Why can a pooling equilibrium be sustained in Spence’s signaling model but not in the Rothschild-Stiglitz screening model? Explain why in both models, the “good” type (high productivity in Spence, or low risk in Rothschild-Stiglitz) lose out in a separating equilibrium.
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Why can a pooling equilibrium be sustained in Spence’s signaling model but not in the Rothschild-Stiglitz screening model? Explain why in both models, the “good” type (high productivity in Spence, or low risk in Rothschild-Stiglitz) lose out in a separating equilibrium.
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- Education as a signal If c = $15,000 ; WH = $40, 000 and WL = $20, 000. For what value of θ is a pooling equilibrium possible?Consider the following Stackelberg model. There are two firms in the market. Firm 1 is the leader and firm 2 is the follower. Firms can decide to produce low or high. The extensive-form representation below presents the profits depending on production decisions of firms. The first value is profit of firm 1 and second value is profit of firm 2 depending on their production decisions. Solve using backward-induction. What are the optimal production levels of both firms? Describe how you found the optimal strategy using words.see the image10. Consider the following figure of the Rothschild-Stiglitz model: Sick ZPL H A ZPL L Healthy a) Is (A, B) a separating or pooling equilibrium? b) Suppose the economy has 90% low risk types and 10% high risk types. Draw the average zero profit line. c) What happens to the contract (A, B)? Explain why.
- Show how education can signal the worker’s innate ability in the labor market. What is a pooled equilibrium? What is a perfectly separating signaling equilibrium?Consider a signaling model in which the first player may be one of two types. What determines the other player’s beliefs about the first player’s type before observing the first-player’s signal? After observing the first player’s signal, what beliefs must the second player have about the first player’s type in a separating equilibrium? What beliefs must the second player have in a pooling equilibrium?Suppose that Alex wants to purchase a boat from Rosette. Alex is willing to pay up to $18,000, while Rosette is not willing to accept any offer below $15,000. Assume that there are a finite number of negotiating rounds. 1.If the discount factors for Rosette and Alex are δR = 0.05 and δA = 0.05, respectively, how much should Alex offer for the boat? 2.Suppose that Rosette’s discount factor is δR = 0.20, and Alex’s discount factor is δA =0.15. 3.How much should Alex offer for the boat? How does this offer differ from your r to part a, and why?
- Can you change the payoffs in the table to the right so that the firms choose to invest in safety? Each firm must consider how safe to make its plant. Extra safety is costly. Safety investments-sprinkler systems, color-coded switches, fire extinguishers-by one firm provide an externality to other firms: That firm's lower incidence of accidents reduces the wage that all firms in the industry must pay. Because each firm bears the full cost of its safety investments but derives only some of the benefits, the firms underinvest in safety. It will be a Nash equilibrium for both firms to invest in safety if O A. the payoffs for both firms investing increase to $750 and the payoffs for both firms not investing decrease to $50. O B. the payoffs for both firms investing go to $0. O C. the payoffs for both firms investing increase to $750. O D. the payoffs for both firms investing increase to $350 and the payoffs for both firms not investing decrease to $50. O E. the payoffs for both firms not…Economics CHOOSE THE CORRECT ANSWER. Remember that in the equilibrium prediction of an ultimatum game, the Proposer will offer the smallest non-zero amount of money possible. First-year Commerce students were asked to play an Ultimatum game where a choice had to be made over the division of R100. Offers could only be made in R10 increments, and the results of the various offers made are reported in the table below. Amount offered by Proposer RO R10 R20 R30 R40 R50 Proportion rejected 100% 60% 50% 30% 10% 0% What is the equilibrium split of the R100 between the Proposer and the Responder? O A. Proposer: R50, Responder: R50 O B. Proposer: R10, Responder: R90 O C. Proposer: R90, Responder: R10 O D. Proposer: R60, Responder: R40 O E. Proposer: R40, Responder: R60Our earlier model focused on the most basic trade-off introduced by the policy. One aspect of the policy that is also heavily debated is the fact that not every household can afford to upgrade their car in order to avoid paying the ULEZ fees. We now want to understand how best to design the scrappage scheme, which subsidises changing cars for those who need it the most. In particular, we want to know whether the scrappage scheme can create a moral hazard problem. To guide our analysis, consider the following simple model. The government would like to introduce a subsidy to help citizens who need their car for work and cannot afford to buy a ULEZ-compliant car. It also wants to ensure that only citizens who need to drive their car regularly use the subsidy. Instead of the two groups of citizens discussed above, we focus on one particular citizen who does not drive very often, only once a year. As a result, this citizen does not emit excessive pollution even with a car that is not…
- Our earlier model focused on the most basic trade-off introduced by the policy. One aspect of the policy that is also heavily debated is the fact that not every household can afford to upgrade their car in order to avoid paying the ULEZ fees. We now want to understand how best to design the scrappage scheme, which subsidises changing cars for those who need it the most. In particular, we want to know whether the scrappage scheme can create a moral hazard problem. To guide our analysis, consider the following simple model. The government would like to introduce a subsidy to help citizens who need their car for work and cannot afford to buy a ULEZ-compliant car. It also wants to ensure that only citizens who need to drive their car regularly use the subsidy. Instead of the two groups of citizens discussed above, we focus on one particular citizen who does not drive very often, only once a year. As a result, this citizen does not emit excessive pollution even with a car that is not…THE PRISONERS' DILEMMA Consider the following simple model of a cocktail party. Alice and Bob are carrying on separate conversations at the party. Alice speaks at volume a and Bob speaks at volume b. The communication benefit to Alice is al(a + b) and the benefit to Bob is b/(a + b). The vocal-strain cost to Alice is ca and the cost to Bob is cb, where c is a parameter. Suppose that the players have two choices: speaking softly at volume 1, or speaking loudly at volume 4. This leads to the following game in strategic form, with Alice choosing the row and Bob choosing the column. a = 1 a = 4 b = 1 0.5-c, 0.5-c 0.8-4c, 0.2-c 0.0400 0.0500 0.0750 0.0800 0.1500 b = 4 0.2 c, 0.8-4c - 0.54c, 0.5-4c For which of the following values of c is this game a prisoners' dilemma? (Mark all values for which this is true.)Can you change the payoffs in the table to the right so that the firms choose to invest in safety? Each firm must consider how safe to make its plant. Extra safety is costly. Safety investments-sprinkler systems, color-coded switches. fire extinguishers-by one firm provide an externality to other firms: That firm's lower incidence of accidents reduces the wage that all firms in the industry must pay. Because each firm bears the full cost of its safety investments but derives only some of the benefits, the firms underinvest in safety. It will be a Nash equilibrium for both firms invest safety if O A. the payoffs for both firms investing increase to $750 and the payoffs for both firms not investing decrease to $50. O B. the payoffs for both firms investing go to $0. OC. the payoffs for both firms investing increase to $750. O D. the payoffs for both firms investing increase to $350 and the payoffs for both firms not investing decrease to $50. O E. the payoffs for both firms not investing…