G
Gavin D
Guest
A firm with “market power” is operating one plant services two markets. The demand curves it faces are,
Market 1: P = 1200 – 20Q1, and
Market 2: P = 800 – 5Q2,
where Q1 and Q2 represent the output in market 1 and market 2, respectively. The total cost function for this firm is
Total Cost = 1500 + 28Q + 2(Q^2)
where Q in this function represents the total output produced.
A. What are the output levels and prices in each market and total profits of this firm if it operates its business as an unregulated monopolist?
B. What are the output levels prices in each market and total profits of this firm if it is regulated to have a normal rate of return?
Problem 2. Suppose the following utility function describes "tastes" for an avid sports fan’s for pay-per-view college football games.
U = G^0.4A^0.6
where G is the number of games purchased on pay-per-view per season and A represents the amount spent on all other goods during a season. Suppose the average fan’s seasonal budget is $1000.
A. If the price of a pay-game-view football is $25, how many games will the average fan purchase?
B. Suppose government officials realize that pay-per-view sports is a veritable gold mine for state revenues and place a $5 per tax on each game viewed. By how many games will the average fan’s viewing be reduced after the tax? How much will the average fan pay in pay-per-view taxes?
C. How much will the average fan be willing to pay to avoid the $5 tax proposed in Part B. above?
D. After the tax is imposed, suppose fans stage a “revolt” and start piling junk TVs on the steps of the legislative hall. In response, legislators decide to rebate total taxes paid by each fan. This will be a cash rebate to the fan. How many games will the average fan watch after the rebate?
E. How much would the government have to rebate (in cash) to the average fan in order to keep the fan’s real income constant (with the tax still in place)? How much of a rebate would the average viewer receive?
F. How much would the government have to rebate to the average fan in order to keep this fan’s original purchasing choice intact (with the tax still in place)? How much of a rebate would the average viewer receive? The original purchasing choice is that found on Part A.
Each of 5000 consumers that are buyers of goods X and Y has the utility function:
U = 56(X^0.3)(Y^0.7)
where X is the number of units of good X consumed and Y represents all other goods that the consumer purchases. The income of each consumer is $1000. You may assume the price of Y is $1 per unit of other goods consumed. Keep in mind that there are 5000 consumers in this market and the utility function given above is for a single, representative consumer.
On the supply side of this market, the short run production function for each of 5 firms producing good X is:
X = 16(L^1/2)(K^1/3)
where L and K are the number of labor and capital units, respectively, used by each firm. The wage rate paid to labor is $166.66667 (i.e. 166 & 2/3) per unit and the price of capital is $0.25 per unit. Assume there are 15,625 units of capital (which includes machinery) being used by each firm.
1. Using this information determine:
A. The equilibrium level of output in this market.
B. The equilibrium price paid by consumers in this market.
C. The amount of labor used by the industry.
D. The profits to the industry.
2. If an 8.50 per cent sales tax is imposed on consumers in this market, determine:
A. The market price paid by consumers and the price received by producers.
B. The unemployment caused in this industry by the sales tax. Express this effect either as the number of unemployed or as a percentage of the pre-tax industry employment.
C. (Bonus) The amount consumers (as a group) would be willing to pay to avoid the tax.
D. (Bonus) The amount producers (as a group) would be willing to pay to avoid the tax.
Market 1: P = 1200 – 20Q1, and
Market 2: P = 800 – 5Q2,
where Q1 and Q2 represent the output in market 1 and market 2, respectively. The total cost function for this firm is
Total Cost = 1500 + 28Q + 2(Q^2)
where Q in this function represents the total output produced.
A. What are the output levels and prices in each market and total profits of this firm if it operates its business as an unregulated monopolist?
B. What are the output levels prices in each market and total profits of this firm if it is regulated to have a normal rate of return?
Problem 2. Suppose the following utility function describes "tastes" for an avid sports fan’s for pay-per-view college football games.
U = G^0.4A^0.6
where G is the number of games purchased on pay-per-view per season and A represents the amount spent on all other goods during a season. Suppose the average fan’s seasonal budget is $1000.
A. If the price of a pay-game-view football is $25, how many games will the average fan purchase?
B. Suppose government officials realize that pay-per-view sports is a veritable gold mine for state revenues and place a $5 per tax on each game viewed. By how many games will the average fan’s viewing be reduced after the tax? How much will the average fan pay in pay-per-view taxes?
C. How much will the average fan be willing to pay to avoid the $5 tax proposed in Part B. above?
D. After the tax is imposed, suppose fans stage a “revolt” and start piling junk TVs on the steps of the legislative hall. In response, legislators decide to rebate total taxes paid by each fan. This will be a cash rebate to the fan. How many games will the average fan watch after the rebate?
E. How much would the government have to rebate (in cash) to the average fan in order to keep the fan’s real income constant (with the tax still in place)? How much of a rebate would the average viewer receive?
F. How much would the government have to rebate to the average fan in order to keep this fan’s original purchasing choice intact (with the tax still in place)? How much of a rebate would the average viewer receive? The original purchasing choice is that found on Part A.
Each of 5000 consumers that are buyers of goods X and Y has the utility function:
U = 56(X^0.3)(Y^0.7)
where X is the number of units of good X consumed and Y represents all other goods that the consumer purchases. The income of each consumer is $1000. You may assume the price of Y is $1 per unit of other goods consumed. Keep in mind that there are 5000 consumers in this market and the utility function given above is for a single, representative consumer.
On the supply side of this market, the short run production function for each of 5 firms producing good X is:
X = 16(L^1/2)(K^1/3)
where L and K are the number of labor and capital units, respectively, used by each firm. The wage rate paid to labor is $166.66667 (i.e. 166 & 2/3) per unit and the price of capital is $0.25 per unit. Assume there are 15,625 units of capital (which includes machinery) being used by each firm.
1. Using this information determine:
A. The equilibrium level of output in this market.
B. The equilibrium price paid by consumers in this market.
C. The amount of labor used by the industry.
D. The profits to the industry.
2. If an 8.50 per cent sales tax is imposed on consumers in this market, determine:
A. The market price paid by consumers and the price received by producers.
B. The unemployment caused in this industry by the sales tax. Express this effect either as the number of unemployed or as a percentage of the pre-tax industry employment.
C. (Bonus) The amount consumers (as a group) would be willing to pay to avoid the tax.
D. (Bonus) The amount producers (as a group) would be willing to pay to avoid the tax.