the marginal cost is not zero here.) The reaction function of Firm 2 would be . If the firms were operating at the Cournot equilibrium point, industry output would be each firm would produce , and the market price would be . (d) For the Cournot case, draw the two reaction curves and indicate the equilibrium point on the graph. (e) If the two firms decided to collude, industry output would be and the market price would equal . (f) Suppose both of the colludjng firms are producing equal amounts of output. If one of the colluding firms assumes that the other firm would not react to a change in industry output, what would happen to a firm's own profits if it increased its output by one unit? (g) Suppose one rm acts as a Stackleberg leader and the other firm behaves as a follower. The maximization problem for the leader can be written as . Solving this problem results in the leader producing an output of and the follower producing . This implies an industry output of and price of 6. Consider a small exchange economy with two consumers, Astrid and Birger, and two commodities, herring and cheese. Astrid's initial endowment is 4 units of herring and 1 unit of cheese. Birger's initial endowment has no herring and 7 units of cheese. Astrid's utility function is U(HA, C A) = H AC A Birger is a more inexible person. His utility function is U(HB,CB) = min{HB,CB} . (Here HA and CA are the amounts of herring and cheese for Astrid, and HB and CB are amounts of herring and cheese for Birger.) (a) Draw an Edgeworth box, showing the initial allocation and sketching in a few indifference curves. Measure Astrid's consumption from the lower left and Birger's from the upper right. In your Edgeword'l box, draw two different indifference curves for each person, using blue ink for Astrid's and red ink for Birger's. (1)) Use black ink to show the locus of Pareto optimal allocations. (Hint: Since Birger is kinky, calculus won't help much here. But notice that because of the rigidity of the proportions in which he demands the two goods, it would be inefficient to give Birger a positive amount of either good if he had less than that amount of the other good. What does that tell you about where the Pareto efficient locus has to be?) (c) Let cheese be the numeraire (with price 1) and let p denote the price of herring. Write an expression for the amount of herring that Birger will demand at these prices. (Hint: Since Birger initially owns 7 units of cheese and no herring and since cheese is the numeraire, the value of his initial endowment is 7. If the price of herring is p, how many units of herring will he choose to maximize his utility subject to his budget constraint?) ((1) Where the price of cheese is 1 and p is the price of herring, what is the value of Astrid's initial endowment? How much herring will Astrid demand at price p
