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Universidad Carlos III de Madrid – Departamento de Economía Principles of Economics – Year 2013-2014 Problem Set 6
Conceptual questions (For grading)
- When do we say that a seller has monopoly power? Please, indicate
some reasons for monopolies to arise.
When a seller is the only one that sells a good which does not have close substitutes, we say that seller has monopoly power since the seller does not have any competitors, it can alter the selling price in order to maximize its benefits. Four reasons for monopolies to arise (See Angel’s slides):
- Only one firm is the owner of an essential resource.
- Only one firm has the exclusive license to produce a good or exploit a resource.
- The cost of production is lower when the good is produced by only one firm (Natural Monopoly).
- One firm adopted methods to limit the entry of its competitors.
- What condition must a firm satisfy in order to maximize its profits when it is
part of a perfectly competitive market? Why is marginal revenue equal to the price in
a perfectly competitive market?
In a perfectly competitive market, the MC=P condition must be satisfied in order to maximize firms’ profits. Here MR=P is because firms are price takers in competitive market; they cannot alter the market price but sell any quantity they want at the market price.
- What condition must the firm satisfy in order to maximize its profits when it is
a monopolist? Why is marginal revenue lower than the monopolistic price? Why does the “price effect” exist in a monopoly?
As a monopolist, the condition MC=MR must be satisfied in order to achieve the maximal profit. The marginal revenue is lower than the monopolistic price is because the marginal revenue is lower than the demand curve. There exists a price effect. In order to sell one more unit, the monopolist has to reduce the price and hence gets less revenue from the units that were already sold out.
- Given the profit-maximizing condition, how does the monopolist know what is the price that consumers are willing to pay for the quantity that maximizes profits?
Given the profit maximizing condition, monopolist determine the quantity to produce, and the price is the one under which all consumers will buy that quantity exactly.
- How is welfare affected when a market goes from perfect competition to
monopoly? Who suffers most the inefficiency or welfare loss that arises from the monopoly? Can an economic authority do something to fix this inefficiency?
Compared with the perfect competition, the price in monopoly is higher and the quantity is lower. The total surplus decreases. Consumers suffer most from this decrease
Answer:
a) Fill the form
Quantity Price in Total Average Marginal demande d
euros of
revenue revenue revenue
of kWh one kWh
(TR) (AR) (MR)
0 8 0
1 7 7 7 7
2 6 12 6 5
3 5 15 5 3
4 4 16 4 1
5 3 15 3 -
6 2 12 2 -
7 1 7 1 -
8 0 0 0 -
The graph of the demand curve is:
The algebraic expression of the demand is a linear equation. The quantity demanded, Qd, can be represented as Qd= a + b p. a is the quantity demanded when p=0, thus a=8. b is
the slope, thus, b =-1. The algebraic expression of the demand is Q d=8-p.
The graph of the marginal revenue is:
b) The graphic representation of the average revenue and marginal revenue:
The average revenue can be expressed as AR= a + b Q. b is the slope, thus, b =-1. We can use the point in Q=1 to calculate a. We will have 7= a + b ·1. Given that b =-1, we will obtain 7= a -1, so a =8. The algebraic expression of the average revenue is AR=8 - Q.
The graphic shows that the marginal revenue is below the average revenue.
c) The quantity that maximizes the monopolist’s profit satisfies MC=MR. The MC is 3 and the quantity for which MR=3 is QM=3. The monopolist price will be the Price for
which the demand is 3. This price is P M=5.
d) In order to remove the inefficiency, the economic authority should chooseP=3 and Q=5. In this point P=MC.
The shaded area in the graphic is the deadweight loss. This loss is due to the fact that with monopoly the quantity produced is lower than the quantity that maximizes the total
surplus.
Please, grade your homework according to the range indicated in the table.
1 2 3 4 5 6 7a 7b 7c 7d 8 Total A B C D A: 9-
B: 7-
C: 5-
D: 1-
Problem (Solved)
The total cost function for a monopolist is CT = Q^2 + 100Q + 500 and the market demand for the product is Q = 4(200 – P).
a) Calculate price and quantity that maximize profits and the value of the latter.
b) If this market magically becomes a perfectly competitive market, what would be the equilibrium quantity and price?
b).)c Under each of the previous conditions, obtain and compare surpluses, of consumer, of producer, and total.
d) Assume that the government knows total cost of production in this market and decides to intervene setting a price equal to that of perfect competition. In addition the government decides to auction a license for just one firm to operate in this market. How much will be monopolist be willing to offer for this sole license?
Solution
a) In order to obtain the price, the quantity and the maximum profits of the monopolist, we are going to change the demand function to its inverse form, that is, price as a function of quantity instead of quantity as a function of price:
Q = 4(200 – P); Q/4= 200 – P; P = 200 – Q/ MR = MC MC is the derivative of TC
The total revenue of the monopolist is TR = P*Q = (200 – Q/4)Q, that is, TR = 200Q – 1/4Q 2. Then, we can obtain the marginal revenue: MR = ΔIT/ΔQ = 200 – 1/2Q. We can also calculate the marginal cost MC = ΔTC/ΔQ = 2Q + 100.
Since MC = MR, we obtain: 2Q + 100 = 200 – 1/2Q. That is, 5/2Q = 100. Thus, Q = 40. Substituting Q = 40 in the inverse demand function, we get P = 200 – 40/4 = 190.
Therefore, the monopolist’s price is P = 190 and the monopolist’s quantity is Q = 40, so total revenue of the monopolist is TR = PQ=19040 = 7600. Now we can calculate
total cost of producing 40 units: TC = 402 + (100*40) + 500 = 6100. Thus, the monopolist’s profits are 7600 - 6100 = 1500.
b).)d In perfect competition, the equilibrium is reached when the demand (P = 200 –
Q/4) equals the offer (CM = 2Q + 100). Since P = CM, that is, 200 – Q/4 = 2Q + 100 we
obtain Q = 44.44. This quantity can be sold at the price P = 200 – 44.4444/4 = 188.
b).)e We calculate now the surpluses and compare them. In the monopoly: CS = 200 and
PS= 2000. Under perfect competition: CS = 246.42 and PS = 1973.58. TS =
