Potential Mid-term Exam Questions
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) 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) 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) Will the monopolist choose high quality or low quality?
b) If monopoly pricing is assumed then is the monopolist's choice of quality efficient?
3. Durable goods monopoly.
a) 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the buyer with 2 periods of use if it is bought in period 1 and only 1 period of use if bought in period 2 (i.e. good is obsolete after period 2).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) 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) Indicate which option in part b) yields the highest welfare.
4. Economies of scale and scope, Market Structure and Market Power
a) Explain the sources of economies of scale and scope
b) Explain the determinants of market structure.
c) 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) 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) Find the profit maximizing prices, quantities and profit if the monopolist can price discriminate.
c) 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) 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) 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) 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) 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.
7. Versioning
a) 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.
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Version
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Student
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Professors
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Consultants
|
|
Basic
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$50
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$x
|
$100
|
|
Full
|
$100
|
$150
|
$400
|
b) 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) Let x = 80. Repeat part b).
8. Bundling and Mixed Bundling
a) What is bundling? Give examples. Under what circumstances is bundling more profitable than selling goods individually?
b) What is mixed bundling? Give examples. Under what circumstances is mixed bundling more profitable than bundling?
c) 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).
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CDs
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Romantic
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Neoclassical
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Tchaikovsky lover
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Sophisticate
|
|
Berlioz/Tchaikovsky
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$8
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$5
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$9
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$2
|
|
Bartok/Stravinsky
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$6
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$5
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$2
|
$9
|
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) 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 (h) and (iv) Welfare (W). Verify that L = H/h.
b) 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 N 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) 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) 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) 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.