Question

1. Set a question related to the issue of “regulation of monopoly”. Provide the appropriate answer to this question.

2. a) Explain why a perfectly discriminating monopolist is efficient.

b) Why will a monopolist that is able to perfectly price discriminate sell more than a non-discriminating monopolist?

3. Popular movie video DVD copies are often sold for $MOP 70 to $150, whereas less popular movies can sell for more than $MOP 200. Why? (Hint: Use the model of third degree price discrimination.)

Answer 1

1.The government may wish to regulate monopolies to protect the interests of consumers. For example, monopolies have the market power to set prices higher than in competitive markets. The government can regulate monopolies through:

• Price capping – limiting price increases
• Regulation of mergers
• Breaking up monopolies
• Investigations into cartels and unfair practises
• Nationalisation – government ownership
• 2.a) if the monopolist can identify buyers by their reservation values and set different prices for different buyers, and buyers do not have the possibility of trading between themselves, then even if it sets a price for each buyer just below her reservation value, that buyer will still purchase the good. Assuming that a buyer who is faced with a price equal to her reservation value buys the good (she is indifferent between doing so and not buying) then the monopolist's optimal strategy is clear: set a price for each buyer equal to her reservation value.

(Note that if the buyers can trade between themselves then this strategy may come unstuck: buyers with low reservation values may be able to buy many units of the good, and re-sell some of them to buyers with high reservation values. In some cases, a monopolist can prevent such trades. For example, in the case of admission to a movie, admission may be granted to an adult only if she is in possession of an adult ticket.)

How much should the monopolist produce in this case? So long as there is a buyer whose reservation price exceeds the monopolist's marginal cost, it is in the interest of the monopolist to sell to that buyer. Thus the monopolist will produce the output y for which MC(y) is equal to P(y). That is,

the optimal output of a perfectly discriminating monopolist is Pareto efficient!

Ordinary price discrimination

A monopolist cannot usually discriminate perfectly between buyers, since it does not know each buyer's reservation price. Nevertheless, it may be able to charge different prices to different types of buyer, achieving some degree of discrimination. (For example, Bell Canada charges different prices to businesses and to individuals; airline charge different prices to people who can reserve in advance and those who cannot.)

Suppose that the monopolist can separate the market into two parts, one in which the inverse demand function is P1 and one in which it is P2. Then its total revenue functions in the two markets are TR1(y) = yP1(y) and TR2(y) = yP2(y). The monopolist's profit-maximization problem in this case is to choose outputs y1 and y2 for the markets to solve

maxy1,y2 (y1,y2) = maxy1,y2 [TR1(y1) + TR2(y2) TC(y1 + y2)].

At a solution to this problem the value of y1 must maximize profit, given the value of y2, and the value of y2 must maximize profit, given the value of y1. Thus the following conditions must be satisfied:

MR1(y1*) MC(y1* + y2*) = 0

MR2(y2*) MC(y1* + y2*) = 0.

We can write these conditions alternatively as

MR1(y1*) = MR2(y2*) = MC(y1* + y2*).

(As in the case of a monopolist setting a single price, values of y1* and y2* that satisfy these equations may correspond to minimum profit rather than maximum profit, and if the monopolist's profit is negative when it chooses y1* and y2* then it should instead produce nothing.)

Relation with the elasticity of demand

We have MR(y) = P(y)[1 1/|(y)|], where (y) is the elasticity of demand at y. Thus if y1* and y2* satisfy the conditions above then

p1[1 1/|1(y1*)|] = p2[1 1/|2(y2*)|].

Suppose that the elasticities are constant, independent of demand. Then the condition is

p1[1 1/|1|] = p2[1 1/|2|],

or

p1		1 1/|2|
	=
p2		1 1/|1|

Thus if |1| > |2| then p1 < p2. [Try 1 = 4 and 2 = 2: then p1/p2 = (11/2)/(1 1/4) = (1/2)(4/3) = 2/3.]

That is:

a monopolist charges a lower price in a market in which demand is more elastic.

3.Third Degree Price Discrimination involves charging a different price to different groups of consumers for the same good. These groups of consumers can be identified by particular characteristics such as age, sex, location, time of use.

In the real world, third-degree price discrimination is quite common. For a firm to practise price discrimination it requires:

• Ability to set prices. Some market power.
• Ability to segment different classes of consumers (e.g. rail card to prove you are a senior citizen)
• Ability to prevent resale. E.g. stop adults using student tickets
• by doing so less popular movies can sell Movie DVD for more than $MOP 200.