# Perfect competition, welfare and entry

Fall 2015

The mid-term exam will be held on Saturday, October 31, 3:30-5:00 pm. The exam will consist

of questions taken from the list of potential questions below. The questions will be exactly the

same as those on the list below except that some of the numbers may change. Allowable exam

aids are a calculator. Exam is 1.5 hours long and consists of 3 questions (no choice).

Potential Mid-term Exam Questions (each question is worth 20 marks)

1.

Perfect competition, welfare and entry. A perfectly competitive market consists of 3 firms.

Total cost functions for each firm are given by C = 2q + 0.25×(q)2 + 256. Market demand is

given by QD = 388 – 2P.

a) (10 marks). Derive the supply curve for each firm (be sure to indicate at what price the

firms shuts down). Solve for the short-run equilibrium (i) price (ii) industry output (iii)

output per firm (iv) profit per firm (v) welfare

b) (10 marks). Solve for the long-run equilibrium (i) output per firm (ii) price (iii) industry

output (iv) number of firms and (v) welfare. Show that entry causes welfare to increase.

2.

Monopoly, welfare and quality choice. A monopolist can produce a high quality product

and face demand of Q = 60 – ½ P, Marginal cost = 12 and Fixed cost = 800 or a low quality

product and face demand of Q = 60 – P, Marginal cost = 4 and Fixed cost equal 100.

a) (10 marks). Will the monopolist choose high quality or low quality?

b) (10 marks). If monopoly pricing is assumed then is the monopolist’s choice of quality

efficient?

3.

Durable goods monopoly.

a) (8 marks). Explain how the market power of the monopolist can be reduced if they sell a

durable good. How can this problem of reduced market power be overcome if the

monopolists leases rather than sells the product.

Consider the following version of the textbook example done in class. A seller has 2 units

of a durable good. The good provides the buyer with 2 periods of use if it is bought in

period 1 and only 1 period of use if bought in period 2 (i.e. good is obsolete after period

2). There are 2 buyers. Buyer 1 values the good at $100 per period in periods 1 and 2.

Buyer 2 values the good at $75 per period in periods 1 and 2. Both buyers get zero value

from the good after period 2. Production costs are zero and there is no discounting.

b) (6 marks) Determine whether the monopolist (i) sells to both buyers in period 1 or (ii)

sells to Buyer 1 in Period 1 and to Buyer 2 in Period 2 or (iii) leases to both buyers in both

periods or (iv) leases to Buyer 1 in both periods.

c) (6 marks). Indicate which option in part b) yields the highest welfare.

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Potential mid-term questions

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Fall 2015

4.

Economies of scale and scope, Market Structure and Market Power

a) (8 marks). Explain the sources of economies of scale and scope

b) (6 marks). Explain the determinants of market structure.

c) (6 marks). What is market power and how is it measured? How is market concentration

measured? What is the relationship between market power and market concentration

according to the Cournot model? How can the relationship between market power and

market structure be explained?

5.

Price Discrimination

a) (10 marks). What is price discrimination? Under what circumstances is it feasible? Why

is it profitable? If a monopolist can practice third degree price discrimination then what is

the profit maximizing pricing rule involving elasticities? Give some examples as to how

this rule is applied in practice. Under what circumstances does price discrimination

increase welfare? Use diagrams to explain your answer.

Suppose that demand is given by qa = 32 – pa in Market A and by qb = 40 – pb in Market B

where pi, and qi are price and output in market i = a, b, respectively. Marginal cost is

constant and equal to 4. Fixed costs are zero.

b) (5 marks). Find the profit maximizing prices, quantities and profit if the monopolist can

price discriminate.

c) (5 marks). Find the profit-maximizing price, quantity and profit if the monopolist

cannot price discriminate. Determine whether it is more profitable to serve both markets

or to serve only Market B.

6.

Two-part tariffs and Block Pricing

a) (5 marks). What are two-part tariffs? Give examples. Why are two-part tariffs more

profitable than linear pricing when buyers buy multiple units? What is the profit

maximizing two-part tariff when all buyers are identical?

b) (5 marks) What is block pricing? Give examples. Why is block pricing more profitable

than linear pricing when buyers buy multiple units? What is the profit maximizing block

pricing quantity and block price when all buyers are identical?

c) (5 marks) Use a diagram to explain the profit maximizing menu of two part tariffs when

there are low demand and high demand buyers. Explain how the monopolist will adjust

the menu when the number of high demand buyers increases

d) (5 marks). Use a diagram to explain the profit maximizing menu of block pricing

quantities and prices when there are low demand and high demand buyers. Explain how

the monopolist will adjust the menu when the number of high demand buyers increases.

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Potential mid-term questions

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Fall 2015

7.

Versioning

a) (4 marks). What is versioning? Give examples. Under what circumstances is versioning

profitable? What are damaged goods?

Suppose that the willingness to pay for different version of a piece of software is given

below for Students, Professors and Consultants. Costs are zero and there are equal

nmbers of Students, Professors and Experts.

Version Student Professors Consultants

Basic

$50

$x

$100

Full

$100

$150

$400

b) (8 marks). Let x = 70.

(i) If the seller offers one version then determine the version offerred, the price of that

version, the number of buyers served, profits and welfare.

(ii) If the seller offers both versions then determine the prices of both versions, the

number of buyers served, profits and welfare.

c) (8 marks). Let x = 80. Repeat part b).

8.

Bundling and Mixed Bundling

a) (4 marks). What is bundling? Give examples. Under what circumstances is bundling

more profitable than selling goods individually?

b) (4 marks). What is mixed bundling? Give examples. Under what circumstances is mixed

bundling more profitable than bundling?

c) (12 marks) The table below indicates the willingness to pay for CDs by various types of

buyers. There are N buyers of each type. Costs are $2.50 per CD. Find prices and profits

when the seller offers the products (i) individually. (ii) as a bundle. (iii) individually and as

a bundle (i.e. uses mixed bundling).

CDs

Berlioz/Tchaikovsky

Bartok/Stravinsky

EC304

Romantic

$8

$6

Neoclassical

$5

$5

Tchaikovsky lover

$9

$2

Potential mid-term questions

Sophisticate

$2

$9

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Fall 2015

9.

Cournot, Market Power and Market Concentration. Consider a market in which there are

two firms who face the inverted industry demand given by P = 260 – Q. Each firm has zero

fixed cost and constant marginal cost given by c1 for Firm 1 and c2 for firm 2.

a) (10 marks). Let c1 = c2 = 170. Solve for the Cournot equilibrium outputs. Use you

solution to calculate the (i) Herfindahl index (H) (ii) Lerner Index (L) and (iii) industry

elasticity () and (iv) Welfare (W). Verify that L = H/.

b) (10 marks). Let c1 = 150 and c2 = 190. Repeat part a). Show that the increase in the

variance of marginal cost has caused H, L and W to rise.

10.

Cournot and entry. Consider an industry consisting of n firms that produce identical

products. There are N buyers in the market and each buyer has a demand curve given by

qd = 20 – P where qd is the amount demanded by each buyer and P is the common

industry price. The number of buyers N is a measure of market size. Market demand is

equal to the amount demanded by all buyers and is thus given by Q = N(20 – P). The

inverted market demand curve is thus given by = 20 − . Each firm chooses output in

Cournot fashion and assumes that price is given by the inverted market demand curve.

Each firm faces constant marginal cost equal to 10 per unit and a fixed cost equal to 100.

a) (6 marks) Solve for the Cournot equilibrium level of (i) output per firm, (ii) industry

output, (iii) price (iv) profit per firm as functions of the number of firms n and the number

of buyers N.

b) (6 marks) If Cournot firms enter until profits are driven to zero then the find the level of

N required for (i) one firm to enter (ii) two firms to enter and (iii) 3 firms to enter.

c) (8 marks). Suppose that N = 20 and n = 2. Use your solutions in a) to find welfare. If a

third firm were to enter (n = 3) then determine whether this firm would earn positive

profits and whether the entry of this firm would raise or lower welfare.

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Potential mid-term questions

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