John's technology for producing apple pie (a) is represented by a = vĪ +2 where Lis labor. His utility function from his consumption of apple pies (a) and his labor (L) is given by u (a, L) = 2a – 4L². Assume John is the only consumer and producer of apple pies in his household and suppose the price of apple pies is set at $1. The market equilibrium wage rate for John's labor supply is a) $1 b) $2

John's technology for producing apple pie (a) is represented by a = vĪ +2 where Lis labor. His utility function from his consumption of apple pies (a) and his labor (L) is given by u (a, L) = 2a – 4L². Assume John is the only consumer and producer of apple pies in his household and suppose the price of apple pies is set at $1. The market equilibrium wage rate for John's labor supply is a) $1 b) $2

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter13: General Equilibrium And Welfare

Section: Chapter Questions

Problem 13.2P

See similar textbooks

Similar questions

Consider a firm for which production depends on two normal inputs, labor and capital, with prices w and r, respectively. Initially, the firm faces market prices of w=$5 and r=$15. Assume the firm has a cost budget of $1,500. a. Using the isoquant-isocost model, graphically show the optimal level of employment for this firm in the long run.b. Suppose the government now imposes a minimum wage of $10 for workers. Using the same graph as part a, graphically show the impact of the minimum wage on the optimal level of employment in the long run.c. Refer to the initial situation described in part a. Now suppose a new innovation causes the price of capital to fall to $10. Using a new isoquant-isocost model, graphically show how this change impacts the optimal levels of employment and capital in the long run. Clearly identify the resulting scale and substitution effects caused by the lower cost of capital.
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)=2 ln x+ln M?. The total provision of firemen hired, M, is the sum of the number hired by each of the two persons: M=M^A+M^B. 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). Suppose that the government recruits additional ? firemen and taxes Ann and Bob equally to cover the cost. Therefore, the total number of firemen is M^A+M^B+N, where M^A, M^B are appropriate individually-optimal contributions of A and B (i.e., the agents behave optimally, conditional on the policy), and each…
A firm uses capital and labor to produce output according to the pproduction function q = 4pKL, for which MPL = 2pK=L and MPK = 2 L=K. a. If the wage w=$4 and the rental rate of capital r=$1,what is the least expensive way to produce 16 units of output? b. What is the minimum cost of producing 16 units? c. Show that for any level of output q, the minimum cost of producingq is $q.
A firm can manufacture a product according to the production function Q=3K1/2L1/2, and capital is fixed at 4. a) When the firm hires 16 units of labor. The average product of labor is......... b) when the firm hires 16 units of labor, the marginal product of labor is....... C) if the firm can sell its output at a price of $ 10 per unit and can hire labor at $ 10 per unit , it should hire?............units of labor maximize the profits.
Consider a production function: Q = f (L), where Q represents the output and L is thefactor of production. Let w be the per unit price of factor L and p be the per unit price ofoutput Q. Using the Envelope theorem determine the supply function and the factor demand function.
Assume an economy consists of two agents, a and b. Individual a has available 1 unit of time which he divides between leisure ra and labor ℓa . Likewise, individual b has available 1 unit of time which he divides between leisure rb and labor ℓb. Commodity x is produced by one competitive firm according to the production function: x=√L , where L denotes labor hired. The firm is fully owned by agent a. The utility function of the two individuals are: u(xa,ra)=xara and u(xb,rb)=xbrb . Taking the price of labor as the numéraire (i.e. w=1), find the competitive equilibrium for this economy.
A college football coach says that given any two linemen A and B, he always prefers the one who is bigger and faster. Is this preference relation transitive? Is it complete? The production function for puffed rice is given by q , where q is the number of boxes produced per hour, K is the number of puffing guns used each hour, and L is the number of workers hired each hour. Calculate the q = 1,000 isoquant for this production function and show it on a graph. If K = 10, how many workers are required to produce q = 1,000? What is the average productivity of puffed-rice workers? Suppose technical progress shifts the production function to , answer parts a and b for this new situation.
Suppose a worker’s utility is U = C 1/2L1/2. C is expenditures on goods, L is hours of leisure. He has a total of 16 hours for work and leisure, and the market wage is $10 per hour. Solve for his optimal C and L (assume V=0
Consider a firm for which production depends on two normal inputs, labor and capital, with prices w and r,respectively. Initially, the firm faces market prices of w=$5 and r=$15. Assume the firm has a cost budget of$1,500.a. Using the isoquant-isocost model, graphically show the optimal level of employment for this firm in thelong run.b. Suppose the government now imposes a minimum wage of $10 for workers. Using the same graph aspart a, graphically show the impact of the minimum wage on the optimal level of employment in thelong run.c. Refer to the initial situation described in part a. Now suppose a new innovation causes the price ofcapital to fall to $10. Using a new isoquant-isocost model, graphically show how this change impacts theoptimal levels of employment and capital in the long run. Clearly identify the resulting scale andsubstitution effects caused by the lower cost of capital. Could you please answer this question using the graphs please.
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)=2ln⁡x+ln⁡M. 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)=2ln⁡x+ln⁡M. 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)=2ln⁡x+ln⁡M. 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=200/3