Problem #1 Competitive Equilibrium Find the competitive equilibrium if types are not observable for the following labor market. Types: 0, = 3, 0, = 6, 0, = 9 Lottery: p(0 = 0,) = 1/3 , p(0 = 0,) = 1/3 , p(0 = 0,) = 1/3 Reservation wages: r(0,) = 3, r(0,) = 9, r(0,) = 6 3, e, = 6, 0, = 9 %3D 2. %3D %3D %3D %3D
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- V4. Suppose that you have the following information about the market for employees in your buisness: Supply: W=20+N Demand: W=40-N a. Suppose that the union negotiates a team size of only 5 employees. Draw this graphically and calculate the new equilibrium wage number of employees. b. Draw this graphically and calculate the equilibrium wage and number of employees hired.Ian works at an iron smelter in Pittsburgh, the center of iron production in America. Due to the difficulty in measuring the productivity of individual employees, Ian's employer as well as the other iron smelters all pay an efficiency wage. Adjust the wage line on the graph to reflect this situation. What characteristic of efficiency-wage jobs is not supported by the situation shown in the graph? Efficiency wage jobs result in a surplus of workers at the wage being offered. Elevated wages serve as an economic incentive to work harder. The wage rate will eventually return to the market-clearing level. Efficiency wages result in an increase in the rate of unemployment. Wage ($ per hour) Quantity of workers (in thousands) Wage SConsider 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.
- (3) Consider a production of a good, X. The market for X is competitive and thus there are many firms producing X. The production of X requires only labour inputs. Moreover, the marginal product of labour for X is constant. However, there are exactly two kinds of workers in the population. One kind has a constant marginal product worth $20 and the other kind has a constant marginal product worth $15. The labour market is competitive and there are equal numbers of workers of each kind in the population. (a) Suppose that the price of X is $1 per unit. The equilibrium wage rate for high- productivity workers is $ workers is $ and the equilibrium wage rate for low-productivity (b) Consider the case of information asymmetry: each firm cannot directly tell the difference between the two kinds of workers. Even after it has hired them, it won't be able to monitor their work closely enough to determine which workers are of which type. In this case, one wage rate will be offered to both kinds of…Question Two A coal-mining company is the only employer in town, and faces this supply curve for labor: W = 48 + ( 72/2000 )L where w is the daily wage, in dollars, and L is the number of workers employed. The company faces this demand curve for coal: P = 60 − ( 9/ 4000 )Q where p is the price of coal, per ton, and Q is the number of tons sold per day. Coalminers produce 8 tons of coal each, per day, regardless of the number hired. The mining company maximizes profit. a) How many workers will be hired, and how much profit will be made? b) Suppose a union is formed, which sets a wage of $120 per day. At this wage, according to the supply curve given above, 2000 miners are willing to work, and the company is free to hire as many of these as it wants. How many will be hired, and how much profit will be made?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 choosesHi to maximize its profit. Do the following: (a) Consider the two firms decideon Hi simultaneously. Derive the Nash equilibrium. (b) Consider the twofirms make decisions sequentially. Firm 1 gets to hire first, followed by firm2. Derive the subgame perfect equilibrium
- Student Enterprises sells two sizes of wall posters, a large 3- by 4-foot poster and a smaller 2- by 3-foot poster. The profit earned from the sale of each large poster is $3; each smaller poster earns $2. The firm, although profitable, is not large; it consists of one art student, Jan Meising, at the University of Kentucky. Because of her classroom schedule, Jan has the following weekly constraints: (1) up to three large posters can be sold, (2) up to five smaller posters can be sold, and (3) up to 10 hours can be spent on posters during the week, with each large poster requiring 2 hours of work and each smaller one taking 1 hour. With the semester almost over, Jan plans on taking a 3-month summer vacation to England and doesn’t want to leave any unfinished posters behind. Find the integer solution that will maximize her profit.Four (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 manufacturer of toys is employing 50 workers and using 15 pieces of equipment to assemble toys. Currently, the marginal product of labor is 5 $ and the marginal product of capital is 25 S. Assume the market prices for labor and capital are $12 and $20, respectively Is this firm maximizing its profit? A)Yes B)No What should this firm do with respect to its employees and its use of equipment? The firm should (1)_ the number of employees and (2)_its use of equipment. (1) A)Maintain B)Reduce C) Increase (2) A)Maintain B)Reduce C)Increase
- (c) Let us now turn to the labor market for grocery store workers in Little town. Recently one of the last two grocery stores in Little town closed leaving only one employer for grocery store workers in this area. This labor market is not very competitive. What type of market structure is this? (d) Draw a typical supply curve (i.e. average expenditure), marginal expenditure, and demand for the grocery store in Little Town. Label the equilibrium wage and number of grocery store workers. (e) Suppose that some time has passed and the population has grown in Little Town and there are now many grocery stores. Now suppose that the grocery store workers unionize. Draw a graph to depict the equilibrium wage and number of workers in this new market.Please help!! Barbara is an economist researcher and commentator. The Eco Books Ltd offers her $13,000 for writing a book about economics principles. Barbara has never written a book about economics principles, but accepts the offer and writes the economics book called 'Principles of Economics'. She assigns the book's copyright for $13,400 to The Eco Books Ltd. The book is published and she is paid. She also sells the book's manuscript to the Eco Books Ltd's library for $4,350 plus several interview manuscripts she has collected while writing the economics book for which she receives $3,200. Discuss each of the above payments to Barbara separately and states if these are income from Barbara's personal exertion. Would your answer differ if Barbara wrote the Principles of Economics' book before signing a contract with The Eco Books Ltd in her spare time and only decided to sell it later? Support your answer by referring to relevant statutory and case law.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) 5