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- Why it is unwise to bid less than your valuation of the good in a sealed bid second-price auction.
- In the first price sealed bid auction, a player gets a positive payoff by doing bid shading. Explain the tradeoff between biding lower than the value of the object and biding very close to value of the object.
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- QUESTION 1 Alice (A) and Bob (B) have an endowment of goods 1 and 2, with Alice's endowment being (wt, w) = (1,2) and Bob's endowment equals (wf , w) = (1,3). Alice's utility is given by u4 (xf, xf) = 2 ln xf + In æ£ , while Bob's utility is uB(xf, x}) = ln xf + 2 ln x? . Suppose that the social planner considers it to be imperative that agent B consumes exactly one uni of good 1 and four units of good 2. Although the social planner can not force the individuals to a particular consumption, they can enforce transfers of good 1 between the consumers (transfers of good 2 are not enforceable by the social planner). What transfer of good 1 would guarantee that in the resulting competitive Walrasian equilibrium consumer B consumes one unit of good 1 and four units of good 2? Answer this please Select one: O a. One half unit of good 1 has to be transferred from agent A to agent B. O b. There is no endowment for which agent B would consume x = 1 and x = 4 in the corresponding competitive…A distillery makes whisky, where its profits from production per bottle are given by T = p – y? where p is the price it charges per bottle and y is the number of years the bottle is aged. There are two types of whisky drinkers, connoisseurs (H type) and casuals (L type). H-type have utility UH (y, p) = 8y – p, while L-type have utility uz (y, p) = 2y – p. There are 10 consumers of each type, and each will buy at most one bottle. Each consumer's utility if she does not buy is 0. If a consumer is indifferent between buying two bottles, assume she will buy the more aged one (the one with higher y). If a consumer is indifferent between buying a bottle and not buying, assume she will buy. Bottles are characterised by (y, p), years of age and price. For each menu of offerings below, calculate the distillery's profit. (1, 9) and (4, 24) (1, 2) and (4, 24) (1, 2) and (2, 24) Calculate the firm's profits when it chooses the optimal menu.Janet's broad attitude to risk (risk averse, risk neutral, or risk loving) is independent of her wealth. She has initial wealth w and is offered the opportunity to buy a lottery ticket. If she buys it, her final wealth will be either w + 4 or w – 2, each equally likely. She is indifferent between buying the ticket and not buying it.
- Market research revealed that the customers can be separated into 5 groups according to their preferences over bundles of goodxs x and y. The respective empirical utility functions were constructed and they look as follows: 1. U1(x,y) = 2x+5y. 2. U2(x,y) = 100/(2x+5y). 3. U3(x,y) = 3(2x+5y)0.5 4. U4(x.y) = 7(2x+5y)². 5. U5(x,y) = -150/(2x+5y). How many different preferences were identified by the market research. O 1 O 3You have preferences u(x,y) = xy over games (X) and videos (Y) you can buy on a platform and a $360 budget, with prices px = 9 and py = 6. How much would you be willing to pay (at most) as a subscription fee for each of the following plans (you can buy any amount of Y in each plan at the original price, unless otherwise stated): (a) Plan A : You can buy (any amount of) X at a discounted price px = 4(b) Plan B : You are given 40 units of X for free, but you cannot buy any more of X. (surely can buy any amount of Y)(c) Plan C : You are given 30 units of X for free, but you cannot buy any more of X; you also have a discounted price for good Y; py = 4.Consider an agent who want to maximize her utility function, u (C₁, C₂) = C₁ C₂ subject to the budget constraint, c₁ + pc₂ = w with C₁, C₂ > 0 indicating consumption of commodity 1 and 2, respectively, while p>0 and w>0 are exogenously given parameters, indicating the relative price of good 2 and the relative wealth in term of good 1's price. Decide whether the following claims are true or false. W • The value of the Lagrange multiplier is λ = 2p False True w² • The value function u(w) is equal to u(w) = 4p True False • λ(w) measures the approximate change in utility that can be obtained from an increase/decrease in wealth w. True False
- Exercise 1.8. Consider the following "third-price" auction. There are n≥ 3 bidders. A single object is auctioned and Player / values the object $v,, with V, > 0. The bids are simultaneous and secret. The utility of Player / is: 0 if she does not win and (v-p) if she wins and pays $p. Every non-negative number is an admissible bid. Let b, denote the bid of Player i. The winner is the highest bidder. In case of ties the bidder with the lowest index among those who submitted the highest bid wins (e.g. if the highest bid is $120 and it is submitted by players 6, 12 and 15, then the winner is Player 6). The losers don't get anything and don't pay anything. The winner gets the object and pays the third highest bid, which is defined as follows. Let be the winner and fix a Player j such that b₁ = max({b,,...,b,}\ {b}) [if GAME THEORY - Giacomo Bonanno 39 max({b,...,b}\{b;}) contains more than one element, then we pick one of them]. Then the third price is defined as max({b₁,...,b}\{b,,b;}).…Consider an economy with 2 goods and 2 agents. The Örst agent has the utilityfunction, u (x1; x2) = ln x1 + 2 ln x2, and the other one has u (y1; y2) = 2 ln y1 + ln y2.The aggregate endowments of the 2 goods are given by (50; 100). Suppose there is asocial planner who cares about agents equally.(a) Set up the plannerís problem b) Calculate the first-best outcome (i.e., the social plannerís solution).Why do sellers generally prefer a Vickrey auction to a regular sealed bid if sellers don’t receive the highest bid in the Vickrey auction? Sellers only have to sell their item if the bid is the highest-price bid. The second-highest bid in a Vickrey auction is generally higher than the highest bid in a regular sealed-bid auction. The second-highest bid is about the same in both auctions. Sellers prefer the final price is not revealed to all bidders. Sellers would never prefer Vickrey auctions.
- Note: The answer should be typed.Consider a first-price sealed-bid auction of a single object with two bidders j = 1, 2. Bidder 1's valuation is v1 = 2, and bidder 2' s valuation is v2 = 5. Both v1 and v2 are known to both bidders. Bids must be in whole dollar amounts (e.g. $1). In the event of a tie, the object is awarded by a flip of a fair coin. (a) Write down this auction as a 2 x 2 matrix game. Hint: note that each bidder can choose a bid from {0, 1, 2, 3, 4, 5, ...}. Your matrix will be incomplete since you cannot write a matrix with infinite rows and columns (b) Eliminate the strictly dominated strategies. Write down the resulting matrix game. (c) An auction is efficient if the good is allocated to the bidder with the highest valuation of the good. What are the Nash equilibria of this game? Are the Nash equilibria efficient?Suppose you manage a factory with ten workers. Each worker’s output is determined by the equation q = e. Output sells in the market for a price of 40. The firm has fixed cost equal to 800, and variable costs aside from labor are 8 per unit of output. Worker utility is U = w – e2. Suppose you are paying workers a wage equal to bq. What is the profit- maximizing value of b? Suppose that the probability of worker error increases as the worker increases effort, and that worker error results in unusable output. Suppose that the probability of worker error is Pr[Error] = e/10. Then for worker effort level e, expected (usable) output is now determined by the equation E[q] = (1-Pr[Error]) x e. However, the problem is that you cannot detect errors until after the product is shipped to customers, meaning you pay workers for output before you know whether it is usable or not, and you have to refund your customers for unusable output. Demonstrate why you should not pay your workers the same…
