Watson, 25.2. You may use a = , so the agent's utility is U₁ = p√√w+b+ (1 - p)√w - 1 if they exert effort. For which values of p will the principal optimally write a contract that tries to encourage high effort?
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- Rachel's objective is to maximize the expected profit, subject to that Emma works for Rachel and Emma puts effort. However, effort level is not observable. Hence, Rachel needs to write a contract based on the observables. Let's say, Rachel pays Emma based on the outcome: when the profit is $0, 2 when the profit is $2000, and zu when the profit is $3,000. Then Emma has three options: (i) Not to work for Rachel (ii) Work for Rachel without effort (iii) Work for Rachel with effort Find Emma's expected utility on each option.9. There are four agents who are trying to decide whether they will buy a publicly shared TV, of which the total cost is $200. The valuations of the TV are $30 for agent 1, S35 for agent 2, $70 for agent 3, and $70 for agent 4. Let c; be how much agent i will pay if the TV is purchased. Suppose c = 20, c2 = C3 = C4 = 60. According to Groves and Clarke mechanism, which one could not be the pivotal agent? A. agent 1 B. agent 2 C. agent 3 D. agent 4b)Rachel’s objective is to maximize the expected profit, subject to that Emma works for Racheland Emma puts effort. However, effort level is not observable. Hence, Rachel needs to writea contract based on the observables. Let’s say, Rachel pays Emma based on the outcome: xLwhen the profit is $0, xM when the profit is $2000, and xH when the profit is $3,000. ThenEmma has three options:(i) Not to work for Rachel(ii) Work for Rachel without effort(iii) Work for Rachel with effortFind Emma’s expected utility on each optionc)ssuming Rachel wants Emma to put effort, her objective essentially becomes to find thelowest contingent payment scheme that is just enough for Emma to work for Rachel, andgives an incentive for Emma to put effort. Formally, we can write this as:min 0.1xL + 0.3xM + 0.6xH ,subject to0.1√xL + 0.3√xM + 0.6√xH − 5 ≥ 15, (1)and0.1√xL + 0.3√xM + 0.6√xH − 5 ≥ 0.6√xL + 0.3√xM + 0.1√xH . (2)What is Constraint (1) called? What is Constraint (2) called?d) or your information, the…
- 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 ut (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.Zac has a current wealth of £400. He gets an email offering him the chance to enter a prize draw that gives £500 prize with a 25% chance and £0 the rest of the time. Zac is an expected utility maximiser with a von Neumann-Morgenstern utility in wealth w of u (w) = Vw. What is the minimum price at which Zac will sell his rights to enter the draw? £106.25 £506.25 O E31.25 £22.5 £56.25Suppose that the expected value of weekly profits for an ice cream shop, before paying the manager, Amy, is where e is Amy's weekly avertime hours. Amy is risk-neutral but incurs a cost for working overtime. Thus, tatal expected surplus is What level of effort maximizes total surplus? The value of overtime that maximizes total surplus is e-hours. (Enter your response rounded to one decimal place.) E(x)=500+10c C(e)=² E(S)-[(x)-C(e).
- Assume, in producing one unit of a good X, an agent can exert either the good effort (G) or the bad effort (L), which cause production defects with probability 0.25 or 0.75 respectively. His utility function in effort e and wage w is U(w, e) = 100 (10/w) c(e) where c(G) = 2 for the good effort and c(L) = () for the bad effort. Production defects are contractible and so can be included in the agent's contract, but effort is not contractible. Good X sells for $20 if there are no defects and $0 otherwise. The principal is risk-neutral and likes profit. Assume the agent has a reservation utility/outside option of U=0. If effort is not contractible then:: Select one: O a. There is insufficient information to know the principal's choice of contract because we do not know the agent's level of absolute risk aversion. O b. the principal will be indifferent between writing a contract to achieve the good effort level and writing a contract to achieve the bad effort level O c. the principal will…What is disadvantages correspondence analysis?When a famous painting becomes available for sale, it is often known which museum or collector will be the likely winner. Yet, the auctioneer actively woos representatives of other museums that have no chance of winning to attend anyway. Suppose a piece of art has recently become available for sale and will be auctioned off to the highest bidder, with the winner paying an amount equal to the second highest bid. Assume that most collectors know that Valerie places a value of $15,000 on the art piece and that she values this art piece more than any other collector. Suppose that if no one else shows up, Valerie simply bids $15,000/2=$7,500 and wins the piece of art. The expected price paid by Valerie, with no other bidders present, is $________.. Suppose the owner of the artwork manages to recruit another bidder, Antonio, to the auction. Antonio is known to value the art piece at $12,000. The expected price paid by Valerie, given the presence of the second bidder Antonio, is $_______. .
- Suppose that 20 risk neutral competitors participate in a rent seeking game with a fixed prize of $500. Each player may invest as much money as he wishes in the political contest. The probability of winning is directly proportional to the candidate's share of the total rent-seeking investment. 1. What is the expected net benefit of a player if all other players invest $20 each? Write the net benefit as a function of the player's investment. 2. Solve the maximization problem to arrive at the profit-maximizing investment. Round to the nearest cent.Two workers independently choose how much effort to put in their jobs. If worker 1 chooses e₁ ≥ 0 and worker 2 chooses e2 ≥ 0, their payoffs are given by u₁(e₁,e2,01,02) = 0₁e₁ + ße₁e₂ · - 1/² u₁ (e₁,e₂,0₁,0₂) = 0₂ €₂ + ßе₁e₂. = ²2 where 0 <ß < 1 and 0 ≤ 0; ≤ 1 for i: = 1,2. Assume that 0; is player i's private information: each player knows her own 0 and believes that the other player's 0 is drawn from the uniform distribution over [0, 1]. Find the Bayesian Nash equilibria of this game.When a famous painting becomes available for sale, it is often known which museum or collector will be the likely winner. Yet, the auctioneer actively woos representatives of other museums that have no chance of winning to attend anyway. Suppose a piece of art has recently become available for sale and will be auctioned off to the highest bidder, with the winner paying an amount equal to the second highest bid. Assume that most collectors know that Yakov places a value of $35,000 on the art piece and that he values this art piece more than any other collector. Suppose that if no one else shows up, Yakov simply bids $35,0002=$17,500 $35,000 2 = $17,500 and wins the piece of art. The expected price paid by Yakov, with no other bidders present, is. Suppose the owner of the artwork manages to recruit another bidder, Bob, to the auction. Bob is known to value the art piece at $28,000. The expected price paid by Yakov, given the presence of the second bidder Bob, is.