33 ANSWER ALL.

1 Two players: The employee (Raquel) and the employer (Vera). Raquel has to choose whether to pursue training that costs 1, 000 to herself or not. Vera has to decide whether to pay a fixed wage of 10, 000 to Raquel or share the revenues of the enterprise 50:50 with Raquel. The output is positively affected by both training and revenue sharing. Indeed, with no training and a fixed wage total output is 20, 000, while if either training or profit sharing is implemented the output rises to 22, 000. If both training and revenue sharing are implemented the output is 25, 000. 1. Construct the pay-off matrix 2. Is there any equilibrium in dominant strategies? 3. Can you find the solution of the game with Iterated Elimination of Dominated Strategies? 4. Is there any Nash equilibrium?

Firms Alpha and Beta serve the same market. They have constant average costs of 2 per unit. The firms can choose either a high price (10) or a low price (5) for their output. When both firms set a high price, total demand = 10,000 units which is split evenly between the two firms. When both set a low price, total demand is 18,000, which is again split evenly. If one firm sets a low price and the second a high price, the low priced firm sells 15,000 units, the high priced firm only 2,000 units. Analyse the pricing decisions of the two firms as a non-co-operative game. 1. In the normal from representation, construct the pay-off matrix, where the elements of each cell of the matrix are the two firms' profits. 2. Derive the equilibrium set of strategies. 3. Explain why this is an example of the prisoners' dilemma game.

Suppose that Tom and Jerry form a production team. They can choose to "Work Hard" or "Shirk" during the team production. Choosing "Work hard" incurs a cost of $5 to an individual, but can increase the final output by $8. Choosing "Shirking" incurs no cost, but does not increase the final output either. If both choose "Shirking", then the value of the total output is 0. Suppose that the working effort during production, hereby individual's contribution to the final output cannot be observed. Whatever the value of the final output is, Tom and Jerry will split it in half. a.Write down the Two-way Payoff Table of the game between Tom and Jerry. b. Is there any Dominant Strategy for Tom? How about Jerry? c.What is the Nash Equilibrium of this game? Why? d.What is the Cooperative Solution of this game? Is it easy for Tom and Jerry to achieve such an outcome? Why? e. Based on the analysis above, why do you think, under some certain circumstances, shirking is inevitable in a team-work environment? (Hint: Pay attention to the key assumption made in the question. Why do you think this assumption might hold inmany cases in reality? )

100) Larry holds a monopoly in the market for pies, with no fixcd costs and a constant marginal cost of c = 24. Moe, Curly, and Shemp are the three consumers who have the individual demand curves 41 (P) = 30 - g2(P) = 20-5 93(P) = 10- *w*v (e) (10) Suppose that Larry is a first-degree price discriminator, who charges a different price for each pie consumed. Find the quantity q' as well as the surplus to consumers CS and producers PS". How much q does each consumer buy and what surplus CS; does each receive? (f) (10) Now suppose that Larry is a second-degree price discriminator who charges different prices depending on the quantity sold, by implementing a two-part tariff T(g) = a +pq. Calculate the parameters of the profit maximizing tariff a'' and p'', and the total quantity q". How much qf' does each consumer buy, and what is the average price p' that each pays? (g) (10) Find the surplus to consumers CSl and producers PS under the two-part tariff, as well as the deadweight loss DWL", How much surplus CS;" goes to each consumer?

Assume that a baseball series lasts 5 games. Suppose a baseball pitcher strikes out an average of 2 players per game;

- Calculate the average number of players struck out by this pitcher per baseball series.

- Calculate the variance of players struck out by this pitcher per baseball series.

- What is the probability that this pitcher strikes out exactly 6 players over a series?