Problem 1
Assume that a monopolistic profit-maximizing publisher has agreed to pay an author a royalty of 15% of the total revenue from sales of a book.
What price will the publisher wish to charge? What price will the author wish to charge? Explain, with the help of diagram(s).
Problem 2
A monopoly firm faces a demand curve P = 120 - Q. The monopolist's marginal cost curve (MC) is constant at MC = $4.
a) Determine the non-discriminating monopolist's profit-maximizing price and quantity (recall that the MR curve has the same intercept as the demand curve, but twice the slope).
b) Now assume the monopolist practices first-degree (perfect) price discrimination, i.e. is able to charge a different price to each customer. What is the quantity sold under this policy? What is the price charged for the last unit just sold?
c) How does the choice of pricing strategy affect allocative efficiency in the economy?
Problem 3
Suppose that Queen's University wishes to reduce the operating deficit of the sports programs and increase student attendance at home football games. A new two-tier pricing structure for season football tickets is being considered. A market survey conducted for the University suggests the following demand relationships:
Public demand: Pp = 225 - 0,005 Op
Student demand: Ps = 125 - 0,00125 Qs.
The budget of the football program covers fixed costs such as salaries, recruiting, insurance and facility maintenance expenses. In addition, the program incurs variable costs of $25 per season ticket holder. These include ticket handling, facility cleaning and security costs. The resulting total cost function is
TC = 1,500,000 + 25 Q.
a) What is the optimal ticket price and quantity in the public market?
b) What is the optimal ticket price and quantity in the student market?
c) What is the operating surplus (profit) when tickets are sold at different prices in the public market and in the student market?
d) Now suppose that under protest from the general public the University charges a single price. Calculate the optimal single price and the resulting quantity sold.
e) What are the key conditions for success of the price discrimination strategy?
f) Give examples of markets where such pricing is practiced (with a one-sentence explanation of each example).
Problem 4
Assume your city government has been contracting with a single garbage collection firm that has been granted an exclusive franchise (sole right to pick up garbage within the entire city limits). It has been proposed that other firms be allowed to compete for business with residents on an individual basis. The following table shows the city government's estimate of the price residents are willing to pay for various numbers of garbage collections per month and of the total costs per resident.
|
Number
of Pickups
|
Price per
Pickup
|
Total
Revenue
|
Marginal
Revenue
|
Total Cost
|
Marginal
Cost
|
Average
Total Cost
|
|
Q.
|
P ($)
|
TR
|
MR
|
TC ($)
|
MC
|
ATC
|
|
0
|
4.20
|
0
|
-
|
3.20
|
-
|
|
|
1
|
3.80
|
|
|
4.20
|
|
|
|
2
|
3.40
|
|
|
5.60
|
|
|
|
3
|
3.00
|
|
|
7.80
|
|
|
|
4
|
2.60
|
|
|
10.40
|
|
|
|
5
|
2.20
|
|
|
13.40
|
|
|
|
6
|
1.90
|
|
|
16.80
|
|
|
Fill in the blank spaces and answer the following questions:
a) What are the fixed costs per month of garbage collection per resident?
b) Considering that the current garbage collection firm the city has contracted with has a monopoly, what is the current number of collections residents receive per month and the price charged for each collection? What is the economic profit received from each resident by the monopoly firm?
c) If competitive bidding were allowed and therefore a competitive market for garbage collection services developed, what would be the number of collections per month and the price charged residents per collection? What is the economic profit received from each resident by the competitive firms?
d) Based on the above analysis, should the city government allow competitive bidding? Why? Would you expect to be any quality difference between the services of monopolistic and competitive garbage collection firms?
Problem 5
A beekeeper lives close to an apple orchard. The orchard owner (farmer) benefits from the bees as each hive (family of bees) pollinates about one acre of apple trees. The farmer pays nothing for this service because the bees come to the orchard without any effort on the part of the farmer.
Since there are not enough bees to pollinate the entire orchard, the farmer must complete the pollination by artificial means, at a cost of $10 per acre of trees. Beekeeping has a marginal cost MC = 10 + 20 where 0 is the number of beehives. Each hive yields $20 worth of honey. What market phenomenon does this situation represent?
a) How many beehives will the beekeeper maintain?
b) Is this the efficient number of hives from the social point of view? Why or why not?
c) Suggest changes (alternative practices or policies) that would lead to the more socially efficient number of beehives.
d) What would be some practical implementation problems with the changes you proposed?
Problem 6
A firm with market power has estimated the following demand function for its product: 0 = 12,000 - 4,000 P,
where P = price per unit and Q.= quantity demanded per year.
The firm's total costs are $4,000 when nothing is being produced. These costs increase by 50 cents for each unit produced.
a) Write the equation for the firm's total cost function
b) Write the equation for the firm's marginal cost function
c) Write the equation for total revenue in terms of Q.
d) Write the equation for the marginal revenue function
e) If the firm's objective is to maximize total revenue, determine
• The optimum output
• The optimum price
• The maximum total revenue, in $ per year
f) If the firm's objective is to maximize total profit, determine
• The optimum output
• The optimum price
• The maximum profit, in $ per year
g) Calculate the price elasticity of demand at the price-quantity combination determined in part (f), and use it to determine the profit-maximizing markup. Compare the actual markup with the profit-maximizing one
h) Assume the firm decides as in (f) and explain whether it will make economic profit
• In the short run
• In the long run
Clearly specify your assumptions and illustrate with a diagram
Problem 7
The industry demand function for bulk plastics is represented by the following equation: P = 800 - 20 Q
where 0 represents tonnes of plastic.
The total cost function for the industry, including "normal profit" (the return shareholders require to stay invested in the industry), is
TC = 300 + 500 0 + 10 0.2 and MC = 500 + 20 0
a) If this industry acts like a monopolist in the determination of price and output, compute the profit-maximizing level of price and output and the industry profit.
b) Assume now that this industry is perfectly competitive, composed of many (500) small firms, and the cost function remains unchanged. What level of output would profit-maximizing firms produce? What profit would they make? How does the profit compare with that under monopoly? Explain.
c) If the competitive solution most accurately describes the industry, is the industry operating under equilibrium conditions? Why or why not? What would you expect to happen?
d) The Clean Water Coalition has proposed pollution control standards for the industry that would change the industry cost curve to TC = 400 + 560 0+ 10 0.2. What is the impact of this change on price, output, and total profits under the monopoly solution?
Problem 8
A private university conducted market research as to its students' reservation prices for room and meal programs. Since costs can be considered fixed, they are ignored. The university identified three types of students: Sleepers (5), Eaters (E) and Hogs (H). The findings are summarized in the table below.
|
|
S
|
E
|
H
|
|
Dorm
|
6,000
|
4,000
|
1,000
|
|
Meal
|
3,000
|
7,000
|
4,500
|
a) If the university prices the two services separately and as a monopolist, what will it charge each?
b) If the university applies pure bundling, what will be the bundle price?
c) Will the university apply mixed bundling? If yes, what will the prices be?