Illustrate the perverse incentive

Exercise 1

Determine whether the following statements are right or wrong

• “As long as consumers are willing to pay the positive price for a good, the larger is quantity produced, the greater is the total surplus from trade.”

• “Consider a monopolist with a constant average cost. The higher is elasticity of demand at the selected 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.”

• “Consider a market with n firms engaged in the Bertrand competition. These firms have in general dissimilar marginal costs however any number of them may also have equivalent marginal costs. There is no such a structure of marginal costs that more than one firm in this industry earns a positive profit.”

• “Assume the local fixed telecommunications company is a monopoly. It costs the company €2 per month to offer 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 additional money if it does offer its service at €5 per month than if it provides this service at €8 per month.”

Exercise 2

The sole producer of the anti-diarrhoea drug STOP supplies two retail pharmacies in an isolated village. The two pharmacies compete à la Cournot in a market classified 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 producer of STOP.

Assume that the marginal cost of STOP is €12 per package and that there are no fixed costs.
Moreover, assume that STOP uses a two-part tariff with a price per package equivalent to S p and a fixed amount f  which both pharmacies need to pay to STOP to become its eligible suppliers.

a. Assume that the fixed amount f is so low that both retailers remain in market. What is the joint equilibrium quantity of the two pharmacies that will be offered as a function of S p?

b. What values of f and S p maximize the profits of STOP?

Exercise 3

Pancakes Creations is considering franchising its exclusive brand of pancakes to stall-holders on Zandvoort beach, which is 5 kilometres long. Pancakes Creations estimates that on an average day there are 1000 sunbathers evenly spread along the beach and that each sunbather will purchase 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 sun bed is estimated at 25 cents for every ¼ kilometre the sunbather is from a stall. Each pancake costs 50 cents to make and it costs €40 per day to operate a stall no matter how many pancakes it makes.

a. Assume that Pancakes Creations award a franchise to only one stall-holder. This beach holder locates its stall in the central point of the beach. Write the stall's demand function for pancakes as a function of price.

b. Assume that the franchise contract requires 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 may rise if he raises the price and subsequently serves only part of the beach. What price must the stall-holder charge in order to maximize the profits? Is he right – will the profits increase because of the new pricing policy?

The fixed franchise fee provides Pancakes Creations to reap a substantial part of the stall-holder's profits. To raise the profits further, the company award a franchise to one additional stall-holder and requires both stall-holders to locate their stalls symmetrically on the beach (that is, one stall will be located at 1/4 and the other one at 3/4 of the way along the beach). Assume that Pancakes Creations fixes the price of pancakes in the franchise contract is such a manner 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.?

Exercise 4

Consider a worker in a firm that has to decide how hard to work. The worker’s effort e, with 0 e ≤≤1, has a disutility for the worker equal to -e/2. The worker gets wage 0 < w < 1. The worker’s utility is therefore

U = w - e2/2

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 chooses effort e to maximize own utility (subject to the constraint 0 ≤ e ≤1). What is his optimal choice of effort e?

The firm doesn’t like the above outcome and decides to monitor the worker with probability P to induce the worker to put forth 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 receives 0 wage. If the firm doesn’t monitor the worker or doesn’t fire him, he gets wage w. The worker maximizes the anticipated wage payment minus the effort cost.

b. Write down the anticipated utility of the worker and solve for the utility maximizing effort e. How does the worker’s optimal effort depend on P? Give intuition.

c. Assume the firm’s monitoring costs are equivalent 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. Suppose now, however, that the worker is altruistic toward the firm. That is, the worker maximizes

W - e2/2 + e α, where the last term is the product of the altruism coefficient α (∈ α  (0,1]) 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 raises?

e. Assume the firm can choose between two applicants for the job: a selfish worker who selects effort according to your answer under c. and an altruistic worker who is insensitive to monitoring and selects effort according to your answer under d. Which worker will the firm hire?

(Hint: the answer based on the monitoring costs parameter γ and the altruism parameter α.)

Bonus assignment

The Wikipedia website comprises an item on ‘perverse incentives’. It describes a perverse incentive as “an incentive that has an unintended and undesirable result which is contrary to the interests of the incentive makers.” The website offers various striking examples of perverse incentives. For illustration, “19th century palaeontologists travelling to China employed to pay peasants for each fragment of dinosaur bone (dinosaur fossils) that they produced. They later discovered that the peasants dug up the bones and then smashed them in many pieces, greatly reducing their scientific value, to maximise their payments.”

a. Illustrate the perverse incentive.

b. What makes the incentive perverse?

c. How could the incentive makers improve the incentive?