Two firms compete for hiring workers in the labour market. The equilibrium wage is w = alpha + beta(H1 + H2), where alpha, beta; > 0 are parameters, and Hi is the number of workers hired by firm i = 1; 2. Firm i's profit is (y - w) Hi, where y is the output per worker. Assume y > alpha . Firm i chooses Hi to maximize its profit. Do the following: (a) Consider the two firms decide on Hi simultaneously. Derive the Nash equilibrium. (b) Consider the two firms make decisions sequentially. Firm 1 gets to hire first, followed by firm 2. Derive the subgame perfect equilibrium
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Two firms compete for hiring workers in the labour market.
The equilibrium wage is w = alpha + beta(H1 + H2), where alpha, beta; > 0 are parameters,
and Hi is the number of workers hired by firm i = 1; 2. Firm i's profit is
(y - w) Hi, where y is the output per worker. Assume y > alpha . Firm i chooses
Hi to maximize its profit. Do the following: (a) Consider the two firms decide
on Hi simultaneously. Derive the Nash equilibrium. (b) Consider the two
firms make decisions sequentially. Firm 1 gets to hire first, followed by firm
2. Derive the subgame perfect equilibrium
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- Suppose that Zamboni Enterprises is the only company that sells zambonis (ice resurfacing machines). To produce the machines, the company hires assembly workers. Since these workers can work in many different companies, Zamboni Enterprises must pay them the market wage, which is equal to $6. The number of zambonis that the company produces, which is denoted by y, is proportional to the number of assembly workers that it hires, which are denoted by N; in particular, the production function is given by y=0.76N. The economywide demand for zambonis is given by the following demand function: y=2191-219p, where y is the number of zambonis that consumers are willing to purchase at price p. Given this market structure, how many assembly workers will Zamboni Enterprises choose to hire? How many zambonis will Zamboni Enterprises produce and sell?Suppose that Zamboni Enterprises is the only company that sells zambonis (ice resurfacing machines). To produce the machines, the company hires assembly workers. Since these workers can work in many different companies, Zamboni Enterprises must pay them the market wage, which is equal to $6. The number of zambonis that the company produces, which is denoted by y, is proportional to the number of assembly workers that it hires, which are denoted by N; in particular, the production function is given by y=0.76N. The economywide demand for zambonis is given by the following demand function: y=2191-219p, where y is the number of zambonis that consumers are willing to purchase at price p. Given this market structure, how many assembly workers will Zamboni Enterprises choose to hire? How many zambonis will Zamboni Enterprises produce and sell? What will be the price of a zamboni? If the market for zambonis were competitive, how many zambonis would be produced? If the market for…Suppose that Zamboni Enterprises is the only company that sells zambonis (ice resurfacing machines). To produce the machines, the company hires assembly workers. Since these workers can work in many different companies, Zamboni Enterprises must pay them the market wage, which is equal to $6. The number of zambonis that the company produces, which is denoted by y, is proportional to the number of assembly workers that it hires, which are denoted by N; in particular, the production function is given by y=0.76N. The economywide demand for zambonis is given by the following demand function: y=2191-219p, where y is the number of zambonis that consumers are willing to purchase at price p. If the market for zambonis were competitive, how many zambonis would be produced? If the market for zambonis were competitive, how many assembly workers would be hired? If the market for zambonis were competitive, at what price would zambonis be sold?
- Suppose that the production function of a salmon farming firm is given by F(L) = 4*root(L) and it faces a price for its product of P = 200. Moreover, the firm acts as a monopsony in the labour market - located in a small town in the south - and the supply curve is w(L) = 3 + L. We ask: (a) Determine the output and level of hiring. (b) How many workers should this firm hire from the point of view of the social optimum?Suppose that in a competitive output market, firms hire labor from a competitive labor market (so that the profit maximization conditions for hiring labor are as we discussed in class). If a profit-maximizing firm in this market gets an improvement in technology that increases the marginal product of labor for any given unit of labor it employs, and if the market wage stays constant, we would expect the firm to Group of answer choices a) offer a lower wage and hire fewer units of labor. b) hire more units of labor. c) do none of the other options. d) keep the number of units of labor the same. e) hire fewer units of labor (i.e., workers) because it could produce more than before with fewer people.Consider the market for labor where both firms and workers are price takers. Output is produced using capital and labor.The marginal product of labor can be described by: 200 – 4L, where L is the number of workers hired. The price of the good produced is 5 per unit. a. Illustrate the demand for labor. Be sure to note the specific value of the vertical intercept. b. Suppose that the competitive firm must pay 100 for each worker. Determine the number of workers hired. (Determine the total income to capital. Show your work for both parts. c. Suppose that the price of the good rises but that the wage remains the same. Illustrate how the optimal choice of labor would change. No need to do the explicit calculation; just show the outcome and briefly explain.
- Suppose that in a competitive output market, firms hire labor from a competitive labor market (so that the profit maximization conditions for hiring labor are as we discussed in class). The firm has a fixed number of machines and can produce the following quantities (Q) associated with the number of workers (L) in a given time period. L Q 0 0 1 12 2 20 3 26 4 30 5 32 The market price of the good this firm sells is $5. If the firm pays a wage of w = $19.90 per time period, then how many units of labor should this firm hire to maximize profit? Group of answer choices a) 1 b) 3 c) 4 d) 2 e) 5Suppose that in a competitive output market, firms hire labor from a competitive labor market. The firm has a fixed number of machines and can produce the following quantities (Q) associated with the number of workers (L) in a given hour. L: 0, 1, 2, 3, 4, 5 Q: 0, 14, 26, 36, 44, 50 The market price of the good this firm sells is $2.50. If the firm pays a wage of W=$19.00 per hour, then how many units of labor should this firm hire to maximize profit? Show your work. a) 1 b) 2 c) 3 d) 4 e) 5Four (TYPE I) firms sell Product X in competitive markets at a price of 10. They each operate with the production function: x = 100L – L². Another firm with monopoly power (TYPE II) sells faces demand curve P = 160 – Y and has production function Y = 5L. All five firms hire as wage-takers in the same market where labour supply is w = 2L. Illustrate and quantify the equilibrium wage and the number of workers hired by each firm. а. Solve for the equilibrium wage and employment by each firm. b. Provide a 3-panel diagram. 6.
- A firm's short run revenue function is given by R = 8e – 4 e^2, and its profit function is given by N = R – w, where "e" is the level of effort provided by a worker and "w" is the wage rate of the worker. Suppose that the worker's problem is to choose the level of e to maximize his benefit function B = 2w – 1.5e. Compute the levels of effort and profit for the following wage arrangement: a) W = 0.4 R; b) W = R – 10; c) Why these different schemes generate different outcomes?A firm's production function is Q = 5 + 25L - .5L2 + 30K – K2, and its demand function is PQ MRQ = d = $30. The prices of L and K are PL = $6 and PK = $12. Use Excel Solver to find the profit-maximizing and cost minimizing amounts of L and K to employ. The profit- maximizing and cost minimizing amount of L is: A. L = 16. %3| L = 25. C. L = 38. D. L = 42. B.Goleta Brewing Company hires only two types of labor, managers and brewing assistants (denoted M and B, respectively). GBC has the following Cobb-Douglas production function F(M,B) = M.5 B.5 and wants to produce 10 barrels of pale ale this week. If the wage of managers is $50 per hour and the wage of brewing assistants is $10 per hour, how many managers and brewing assistants should the firm hire (round to nearest whole number)? How does your answer change when the wage of managers decreases to $30 per hour and the wage of brewing assistants remains constant. Is this result consistent with your intuition?