firm has a production function Y=150N^0.6. The real wage is W=30. The production process of this firm causes pollution. The government passes a law that requires the firm to stop polluting. This firm discovers that it can prevent pollution by hiring 0.2 additional workers for each worker in the production process to clean up. Let N denote the amount of labor hired on the production line. If the firm wants to maximize its profit, what should be the value of N?
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A firm has a production function Y=150N^0.6. The real wage is W=30. The production process of this firm causes pollution. The government passes a law that requires the firm to stop polluting. This firm discovers that it can prevent pollution by hiring 0.2 additional workers for each worker in the production process to clean up. Let N denote the amount of labor hired on the production line. If the firm wants to maximize its profit, what should be the value of N?
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- The relationship between a worker’s daily wage, w, and her daily output, q, is q = 0.1 w2 - 0.0005 w3 so that the worker’s marginal product with respect to her wage is MPw = 0.2 w - 0.0015 w2. What is the optimal efficiency daily wage for the firm to pay? How much output will the worker produce each day? How much profit does the firm earn on the worker’s output each day if the price of output is fixed at $0.80 per unit?Anna and Bob are the only residents of a small town. The town currently funds its fire department solely from the individual contributions of these two residents. Each of the two residents has a utility function over private goods xx and total number of firemen MM, of the form: u(x,M)=2lnx+lnMu(x,M)=2lnx+lnM. The total provision of firemen hired, MM, is the sum of the number hired by each of the two persons: M=MA+MBM=MA+MB. Ann and Bob both have income of 200 each, and the price of both the private good and a fireman is 1. They are limited to providing between 00 and 200200 firemen. For the purposes of this problem, you can treat the number of firemen as a continuous variable (it could be man-years). How many firemen are hired if the government does not intervene?A particular road is used by N drivers each day. Each driver obtains a benefit v from the journey and incurs a cost c(N) that increases with the number of drivers on the road due to congestion. Suppose that the cost incurred is given by c(N) = a + bN, for some positive numbers a, b. If the agent decides not to use the road, they receive 0. You may assume throughout that the number of drivers N can be any real number (rather than an integer). Each driver uses the road at most once. Suppose that the government charges a toll t (a congestion charge) for each journey. Find the optimum toll. Interpret your answer in terms of the externality that each driver imposes on others
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- A firm’s total cost C is given by the function: C = 4X2 Where X is the level of output and C is the cost. The firm can sell any number of units of output at a price of 64. However, production inflicts damage on the firm’s neighbours. The total damage D inflicted depends on the firm’s output: D = 4X + X2 (a) Assume that the firm has the property rights: (i) In the absence of an agreement with its neighbours, what would its level of output be? (ii) Suppose that the neighbours negotiate with the firm. To what level of output would the negotiations lead? (iii) What is the minimum payment that the neighbours must make to the firm to achieve this change in output? (iv) What is the maximum payment that the neighbours must make to the firm to achieve this change in output? (b) Assume that the neighbours have the property rights: (i) In the absence of an agreement between the firm and its neighbours, what would the level of output be? (ii) If an agreement between the firm and…Anna and Bob are the only residents of a small town. The town currently funds its fire department solely from the individual contributions of these two residents. Each of the two residents has a utility function over private goods x and total number of firemen M, of the form: u(x,M)=2lnx+lnM. The total provision of firemen hired, M, is the sum of the number hired by each of the two persons: M=MA+MB. Ann and Bob both have income of 200 each, and the price of both the private good and a fireman is 1. They are limited to providing between 0 and 200 firemen. For the purposes of this problem, you can treat the number of firemen as a continuous variable (it could be man-years). Consider the setup from above. Suppose that the government recruits additional ?N firemen and taxes Ann and Bob equally to cover the cost. Therefore, the total number of firemen is MA+MB+N, where MA,MB are appropriate individually-optimal contributions of A and B(i.e., the agents behave optimally, conditional on the…Anna and Bob are the only residents of a small town. The town currently funds its fire department solely from the individual contributions of these two residents. Each of the two residents has a utility function over private goods x and total number of firemen M, of the form: u(x,M)=2lnx+lnM. The total provision of firemen hired, M, is the sum of the number hired by each of the two persons: M=MA+MB. Ann and Bob both have income of 200 each, and the price of both the private good and a fireman is 1. They are limited to providing between 0 and 200 firemen. For the purposes of this problem, you can treat the number of firemen as a continuous variable (it could be man-years). Consider the setup from above. The government proposes an alternative, market-based solution. They charge each citizen the price p for every firemen stationed at the local fire station. Then, the price is being set at a level p∗ at which each individual demands the socially optimal number of firemen. What is the…
- Anna and Bob are the only residents of a small town. The town currently funds its fire department solely from the individual contributions of these two residents. Each of the two residents has a utility function over private goods x and total number of firemen M, of the form: u(x,M)=2lnx+lnM. The total provision of firemen hired, M, is the sum of the number hired by each of the two persons: M=MA+MB. Ann and Bob both have income of 200 each, and the price of both the private good and a fireman is 1. They are limited to providing between 0 and 200 firemen. For the purposes of this problem, you can treat the number of firemen as a continuous variable (it could be man-years). Consider the setup from above. Suppose that we identify the social welfare in this town by the sum of utilities of Ann and Bob. What is the socially optimal number of firemen? a. M=400/3 b. M=80 c. M=400 d. m=200/3Ten workers work jointly on a project. All 10 workers are equally skilled. The total value of the output produced is $100 times the sum of the number of hours worked by all 10 workers. Each worker's utility is equal to his income minus the square of the number of hours he works. Each worker is selfish. The employers have no way of keeping track of any individual's work effort, so they decide to let each person work as long as he wants to and they divide the total value of the output equally among the workers. How much income will each worker get?Consider a fishery with the following production function where L is the number of fishermen and TP (total product) is the total number of fish caught among all fishermen. (And assume they are divided equally among the fishermen.) L 1 2 3 4 5 6 7 8 9 10 TP 18 34 48 60 70 78 84 88 90 90 The price of fish is $3 and the wage of a fisherman is $36. a. If the fishery is private property, how many fishermen will the owner hire? [1] b. If the fishery is common property, how many people will come to fish? [2] (Assume people fish as a job and not for recreation here.) c. What is the efficient number of fishermen? [3]