equilibrium of a perfectly competitive equilibrium, each firm must produce the quantity corresponding to the minimum point of its long run average cost curve. In an Edgeworth box model of production, if the excess demand for one individual’s labor is zero, then the excess demand for the other individual’s labor must also be zero. In a general equilibrium model, an exogenous change in the wage rate will affect the demand for labor and capital, but will not affect output prices. If A is Pareto efficient allocation, then no one can be made better off than he or she is at point A. The welfare theorems say that in a pure exchange economy, for any endowment point and any price ratio, a competitive equilibrium exists. Problems The handmade sweater industry is composed of 100 identical firms, each having short run total costs given by SRTC = 0.5q2 + 10q + 5 where q is quantity produced. What is the short run supply curve for each firm? What is the short run supply curve for the market? Suppose market demand is given by Q = 1100 – 50P. What will be the equilibrium price in this market in the short run? What will the profits of each firm be? Suppose that Juan and Pablo are stranded on a desert island. The food they brought with them to the island consists of 60 pieces of bread (B) and 30 pieces of cheese (C). There is no production on this island. Initially, Pablo has 20 pieces of bread and 20 pieces of cheese (Juan has the rest). Suppose that Juan wants to maximize his utility without leaving Pablo worse off than he was initially. Their two utility function are given by: U(Juan)=B1/3C2/3 U(Pablo)=B2/3C1/3 Set up Juan’s constrained maximization problem and explain how you set the constraint. Solve Juan’s maximization problem. How much bread and cheese would Juan assign to each of them? What utility would Pablo achieve? What utility would Juan achieve? What is the value in terms of utility to Juan of being able to lower Pablo’s utility by a very small amount? If Juan cannot directly assign the bread and cheese but must simply set a market exchange rate between the goods and allow the competitive market to work, will he be able to achieve the utility level you found in part b? 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Normal.dote I.T.A.M.te2T.Microsoft Word 8.0f@6FК@nH:‚П@fыgcЉП` ўџеЭеœ.“—+,љЎDеЭеœ.“—+,љЎL hp€ˆ˜  ЈАИ Р шфI.T.A.MЄj Practice Questions for Exam Title˜ 6> _PID_GUIDфAN{1752393A-EDE3-11D3-BE25-00A024A1A1AB}јyzm p q t  ‚ ƒ † у 0!2!p! (1111N6P6Z6\6f6h6x6z6„6†66’6Ђ6Є6Ў6А6К6М699$;&;0;2;>;@;J;L;њ@§ћћћћћљѕљљѕљѓѓѓѓѓѓѓѓѓљѓѓѓѓH*6>*6H*>*2Аа/ Ар=!А"А# $ %АPractice Questions for Exam The following as questions from various old exams. They are similar to what will be on your upcoming exam. True/False and Multiple Choice In game theory, equilibria in which one of the players uses an  incredible threat strategy are an example of non-subgame perfect Nash equilibria. Suppose a game with two players each with two pure strategies, and suppose one of the players has a strictly dominant strategy. There can be a mixed-strategy equilibrium of this game in which this player gives strictly positive probability to both of his pure strategies. First degree (perfect) price discrimination is illegal because it causes large dead weight losses (costo de bienestar) to society. A monopolist in any market will always have strictly positive (and extraordinary) profits. In the model of spatial competition in which firms set prices (with identical and constant margial costs), the equilibrium is identical to the Bertrand outcome with homogeneous products, in which price is equal to marginal cost and the firms have 0 extraordinary profits. The game of  rock, scissors, paper can be described as a game with One pure strategy Nash equilibrium. One Nash equilibrium that is not subgame perfect. Only a mixed strategy equilibrium. None of the above. In the standard Bertrand game, if one of the firms has a higher cost than the other, then the equilibrium of this game will result in: An efficient outcome because the lower cost firm will supply to the whole market, and it will charge a price equal to its marginal cost of production. An inefficient outcome because the higher cost firm will produce. An efficient outcome because the higher cost firm goes out of the market. An inefficient outcome because the lower cost firm supplies to the whole market but charges a price higher than its own marginal cost of production. When firms can take sequential actions, the Stackelberg model of quantity leadership becomes problematic because Both firms want to be followers. Both firms want to be leaders. Each firm plays its best response function, taking as given the strategy of the other firm. None of the above. Problems Consider the following version of a  Battle of the Sexes game HusbandWifeBoxing fightOperaBoxing fight3,1-1,-1Opera-1,-11,3Does this game have a Nash equilibrium in pure strategies? Is this equilibrium unique? Find a Nash equilibrium in mixed strategies. Show your work carefully. Consider the following majority voting game. There are three citizens in country K. Their names are A, B and C. There are three possible alternatives to vote for: X, Y, and Z. The alternative that gets the majority of votes wins. The payoffs of the players depend exclusively on which alternative is chosen through voting. Their payoffs are as follows: UA(X)=UB(Y)=UC(Z)=2; UA(Y)=UB(Z)=UC(X)=1; UA(Z)=UB(X)=UC(Y)=0. (You cannot draw a box diagram for this game, since there are more than 2 players.) Use the definition of Nash equilibrium to determine whether there are any Nash equilibria in pure strategies for this game. Show your work carefully. (You may find more than one Nash equilibrium). Suppose a monopolist can produce any level of output it wishes at a constant marginal=average cost of $5 per unit. Assume this monopolist sells its product in two different markets that are separated by a great distance. The demand curves in these markets are given by Q1=55-P1 and Q2=70-P2. If the monopolist can maintain perfect separation between these markets, what price will he charge in each market, and what quantity will be produce in each market? What are the monopolist s total profits? Suppose now that it costs any buyer $5 per unit to transport goods he has bought in one market and sell them in the other market. What prices would the monopolist charge now, and what would be the quantities sold in each market and the profits of the monopolist? Now suppose that it costs nothing to transport the goods from one market to the other. Can the monopolist now discriminate in prices? Why or why not? 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