2. Suppose you manage a factory with ten workers. Each worker's output is determined by the equation q = e. Output sells in the market for a price of 40. The firm has fixed cost equal to 800, and variable costs aside from labor are 8 per unit of output. Worker utility is U=w-e². a. Suppose you are paying workers a wage equal to bq. What is the profit- maximizing value of b? b. Suppose that the probability of worker error increases as the worker increases effort, and that worker error results in unusable output. Suppose that the probability of worker error is Pr[Error] = e/10. Then for worker effort level e, expected (usable) output is now determined by the equation E[q] = (1-Pr[Error]) x e. However, the problem is that you cannot detect errors until after the product is shipped to customers, meaning you pay workers for output before you know whether it is usable or not, and you have to refund your customers for unusable output. Demonstrate why you should not pay your workers the same piece rate you calculated in part a under these conditions.

2. Suppose you manage a factory with ten workers. Each worker's output is determined by the equation q = e. Output sells in the market for a price of 40. The firm has fixed cost equal to 800, and variable costs aside from labor are 8 per unit of output. Worker utility is U=w-e². a. Suppose you are paying workers a wage equal to bq. What is the profit- maximizing value of b? b. Suppose that the probability of worker error increases as the worker increases effort, and that worker error results in unusable output. Suppose that the probability of worker error is Pr[Error] = e/10. Then for worker effort level e, expected (usable) output is now determined by the equation E[q] = (1-Pr[Error]) x e. However, the problem is that you cannot detect errors until after the product is shipped to customers, meaning you pay workers for output before you know whether it is usable or not, and you have to refund your customers for unusable output. Demonstrate why you should not pay your workers the same piece rate you calculated in part a under these conditions.

Principles of Microeconomics

7th Edition

ISBN:9781305156050

Author:N. Gregory Mankiw

Publisher:N. Gregory Mankiw

Chapter21: The Theory Of Consumer Choice

Section: Chapter Questions

Problem 9PA

See similar textbooks

Similar questions

(a) Assuming working at home gives you a wage of $100, what would your wage be working in thecubicle office? In the shared workspace?(b) What is the compensating wage differential between these jobs?(c) Explain why the wage is different in each situation, and give an example of another industry-/situation with a compensating wage differential.
If the marginal product of labor is 40 units and the marginal product of capital is 200 units, while the price of labor is $50 per worker and the price of capital is $300 per unit of capital, what would the producer do? Group of answer choices The producer would use more labor and less capital. The producer would use the same amount of both capital and labor as before. The producer would use more capital and less labor. The producer would use less of both capital and labor. The producer would use more of both capital and labor.
Q40 If one worker in southern Ontario worker can pick $30 worth of tomatoes two workers together can pick $70 worth of tomatoes, the Multiple Choice data given are insufficient to determine the marginal revenue product of either worker. data given suggests diminishing returns. marginal revenue product of the first worker is $40. marginal revenue product of each worker is $35. marginal revenue product of the second worker is $40.
(5) Steven has non-labor income each week of $500. He can work up to 100 hours per week foran hourly wage of $10 per hour. His utility for recreation (R) and consumption (C) is given byU(R, C) = 2R2C. What is Steven’s reservation wage if the price of consumption is unity?(a) $30(b) $40(c) $50(d) $60(e) None of the above
The marginal product of effort, a typical worker in fast-food burger joint, is one- fourth burgers per hour; that is, MPe = .25The price of a burger is $2. The figure graphs Mac’s marginal cost of effort. If Mac increases his effort by one unit per hour, the change in the burger joint’s revenue is $ per hour. That is, what is VMPe , the value of Mac ‘s marginal product of effort ? Plot the VMPe curve in the figure. Mac efficient effort e^ is the solution to what equation? Illustrate the solution in the figure. Mac efficient…
5. A consumer's utility function over leisure and consumption is given by u(L, Y) = LY. Wage rate is w and the price of the composite consumption good is p = 1. (a) Suppose w = 10. Find the optimal leisure - consumption combination. (b) Suppose the overtime wage law is passed so that the firm must pay 1.5 times the normal wage for hours worked beyond the first 8 hours. Find the effect on the hours worked. Decompose the effect into substitution effect and income effect.
7. An individual's utility function is given by U =1000x, +450x, +5 x,x, -2x - x where x, is the amount of leisure measured in hours per week and x, is income earned measured in cedis per week. Determine the value of the marginal utilities, when x, = 138 and x, = 500. Hence estimate the change in utility if the individual works for an extra hour, which increases earned income by GH¢15 per week. Does the law of diminishing utility hold for this function?
A firm is thinking of hiring an additional worker to their organization who can increase total productivity by 100 units a week. The cost of hiring him is $1,500 per week. If the price of each unit is $12, which of the following is correct? Group of answer choices the MR of hiring the worker is $1,500. The MC of hiring the worker is $1,200. The worker should be hired at that wage because the marginal benefit exceeds the marginal cost. All of the above are correct. None of the above is correct.
. An individual's utility function is given by u = 1000 x, + 450 x. + 5x, x. - 2x-x where x, is the amount of leisure measured in hours per week and x,is income earned measured in cedis per week. Det er mine the value of the marginal utilities, when x, = 138 and x= 500. Hence est imate the change in utility if the individual works for an extra hour, which increa ses earned income by GH¢ 15 per week. Does the law of diminishing ut ility hold for this function? %3D
falling. follows. 6. Assume that the units of variable input in a coal-production process are 1, 2, 3, 4, and 5 and the corresponding total outputs (in tons) are 10, 19, 26, and 31, respectively. The marginal product of the third unit of input must be 7 tons. a. True b. False 7. Consumer equilibrium is achieved at the point of tangency between the budget line and the highest attainable indifference curve. a. True b. False 8. The slope of the total product curve is the average product curve. a. True b. False 9. The marginal utility of a good will eventually fall as more of it is consumed. a. True b. False 10. Marginal utility is at a maximum when it is zero. a. True b. False Indicate the answer choice that best completes the statement or answers the question. 11. Assume that a person is consuming the utility-maximizing quantities of pork and chicken. We can conclude that: a. the price of pork equals the price of chicken. b. the marginal utility of pork equals the marginal utility of…
This question will analyze the impact on a person's labour supply from a shock to their partner's job. Assume leisure is a normal good. Let's assume Vanessa has a wage rate of $20 per hour. Recently her partner, Bill, had to take a wage cut at work, with his wage falling from $45 per hour to $30 per hour, but allowed them to continue working 40 hours per week. Analyze the decision of the household over choice consumption and Vanessa's leisure, taking Bill's hours as given (constant).
Sven runs a daycare for some of the neighborhood children, where he earns $300/day inrevenue. He runs the daycare out of his home, for which the mortgage costs $3,000 per month($100 per day). Each day, Sven spends $50 on food, diapers, and other supplies. He also hassome toys and playground equipment that originally cost $500, but which he wouldn’t getany money for reselling today. Sven looks after all the children himself, so he doesn’t pay anymoney in labor costs. If he weren’t busy with the daycare, he could earn $120 per day as aprivate nanny. What is Sven’s daily economic profit from the daycare? (Select one from below) (a) $300: Economic profit is equal to revenue.(b) $180: That is his revenue minus opportunity cost.(c) $150: That is his revenue minus input cost.(d) $130: That is his revenue minus variable cost.(e) $50: That is his revenue minus accounting cost.(f) $30: That is his revenue minus economic cost.(g) $0: In the long run, all firms must make zero profits.(h) –$200:…