PSet250AucVCG.pdf X Create account :Login 2. First Price Auction (Modified) A first edition copy of The Tragically Divine is being auctioned off. A, B and C are the only bidders for the book. A values the copy at vA = $10, B at Up = 20 while C values it at vc = 40. The three must simultaneously submit one of the following bids, $0, $10, $20, $30, $40. Let the highest bid be denoted by b. If there are m highest bidders and i is one of them then the payoff to i is Mi -b. All others get a payoff of 0. a) Is each player bidding their own valuation a Nash Equilibrium? b) Is there a Nash Equilibrium where A is the only highest bidder? If so write down the bids; if not explain why. c) State the bids of a Nash Equilibrium that results in only C winning the auction. 3. Fish and Steel 20 Firm S produces steel, s, with cost function, Cs(s, x) = s2 + (x - 4)2. Fishery F produces fish, f, with cost function cf(f, x) = f2 + xf. Both firms are price takers. In particular, steel is sold at a per unit price of Ps = 12 while the unit price of fish is pf = 10. a) If the two firms cared about maximizing their own profits how much steel and fish would be produced? What would the resulting profit levels be for the two firms. b) Suppose instead that the two firms merged and made their production choices to maximize the sum + of profits. What would be the new production and profit levels? c) Suppose now that the fishery held the right to clean waters. Firm S would have to buy the right to pollute for each unit of pollution it produced at a per unit price of Pr. For what price level Pr would the demand for units of pollution equal its supply? What would be the level of production of steel, fish and pollution in this scenario? State also the profit levels of each firm. 4. VCG Mechanism O P 9:46 AM 3/27/2023 9