Kindly solve these questions
Collusive Monopsony. Assume that there are two teams {for simplicity, call them team 1 and team 2} that produce rugby games. Each team is a monopolyr in their product market with demand curve: Hg] = 10-11 2c; The production function for each team is given by: gm = k where k is the quantityr of labor hired by the team. The aggregate supply:r of labor is: ML] 2 20 + 2L where L 2 k1 + k2 is the total amount of labor hired by the two teams. 2. Now, assume that the two teams collude as a league. a] Find the aggregate demand in the product market for the league. {Hint Aggregate the two teams' identical product demand curves.) b} What is the equilibrium amount of labor in the market {L}? c] 1What is the new equilibrium wage? d] Ifthe teams agree to split the prots, how much labor is hired by each team {It}? and what is the profit for each team? Problem 3. (25 points) Suppose there are two teams in the NHL. Each team has a monopoly in the product market with a demand curve given by: P(q) = 20-qu where q represents the number of games and P is the price per game. The production function for goalies is given by: 9(0) =1 That is, you need one goalie for each game. The supply curve for goalies is given by: w=8+LB where L = 61 + 62 is the total number of goalies, 61(62) is the total number of goalies hired by team 1 (team 2), and w is the wage in hundreds of thousands of dollars. Therefore, the total supply of goalies is L. Answer all problems in the units given in the problem. Don't worry if the numbers are in decimals. You could think of 0.5 or 0.3 of a goalie as a goalie who doesn't play the entire season in the majors. a (5 points) What is the equilibrium number of goalies for each team? b (2 points) What is the equilibrium wage? c. (2 points) What is the surplus (profit) for each team? Now suppose teams act as monopsonist in the labor market (ie., they collude). For your reference, the aggregate demand curve for labor is: w = 20 - L d (4 points) What is the equilibrium number of goalies for each team? e (2 points) What is the equilibrium wage? f (2 points) What is the surplus (profit) for each team? g (2 points) What is the best response for team 1 if team 2 sets the collusive amount of labor?I Consider the following game between Joe, a milk farmer, \"Meyer Dairy" (M) and \"the Creamery\" (C). Joe rst chooses a price or 2 E] to charge for each gallon of milk that he supplies to M and C. (He must choose the same price for both M and C) This price in is observed by both M and 0, who then decide simultaneously how much ice cream to supply that day, (my, go 2 0. Suppose that if M and C decide to respectively supply QM, go gallons of ice cream, the price that they can charge to consumers is given by the demand curve: P=2009MQc- Now suppose that the prots of the two ice cream shops and the prots of Joe are given as follows: \"J(ma 9M, tic) = 1'\"th + tic], 1mm, (in. tic) = (200 an voles man, now, (I'M; so) = (200 an eclqc mec- This is because each ice cream shop can transform a gallon of milk into a gallon of ice cream and so M and C respectively incur costs of qu and rage for supplying QM and (10 gallons of ice cream. Moreover, Joe makes prots (without any costs of producing milk) by selling his milk to the two ice cream shops. Part a: Suppose that Joe charged a price of m per gallon of milk. What is the Nash equilibrium of the subsequent Cournot duopoly between Meyer Dairy and the Creamery? What are the prots of each ice cream shop? Your answer should he expressed in terms of m. Port b: What is the subgame perfect Nash equilibria of this game? What are the prots of J oe, M , and C in this equilibrium? (You can leave all prots as fractions) Part C: Now suppose that the Centre County government decides to impose a tax of 10 dollars per gallon of milk (but no tax on ice cream). Thus, the prots of the three players change as follows: uilmi an. tic) = (m - when + 10), \"Mirna QM. tic) = (200 ~ 9M trainer man, seen, an, tic) = (200 9M soles mec- Solve for the subgame perfect Nash equilibrium of this game. Does this tax benet any of the players in this game? How much tax revenue is generated? Part d: What happens if instead of taxing milk, Centre County government decides to impose a tax of 10 dollars per gallon of ice cream. Solve for the subgame perfect Nash equilibrium of this game. Which situation does Joe prefer between part c and part (:1? What about for Meyer Dairy? How does the tax revenue generated here compare to that generated in part c
