求助题目解答：两道高级微观经济学习题

题目1：Consider the Cournot competition model discussed in the lecture (linearinverse demand function p = α − Q, and the two firms’ cost functions are c1(q) = cq1,c2(q) = cq2). Now suppose that firm 1 instead wishes to maximize its market share,conditioning on not making a loss in its profit; and firm 2 still wishes to maximize itsprofit.(a) Please solve the Nash equilibrium of the above game.Now let us consider another game. Suppose the inverse demand function is p = 10 −(q1 + q2). Assume that producing q units of goods costs the first firm 2q units ofmoney and costs the second firm q2 units of money. That is, firms’ cost functions arec1(q) = 2q and c2(q) = q2, respectively. Both firms are profit maximizer.Suppose the two firms choose their producing units at the same time.(b) Solve the Nash equilibrium of this game.

题目2：Consider a second-price sealed-bid auction with two bidders in which eachbidder’s valuation is drawn independently from a uniform distribution U[0, 1]. Supposethat the seller imposes the reserve price r. That is, if both bids are less than r, theobject is not sold (and neither bidder makes any payment), if one bid is less than rand the other is at least r, the object is sold at the price r, and if both bids are atleast r, the object is sold at a price equal to the second highest bid.
(a) Show that for each bidder (and any value of r), a bid equal to her valuation weaklydominates all her other bids.(b) For the Nash equilibrium in which each bidder submits her valuation, find thereserve price r that maximize the expected revenue for the seller.

题目3：见图片附件