1.a) Assume the market for milk in a particular town is perfectly competitive. The market demand is:
Q = 16 – 20P
where Q is the quantity of milk in the market in hundreds of thousands of litres per day. There are one hundred firms in the industry and each has the following marginal cost function:
P = .44 + 4q
where q is the quantity produced by each firm.
Firms have fixed costs of $80.00 per day.
Using this information, derive the short and long run equilibria in this market. Assume for simplicity that the firm is currently operating at its most efficient scale.
Hint: TC = a+.44q + 2q²
(derived from your calculations by integrating the MC function where a is the fixed cost of the firm)
b) Now assume that the milk market described above is supplied by a monopoly rather than a perfectly competitive market. We therefore have the following functions describing the market:
Demand Q = 16 – 20P
Marginal cost MC = .44 + .04Q
Total cost TC = .08 + .44Q+ .02Q²
Here it is assumed that the fixed costs of the monopolist are the sum of the fixed costs of all the competitive firms. The units are the same as in part (a).
What is monopoly output, price and profit?
2.In metro Toronto there is a pleasant little Mexican restaurant, the Mexicali Rose. In addition to the regular fare, the menu contains several different plates for children under 12 years of age. Interestingly, all the items on the menu are available for take-out except the food on the children’s menu. Why do you think the Mexicali Rose does not sell children’s plates for take-out?
3.Two soft drink producers, Savvy Cola and Rocket Cola, secretly collude to fix prices. Each firm must decide whether or not to abide by the agreement or to cheat on it. The payoff matrix is as follows:
a.What strategy will each firm choose, and what will be each firm’s profit? Is this a Nash equilibrium? Explain
b.Does it matter whether this is a one-shot agreement or whether it is meant to continue for some time?
c.Is this game an example of the prisoner’s dilemma?
4.Two firms produce vision systems. The demand curve for vision systems is
P = 200,000 -6(Q1 + Q2)
Where P is the price of a vision system (in dollars), Q1 is the number of vision systems produced and sold per month by Firm 1 and Q2 is the number of vision systems produced and sold per month by Firm 2. Their respective total cost functions are:
TC1 = 8,000Q1
a.If each of these two firms sets its own output level to maximize its profits, assuming that the other firm holds constant its output level, what is the equilibrium price?
b.What will be the output of each firm?
c.What will be the profit of each firm?
5.Valair is an airline flying a particular route that has seasonal demand. The firm’s total demand is given by Q = 600 – 4P
Where Q is the number of passengers per year, in thousands, and P is the fare (in $). In the peak season the demand is given by:
QH = 320 – 1.5pH
And in the off season the demand is given by:
QL = 280 – 1.5pL
Assume that fixed costs are $6 million per year and that marginal costs are constant at $60 per passenger, thus the cost function is given by
C = 6000 + 60 Q
Where C is total cost (in $’000)
a.Calculate the profit-maximizing price and output without price discrimination and the size of the profit.
b.Calculate the profit-maximizing price and output with price discrimination, and the size of the profit.
c.Calculate the demand elasticities of the two segments at their profit-maximizing prices.
6.The Mackenzie Company estimates its average total cost to be $10 per unit of output when it produces 10,000 units, which it regards as 80 percent of capacity. Its goal is to earn 20 percent on its total investment, which is $250,000.
a.If the company uses cost-plus pricing, what price should it set?
b.Can it be sure of selling 10,000 units if it sets this price?
c.What are the arguments for and against a pricing policy of this sort?
Assume it is 1991…….
7.On November 13, 1991, US Senator Alphonse D’Amato introduced a bill into the US Senate that would require banks to lower the interest rates that they charge on their Mastercard, Visa, and other credit cards. The D’Amato bill did not allow banks to charge more than four percentage points above the rate that the IRS charges taxpayers in the US for overdue taxes (which was 10 percent at the time). As many of you may have experienced, in addition to interest on outstanding balances, many banks charge an annual fee for their credit cards. Moreover, most credit cards are only offered after the applicant has submitted to a credit and background check. In addition to credit, many banks offer ancillary services in conjunction with their credit cards. For example, the Visa credit card issued by Citibank offered a number of services including: (1) cash advance through ATMs; (2) car rentals charged to Citibank credit cards were covered for collision, theft, or fire damage at no additional charge; (3) travel accident insurance was provided at no extra charge if the Citibank credit card was used to purchase tickets (airline, train, bus or ship and the insurance was to a maximum of $350,000); and (4) using a Citibank credit card to purchase retail items automatically insured the purchases against loss, theft, fire or accidental damage for 90 days from the date of purchase.
Now suppose the D’Amato bill becomes law and banks are forced to lower their interest charges on credit cards. What do you predict will happen to the level and types of services offered in conjunction with credit cards in 1992 and beyond?