# Given only the information provided above, what is the maximum amt of profit the firm can…

The agent is risk-averse and the agent’s output is an increasing, non-stochastic function of the agent’s effort level. b. The agent is risk-neutral and output is an increasing, stochastic function of the agent’s effort. c. The agent is risk-averse and output is a stochastic function of the agent’s effort in which the lowest possible output level is finite, strictly increasing in the agent’s effort level, and has a strictly positive probability of occurring. 2. Optimal Pay Schedule Assume a worker (W) can produce output (X) for an employer by increasing his effort (E) according to the following equation: X = (1.5)E. Assume that the compensation paid by the employer (Y) increases the utility of the worker, while the amount of effort decreases his utility as such: U(E,Y) = Y – (E2)/2. Assume that price of output is 1 and that labor costs are the only costs of production, such that total profit, p, equals p = Y – X. Assume that the next-best option for the worker provides them a utility of zero. (a) Given only the information provided above, what is the maximum amt of profit the firm can earn? (b) If the employer did not want to stipulate the output (and cannot verify the effort level), then, using a pay-schedule, what level of base-pay will render the same level of profit (as in (a)) when the piece-rate pay is 1? (c) Assume that the worker’s risk-aversion level is measured by R = 2. Also, assume that output is stochastic, such that the expected output from a given level of effort is E[X] = (1.5)E – E[Z], where the average value of Z is E[Z] = 0 and its variance is Var[Z] = 2. What is the loss of profits for the employer if they choose a new optimal B, while keeping the piece-rate pay at 1? (d) Can a different piece-rate pay be chosen by the employer such that their profits are maximized under the conditions of question (c)? If so, what is this optimal level of P? 3. Bowles Labor Extraction Model Use the table below to answer the following questions. Labor Economics Problem Set 4 Spring 2011 (a) Derive the Unit Labor Costs (ULC) from the wage-output schedule below. Weekly wage Z ULC 0 0 100 0 150 10 250 19 350 27 400 34 450 40 500 45 550 49 600 52 650 54 700 55 (b) What is the fall-back wage, w, according to this schedule? (c) What is the weekly unemployment insurance benefit per week using Equation 12.3 on page 298 of Bowles, et al(2005)? (d) What is the optimal weekly wage that the employer will use to induce an optimal amount of output (or effort) from the worker? 4. Surplus Extraction (a) Assume a competitive labor market. Draw the demand of labor curve for an individual firm. Assume that the firm faces a labor supply curve that is neither perfectly inelastic nor perfectly elastic. If the firm has the ability to command more effort and output from workers once they are hired, then what is occurring to the labor demand curve? Demonstrate your answer with the help of a graph.

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