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Debt as a means of mitigating the common-pool problem. (Chari and Cole, 1993.) Consider the same setup as in Problem 12.15. Suppose, however, that there is an initial level of debt, D. The government budget constraint is therefore
(a) How does an increase in D affect the Nash equilibrium level of G?
(b) Explain intuitively why your results in part (a) and in Problem 12.15 suggest that in a two-period model in which the representatives choose D after the first-period value of G is determined, the representatives would choose D > 0.
(c) Do you think that in a two-period model where the representatives choose D before the first-period value of G is determined, the representatives would choose D > 0? Explain intuitively.
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- Part 3: Environmental Regulation & Economic Incentives Consider the following two variations of the payoff matrix for the environmental “game" shown in Figure 11-7 (and projected in class on Friday, November 13); note that each number in the cell represents total net domestic welfare for each country. VERSION 1: Regulate Foreign Don't regulate 70 50 Regulate 70 70 Home 70 50 Don't regulate 50 50 VERSION 2: Regulate Foreign Don't regulate 80 100 Regulate 80 Home 50 70 Don't regulate 100 70 50The town of Grayling has 10 thousand residents who produce fish from fish farms and lakes. Each person who works on a fish farm produces 2 fish per day. Each person who fishes in a lake produces 10-X fish per day where X is the number of people (in thousands) who fish in the lakes. If every individual who fishes a lake is charged a tax of T fish, what value of T causes the Nash Equilibrium behavior to produce the largest possible number of fish for the town as a whole? (You can assume that the 'taxes' collected are shared among all of the residents)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 image
- Alice and Bob negotiate over a deal which generates a surplus of 10 (payoffs in thousands of dollars). They negotiate as in the standard Rubinstein Stahl bargaining model from Chapter 11- Alice offers x, € [0,10] representing her share of the surplus, Bob accepts or rejects, if Bob rejects then the roles reverse and Bob offers x2 € [0,10], and so on – with a twist: There is no time discount. Instead, the size of the surplus remains the same (so, offers are always from 0 to 10), but for every rejection, both players' payoffs are reduced by 1 to pay for lawyer fees. (Ex: if there are two rejections and then an acceptance of an offer of x3 = 5, then the payoffs are 3 and 3). a. Solve the SPNE for the ultimatum game (T=1). Bob accepts any offer x, s 10. Alice sets x, = 10. b. Describe the SPNE outcome (does agreement occur, when, who offers, what is the offer) for T=3. c. Describe the SPNE outcome for T=4.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.)Two cigarette manufacturers repeatedly play the following simultaneous-move billboard advertising game. If both advertise, each earns profits of $0 million. If neither advertises, each earns profits of $10 million. If one advertises and the other does not, the firm that advertises earns $20 million and the other firm loses $1 million. If there is a 10 percent chance that the government will ban cigarette sales in any given year, can the firms “collude” by agreeing not to advertise?
- Determine the optimal strategy for the situation by representing it as a game and finding the saddle point. State your final answer in the terms of the original question.A Republican and a Democratic candidate are running for office in a heavily Republican county. A recent newspaper poll comparing their views on taxes and welfare reform showed that when compared on taxes or on welfare reform, the Republican leads by 20%. When comparing the Democrat on welfare reform to the Republican on taxes, the Republican leads by 35%. But when comparing the Democrat on taxes to the Republican on welfare reform, the Republican leads by only 15%. Use this information to decide what each candidate should discuss at their next debate. (Let T represent taxes and W represent welfare reform.) Democrat T W Republican T W % % % % =H6. Consider the GSP auction used by Google for selling its advertising slots. Suppose there are two slots and three bidders. The clicks received by slots 1 and 2 are 500 and 300, respectively. The three bidders 1,2, and 3 have values 10, 8, and 5 respectively for a click. As usual, we consider Symmetric Nash Equilibria (SNE). In particular, you need to focus on the SNE equilibrium bids that are optimal for Google. Write down the corresponding SNE bid submitted by bidder 2. Use the decimal representation, not the fraction.The US and Canada have overfished North Atlantic cod stocks nearly to the point of extinction. Both countries wish to preserve the cod industry (and hence the cod stocks), so the two countries sign an agreement to limit fish hauls. Each country has two possible strategies: comply with the agreement (limit fishing) or renege on the agreement (overfish). Each country’s payoffs for different strategy combinations are given in the matrix below. The numbers in the cells represent utilities, and the payoff ordering is (US, Canada). QUESTIONS: 1.If this is a one-shot game (i.e., it is played once), do the players have a dominant strategy? If so, what is it? Briefly explain your answer. 2.What is the equilibrium of this game? Is it Pareto-optimal? How do you know?
- Q1. (a) Prove that competitive equilibria are always Pareto efficient. (b) Consider two-persons, two-goods exchange economy. Person A has an endowment of (1, 0) and preferences UA = C₁AC₂A. Person B has an endowment of (1, 2) and preferences UB=Min [2C₁³ 3C₂³]. Using an Edgeworth Box draw their offer curves. Find competitive equilibrium prices and quantities.A pharmaceutical company advertises to consumers that their drug HeartONE helps lower the chance of heart attacks, but does not advertise that the drug also helps to lower the chance of kidney disease. Under this asymmetric information, it is clear that relative to the efficient equilibrium, the market is supplying too many HeartONE drugs, because some units of the drug are sold that are valued less than costs supplying too few HeartONE drugs, because some units of the drug are not sold that are valued more than costs O demanding too many HeartONE drugs, because some units of the drug are sold that are valued less than costs. demanding too few HeartONE drugs, because some units of the drug are not sold that are valued more than costs.Lawmakers must decide on government budget fast: will they prioritize increasing budget for the Department of Health given the COVID-19 epidemic or Department of Education to support the online needs of teachers and students. They must decide and obtain a majority agreement among themselves. A) Dilemma arising from Obligation B Multi-person Dilemma Dilemma arising from Prohibition Epistemic Dilemma E) Single Agent Dilemma F) World Imposed Dilemma G) Self-imposed Dilemma H) Ontological Dilemma