Problem 1
Evaluate whether the following statements are True or False
• "As long as buyer are willing to pay a positive price for a good, the larger is the quantity produced, the greater is the total surplus from trade."
• "Suppose a monopolist with a constant average cost. The higher is the elasticity of demand at the chosen monopoly price, the higher is the monopolist's profit-to-revenue ratio."
• "If for a particular market, the concentration ratio CR4 (the combined market share of the 4 largest firms) is 1, its Herfindahl index is at least 0.25."
• "Suppose a market with n firms engaged in Bertrand competition. These firms have in general different marginal costs but any number of them can also have equal marginal costs. There is no such a structure of marginal costs that more than one firm in this industry earns a positive profit."
• "Consider the local fixed telecommunications company is a monopoly. It costs the company €2 per month to provide voice messages service to a customer. Elasticity of demand for voice messages service is 4/3 (at any price). Then the phone company will make more money if it does offer its service at €5 per month than if it offers this service at €8 per month."
Problem 2
The sole producer of the anti-diarrhea drug STOP supplies two retail pharmacies in an isolated village. The two pharmacies compete à la Cournot in a market characterized by an inverse demand function
P(Q) = 100-Q
where p is the price consumers pay for a package of pills. The costs the pharmacies have per package sold are €40 plus the amount they have to pay for a package to the producer of STOP.
Consider that the marginal cost of STOP is €12 per package and that there are no fixed costs. Furthermore, suppose that STOP uses a two-part tariff with a price per package equal to S p and a fixed amount f which both pharmacies need to pay to STOP to become its eligible suppliers.
a.Consideer that the fixed amount f is so low that both retailers remain in the market. Evaluate the joint equilibrium quantity of the two pharmacies that will be offered as a function of pS ?
b. What values of f and pS maximize the profits of STOP?
Problem 3
PanCakes Creations is considering franchising its unique brand of pancakes to stall-holders on the Zandvoort beach, which is 5 kilometers long. PanCakes Creations evaluates that on an average day there are 1000 sunbathers evenly spread along the beach and that each sunbather will buy one pancake per day provided that they cost no more than €5. The effort of getting up from the sand to get a pancake and return to the sunbed is estimated at 25 cents for every ¼ kilometer the sunbather is from a stall. Every pancake costs 50 cents to make and it costs €40 per day to operate a stall no matter how many pancakes it makes.
a. Consider that PanCakes Creations award a franchise to only one stall-holder. This beach holder locates its stall in the middle of the beach. Write down the stall's demand function for pancakes as a function of price.
b. Consider that the franchise contract needs the stall-holder to cater to all consumers on the beach. What price will the stall-holder charge and what will be its profits?
c. The stall-holder is unsatisfied with the profits it makes. He argues that his profits might increase if he raises the price and consequently serves only part of the beach. What price could the stall-holder charge in order to maximize the profits? Is he right - will the profits increase due to the new pricing strategy?
The fixed franchise fee allows PanCakes Creations to reap a substantial part of the stall-holder's profits. To gain the profits further, the company award a franchise to one additional stall-holder and needs both stall-holders to locate their stalls symmetrically on the beach (i.e., one stall will be located at 1/4 and the other one at 3/4 of the way along the beach). Consider that PanCakes Creations fixes the price of pancakes in the franchise contract is such a way that the two stalls together serve the entire beach.
d. What will be the quantity sold by each stall? Are the combined stall-holders profits higher than the profits a single stall-holder makes according to your answer under c.?
Problem 4
Suppose a worker in a firm that has to decide how hard to work. The worker's effort e , with 01 e ≤≤ , has a disutility for the worker equal to 2/2 e - . The worker gets wage 01 w << . The worker's utility is thus
that is, the wage net of the effort cost. The production of the firm is e and the good is sold at price 1.
a. The worker selects effort e to maximize own utility (subject to the constraint 01 e ≤≤ ). What is his optimal choice of effort e ?
The firm does not like the above outcome and decides to monitor the worker with probability P to induce the worker to exert more effort. If the firm monitors, it catches the worker shirking with probability1 e - , after which it fires him. If the worker is caught shirking and is fired, he gets 0 wage. If the firm does not monitor the worker or does not fire him, he gets wage w . The worker maximizes the expected wage payment minus the effort cost.
b. Write down the expected utility of the worker and answer for the utility maximizing effort e . How does the worker's optimal effort depend on P ? Provide intuition.
c. Suppose the firm's monitoring costs are equal to γP2 . What is the profit- maximizing level of monitoring? (Hint: The firm pays the wage w with probability 1 - P + Pe)
We now return the situation without monitoring. Assume now, however, that the worker is altruistic toward the firm. That is, the worker maximizes w - e2/2 + ae, where the last term is the product of the altruism coefficient α ( (0,1] α ∈ ) and the production of the firm.
d. Solve for the utility maximizing effort. How does the worker's effort change when the altruism coefficient α increases?
e.Consider the firm can select between two applicants for the job: a selfish worker who chooses effort according to your answer under c. and an altruistic worker who is insensitive to monitoring and chooses effort according to your answer under d. Which worker will the firm hire?