Could you please explain the solution? 14. On a certain market two types of workers are available: they are characterized by their unit production costs which are t-2, and T=3, respectively, for any production level q. Moreover, the respective frequencies of the two types are given by the distribution prob(t)=1/3, prob(T)-2/3, and a principal with a revenue function S(g)= q+2q2/3 knows such a distribution but is unable to distinguish (ex-ante) between type t-workers and type T-workers. Then, the optimal contract proposed by the principal will require the following production levels for type t and type T:
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- Each employer faces competitive weekly wages of $2,000 for whites and $1,400 for blacks. Suppose employers undervalue the efforts/skills of blacks in the production process. In particular, every firm is associated with a discrimination coefficient, d (0 ≤ d ≤ 1). In particular, although a firm’s actual production function is Q = 10(EW + EB), the firm manager acts as if its production function is Q = 10EW + 10(1 - d ) EB . Every firm sells its output at a constant price of $240 per unit up to a weekly total of 150 units of output. No firm can sell more than 150 units of output without reducing its price to $0.a. What is the value of the marginal product of each white worker?b. What is the value of the marginal product of each black worker?c. Describe the employment decision made by firms for which d = 0.2 and d = 0.8 respectively.d. For what value(s) of d is a firm willing to hire blacks and whites?Consider a worker/consumer with non-labor income, V, of 2 dollars. Time endowment is T=24 and denotes labor supply by h. Suppose the hourly wage is 5, and the consumption good's price is 1. Suppose that the optimal labor supply (given the prices) is h*=8. Suppose that the worker is offered the following contract: For every one of the first 8 hours, the wage per hour is 5. If the worker chooses to work for more than 8 hours the wage rate is 10 for each extra hour (above 8). A new graph depicts the budget set. Can you determine how labor supply changes? (comparing it to the case in which the wage rate is fixed at 5 dollars per hour)..Suppose a campus restaurant increases the number of workers it hires from 3 workers per day to 11 workers per day. As a result, its total revenue increases from $135 per day to $550 per day. a. Assuming that each worker is equally productive, what is the marginal revenue product per day of each additional worker? $ b. Assuming the restaurant is using its resources in a profit-maximizing way, and that each worker works 5 days each week, what is the current weekly wage rate in the labor market? $ per week
- 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 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?A city government is considering renting space in an all‑day parking garage for its 100 employees. The government estimates these employees' demand function for parking spaces is 150 ‑ 50P (P ≥ $1), where P is the per-day price of parking, and the city will pass on the cost. (a) If the city needs not charge each of its employees the same price for a parking space, what is the maximum amount the city could pay for the 100 spaces, and what would be the average cost per space? (b) Assume the employees’ union insists that – per their contract – each employee must be charged the same price for parking, and the city’s response is to intend charging the price that maximizes its parking fee revenue. What price per space would the city charge under this circumstance, and how much less total dollar benefit would the employees receive?
- Consider a self employed worker who owns a firm that produces output q which sells for a price of p = 1. Output depends on effort, e, so the production function is q = γe, where γ > 0 is a parameter. Effort reduces utility, and the cost of effort is c(e) = 1 2 e2. Note that there is no principal-agent problem here because the worker is the owner of the firm (and therefore has a claim on all profits), in addition to personally incurring the cost of effort. The self employed worker’s utility is a linear function of revenue net of effort costs, U(e) = q− c(e) = γe− 1 2 e2Consider 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.Consider a firm which produces q units of output using L units of labour and whose market demand for labour is given by L* = 57- w/(14p), if w/(14p)<57 and L*=0, otherwise where p denotes the price of output and w denotes the price of labour. What is the change in the profit of the firm if the price of labour changes from w= 1 to w = 4 assuming the price of output is p=57?
- Assume in a given company the marginal productivity can be characterized by the following function MPL = 100 - L, where L denotes the number of higher workers.If the price of the good purchased by the company is 10 gel, and the workers wage is set at 600 gel. How many workers should a company hire to achieve the maximum profit? Select one a - 40 b - None c- 99 d- 60Suppose that a firm's production is given by: Q= 10L-L² , for L= 0 to 5, where L is labor input per day and Q is output per day. Derive and draw the firm's demand for labor if the firm's output sells for $10 in a competitive market. The marginal product of labor is 10-2L. a. How many hours of labor will the firm use when the wage is $30 per day? b. How many hours of labor will the firm use when the wage is $70 per day?Derive the firm’s demand schedule for labour if it were a monopolist that could influence the price at which it sells its output. That is, relax the assumption that product prices are fixed, and trace the implications.