Explain why, in a first price sealed bid auction for a good with only private value, the good being auctioned is not always sold to the bidder with the highest valuation.
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- Suppose that two individuals, Jon and David, form a community and would like to construct a communal fort that would protect them from attacks. They consume both good X, a private good, and the protection from the fort, P. One unit of good X costs 1 unit while one unit of P costs 2 units, so the budget constraint for each is given by: Xi + 2Pi = 100. Both Jon and David have an income of 100 and a utility function of the form: U = log(Xi) + 2log(Pj + Pd) (a) How much protection, P, will be privately provided? What is optimal consumption of X, the private good? (b) What are the socially optimal amounts of protection, P, and consumption, X, of the private good? How do the socially optimal amounts compare to that privately provided? Explain why.Suppose that two individuals, Jon and David, form a community and would like to construct a communal fort that would protect them from attacks. They both consume good X, a private good, and the protection of the fort, P. One unit of good X costs 1 unit of currency, and one unit of P costs 2 units of currency. Both Jon and David have an income of 100 and a utility function of the form: U = log(Xi) + 2 × log(PJ + PD)The budget constraint for each is given by:Xi + 2 × Pi = 100 (a) Find the amount of protection Jon will provide as a function of how much David provides, and explain why the relationship is the way it is.Two parties, Juan and Ben, have been negotiating the purchase by Ben of Juan's car. Juan receives a new and higher bid for his car from Adriana. How might Adriana's bid change Juan and Ben's threat values? The threat values are unchanged. Juan now values the car at the price of Adriana's bid, her bid is his opportunity cost of selling the car to Ben, and that opportunity cost is Juan's new threat value. Juan's new threat value is the product of the difference between Ben and Adriana's offers and the probability the car will be sold to Adriana. Juan's threat value is unchanged, but Ben has to consider his new opportunity cost
- Are these statements true or false? Provide a detailed explanation as to how you arrived at your answer: 1. If someone has linear indifference curves between contingent commodity bundles, then they must be risk averse and the risk premium is positive. 2. If a game has a Pareto efficient outcome, there exists a Nash equilibrium that leads to this outcome. 3. If a quantity tax is imposed on a profit maximising monopolist, consumer bear a higher burden of the tax than producers.A famous local baker has approached you with a problem. She is only able to make one wedding cake each day and 5 people have requested a wedding cake on the same day. Rather than pick randomly which person she will sell the cake to, she decides to have an auction. Is this auction more representative of a private value or common value auction? Why? Which auction method(s) do you recommend the baker choose to maximize the amount of money she can make, and why?Common pool resource game) Consider a common pool resource game with two appropriators. (If you don’t know what is a common pool resource, read the Wikipedia article about the ”Tragedy of the Commons”.) Each appropriator has an endowment e > 0 that can be invested in an outside activity with marginal payoff c > 0 or into the common pool resource. Let x ∈ X ⊆ [0, e] denote the player’s investment into the common pool resource (likewise, y denotes the opponent’s investment). The return from investment into the common pool resource is x x+y · ((x + y) − (x + y) 2 ). So the symmetric payoff function is given by π(x, y) = c · (e − x) + x x+y · ((x + y) − (x + y) 2 ) if x > 0 and c · e otherwise. Assume 1 − e < c < 1. Find Nash equilibrium of the game. Proceed by deriving the best response correspondences first. How does Nash equilibrium depend on parameters c and e (varying one at a time and keeping the others fixed)?
- “While auctions are appealing in theory, the challenges of auction design in practice are insurmountable” discussBargaining power may exist for a seller if they have another buyer to whom they can sell the product.True or False?How to solve this question? Consider an antique auction where bidders have independent private values. There are two bidders, each of whom perceives that valuations are uniformly distributed between $100 and $1,000. One of the bidders is Sue, who knows her own valuation is $200. What is Sue's optimal bidding strategy in a Dutch auction?
- Under what circumstances are the auctions likely to lead to an 'efficient" price for the item being sold?If there is only one buyer and one seller meeting to exchange, then any price that they agree upon must be between the willingness to pay of the buyer and the willingness to sell of the seller.True or FalseRod's Auction House holds sealed-bid auctions for used computers every Tuesday. Each used computer is sold to the highest bidder at the second-highest bidder's bid. On average, half of the computers sold at Rod's Auction House are lemons, and half are good, used computers. A good, used computer is worth $750 to any buyer, and a lemon is worth only $200.Buyers are allowed to look over the used computers for a few minutes before they are auctioned. Almost all the buyers who attend the auction can do no better than random choice at picking good computers from among the lemons. The only exception is Al. Al can sometimes, but not always, detect a lemon by touching the tower and feeling its vibrations. The vibrations generated by a good computer's tower are always very regular and soft. On the other hand, the tower of 1/3 of the lemons emits very irregular and strong vibrations, while the tower of the remaining 2/3 of the lemons emits vibrations that are no different from those of a good…
