Problems Sheet I. Concentration, Monopoly and Prices Discrimination
Industrial Economics
Universidad Carlos III
1. Given the following percentage concentration measures in two different industries (A and B)
% /A
/B
The largest 4 / 40 / 60The “ 8 / 70 / 80
The “ 12 / 90 / 84
The “ 20 / 100 / 90
Total enterprises number:20 / 40
a) Draw up the concentration curves for the two industries (A and B) and arrange them in accordance with the concentration degree.
b) If we use the concentration index of the largest 4 and 12 enterprises of each industry, what would the order (as per concentration degree) be reached? What don’t index desirable properties comply this measure?
c) Draw up the concentration curve of an industry involves a number n of enterprises with the same size (and sales). But it might go up when a new enterprise break in , so they don’t meet all the Hannah and Kay criteria. Accordingly, it gives rise to a serious problem. Therefore this index has to be cautiously used. Comment.
2. In the light of Table I:
a) Comment if the concentration degree in the British industry seems to you reduced or high and why.
b) Arrange the indicated industries with an asterisk according to its concentration degree by using RC5 and the inverse of the producers number. Do the results coincide? Explain why and what of the two measures seem to you the best.
d) In case you could draw the concentration curves of these industries Do you think that any of these would cross each other? Give some examples and argument your answer.
c) The Herfindahl index measures the concentration in the industry
d) In the light of the data what would you tell about the relative size of the sixth enterprise of the sugar sector?
3. Be P(q)= 52-2q the demand inverse curve of a goods recently introduced in the market and C(q)=90+5q2 its total production costs. Suppose the government made a prices regulation in such a manner than they have to be equal to the average costs. In this very case,
a) What is the efficient number of enterprises (on the basis of minimal cost) in this industrial sector? Justify your answer.
Along the time, the consumers worth better the goods (a larger portion of people know it) by resulting in an increase of the demand up to P(q)=55-2q. The fixed costs decrease and during this period their value is 62.5
b) Demonstrate the sector drops out to be a natural monopoly.
TABLE I
INDUSTRIES (FOUR DIGITS) HIGHLY CONCENTRATED IN THE MANUFACTURES, UNITED KINGDOM [1]
CONCENTRATIONRATIO / PRODUCERS
TOTAL NUMBER
GROUP 1 (C5 > 95%)
* Sugar / 99.9
* Margarine / 100.0 (7) / 7
Gin / - / 9
* Cigarettes / 100. 0 (7) / 7
* Other manufactured tobacco / 98.8 / 8
* Petroleum derivate / 100.0 (7) / 7
* Hydrocarbon derivated Halogens / 99.9 / 9
* Asphalt / 100.0 (7) / 7
* Additives for liquid combustibles and oils / 95.1 / 28
* Telecommunication wires / 95.3 / 14
* Telegraph and Telephone installations / 98.9 / 13
* Tractors / 95.7 / 11
* Cars / 98.2 / 20
* Aeronautic Industry / 100.0 (7) / 7
Refinement of precious metals / - / -
* Artificial and synthetic fibres / 95.4 / 14
* Tyres and air chambers / 96.4 / 8
GROUP 2 (C5 > 90%)
* Cornflakes for breakfast / 91.4 / 16
* Ice creams / 90,9 / 29
* Crisp / 94.7 / 10
* Pets feed / 94.4 / 39
* Coffee / 90.6 / 20
* Synthetic Rubber / 91.9 / 12
* Roller Bearing / 92.4 / 15
* Batteries and Accumulators / 90.8 / 19
* Internal combustion Machinery / 91.4 / 20
* Tins and Cans / 91.5 / 57
* Cement / 93.0 / 10
4. A monopolist sells an homogeneous goods with facing a demand given by P = A-BQ. The monopolist fixes an unique price in the market. Demonstrate the monopolist will never sell a quantity higher than (A/2B) regardless the costs function. When will the monopolist production optimal quantity be A/2B?.
5. A monopolist comes up against a demand curve given by P=A-BQ being its costs function C=Q2.
a) Calculate the quantity and the price that maximize the monopolist profits.
b) From the social point of view what is the optimal quantity?. Calculate the well being loss due to the monopoly.
c) What are the monopolist profits if it produces the socially optimal quantity?
d) Let’s suppose the government restrict the monopolist to fix a price higher than Po, that is 0>Po>A. What is the effective demand curve the monopolist come up against?
e) Demonstrate that there is a maximum price leading the monopolist to produce the optimal quantity from the social point of view (the one that the marginal cost is equal to price)
6. Be the monopolist costs function C(q)=2q and the demand the monopolist come up against D(p)=10-p
a) Calculate the subsidy to the quantity produced by the monopolist if it is intended that this is the optimal quantity from the social point of view. (Suppose the government knows the demand and the costs conditions)
b) Suppose that the government doesn’t know the marginal cost is equal to 2. But it advises the monopolist about the subsidy policy stressed in the paragraph (a) and is asked about its marginal cost c. Demonstrate the monopolist is prompted not to tell the truth. What is the c optimal notice for the monopolist?
7. Suppose a monopolist with constant marginal costs and lineal demand p=1-Q. Its demand landslide as result of the entry of a new group of consumers to the market. The tax income distribution and preferences of the new consumers are the same as the initial population. How will the monopolist optimal price change?. Make it up.
8. The inverse function of the market demand of a goods is p(x)=30-x. In the market a monopolist whose costs function C(x)=10x2+x exist.
a) Find out the quantity offered by the monopolist, the market price and the corresponding profits.
b) Define and calculate the Lerner market power index. Also, find out the demand resilience in comparison with the price.
c) Let’s suppose the monopolist faces a lineal demand, p(x)=a-x and it produces with the costs (C(x)=cx Calculate in what ratio an unit increase will be apply on the unit costs in c at the balance price pm (this ratio will be given by dpm (c )/dc).
9. Be the demand inverse functions of two goods:
P1=12-q1-eq2
P2=12-q2-eq1
Where e>1
a) For what values of e are the goods substitutive? Complementary? Independent?
b) Be C1(q1)=2q1 and Cx(q2)=2q2 the production costs of the goods produced by a monopolist. Compare the Lerner index in each market with the inverse one of the demand resilience for e different value.
c) Resolve for e=1/2 and e=-1/2. In what of the two cases are the prices higher? Why?
10. A monopolist has an unique consumer with demand function q=74q. Its marginal cost is equal to 0.
a) What is the optimal fixed price on the basis of a lineal tariff? And based on a tariff in two parts? Compare the previous examples in terms of social welfare. Comment.
b) Let’s suppose that there are two type of consumers with aggregated demands q1=66-p1 and q2=82-p2 at equal proportions and each equal to 0.5. Suppose that there is perfect arbitrage among the single flock consumers but not among the different type consumers. And, yet, the monopolist knows how to recognise the type of consumers that break in his outlet. What type of prices discrimination can the monopolist apply? Calculate the profits by explaining of the necessary steps to obtain the result.
Answer the following question without any calculation. Will the welfare increase whether the government prohibit any sort of prices discrimination?
c) Suppose the monopolist is unable to recognise the type of consumer that break in its outlet. As yet, no arbitrage among the single flock consumers exist. Nor among different type consumers? What type of prices discrimination could the monopolist apply?. Divide the optimal tariff in two parts? Calculate the monopolist profits?
11. Consider a monopolist that faces a lineal demand p=a-bx and produces with the costs C(x)=cx
a) Demonstrate the demand resilience is a growing function in x.
b) Compute the well being loss owing to the monopoly existence (compare the monopoly total surplus with the one of the perfect competitiveness. How does this relative loss change in respect to the parameter b? (Use a graph to draw up the changes in the excess).
c) If the monopolist discriminate in first degree in prices, find out the consumer excess plus the producer excess and compare them with the perfectly competitive case. Is there welfare loss?
d) Suppose that the monopolist faces the lineal demand p=90-x and produces with the total costs C(x)=2x+F, where F=90 is the fixed cost the monopolist has to apply if his produces a positive output. The Regulator Authority intend to reach the optimal TOP.
It suggest the monopolist to follow the rule, p=marginal cost. Find the monopolist profits and the total excess.
e) Without regulation, what would the balance of monopolist be? Would the optimal TOP be reached? Calculate the difference in terms of welfare between the initial allocation (with regulation) and the alternative allocation
12. A monopolist comes up against two types of consumers. There are 100 identical consumers of each type. The production has cost 0. The individual demand function for a consumer of type I, I=1,2 are given by:
D1(p)=1-0.02p
D2(p)=1-0.04 p
a) Suppose a monopolist has no information about the type of consumer and intend to practice a second degree discrimination by fixing a tariff in two parts such as T(q)=A+ pq. Calculate the A and p values as per tariff in two optimal parts. Calculate the consumers excess.
b) Suppose that a new decoder (at 0 cost) has been developed with enabling the monopolist know the type of each consumer. As yet, the goods is as such manner than arbitrage among consumers is not possible. The monopolists intend to practice discrimination with fixing tariffs such as type Ti(q)=Ai+piq for consumers type I, I=1,2. Determine the Ai and pi optimal values. Does the well being maximize?
c) Suppose the situation is the same as the case (b) except that the perfect arbitrage among the single flock consumers is possible, but not among consumers of different type. Calculate the price and the quantity sold in each market under a third degree discrimination. Compare the total excess of the cases (b) and (c).
13. A monopolist produces a goods x for two markets, the domestic, country a, and the export, country b. Both markets are segmented, that is, there is no arbitrage chance for consumers. The monopolist doesn’t know the goods assessment by each consumer (only knows he the each market total demand). Both country has the same currency (there is no exchanging rate). The monopolist faces two demands, one in each country that are, respectively:
qa=100-pa
qb=200-2pb
And produces with a production costs: C1(q)=q
a) In what market does a larger demand resilience occur?
b) Find out the monopolist balance, how much he will produce and at what price in each country?. What type of price discrimination will the monopolist practice?
c) Stress if does the resilience inverse rule in the prices policy applied by the monopolist complies.
d) Give an example where the inverse resilience rule for a multiproduct monopolist does not comply.
14. Suppose that a goods monopolist sells consumers located in different regions of the country. The goods demand functions in each region are:
Q1=1-p1 and q2=0.5-p2
And for the following case, suppose the production costs are equal to 0.
a) If the monopolist has to charge an uniform price (lineal) in both regions, calculate the uniform price that enables to maximize the profits.
b) Suppose the monopolist can adopt a third degree prices discrimination. Calculate the profits maximum driven prices in each region.
c) The third degree prices discrimination does it enable to increase or to decrease the mean welfare, in this very case, by the sum of the consumer and the producer excess? Is that an overall result when the monopolist uniform prices are compared with the third degree discriminator prices?
15. Consider a company that offers its product in two countries. The selling price in the domestic market is higher that in the foreign market. The company profits are distributed in the origin country. This practice is called “dumping” is pursued by the GATT and b some governments as well.
a) What type of prices discrimination represents the “dumping” practice?
The goal of this exercise is to analyse the “dumping” effects on the walfare and to determine who wins and who loss.
Suppose that the company is a monopoly in both markets, that the costs are lineal C(q)=cq, the domestic demand function is q=1-p and the foreign demand es q=1-Bp where B>1.
b) Demonstrate or refuse each of the following assertions for the proposed model: The consumers of the foreign country prefer the dumping at an uniform price in both countries whereas the origin country consumers prefer the uniform price.
c) From the efficiency point of view dumping is good for the world wide economy (on the grounds that it gives rise to a Total Surplus higher than an uniform price). The efficiency in the foreign country increases by the dumping effect, as well.