Economics GU 4251: Industrial Organization
Spring 2024: Problem Set 3
Handed out: February 20, 2024
Due: February 29, 2024, 11:59pm
Problem 1.
Consider a Cournot oligopoly with n = 2 firms. Firm 1 cost function is TC1 (q1) = 20 + 12q1 + q1(2), while firm 2 cost function is TC2 (q2) = 50 + 8q2 + q2(2) . The total market demand is P(Q) = 50 − 2Q, where Q is the total quantity produced by all (active) firms in the industry.
a- Compute the Cournot equilibrium total quantity, price, quantity for each firm, and profit for each firm. Which firm is making higher profits?
b- Consider the situation in which a third firm (firm 3) enters the market. What is the total equilibrium quantity, price, quantity and profit for each firm if TC3 = TC1 ? [hint: q1 and q3 will be the same, since 1 and 3 are identical]
c- How would your answer at point b change if instead TC3 = TC2 ? Would consumers prefer firm 3 to enter with the total cost of firm 1 or firm 2?
d- What would be the highest one-time cost that firm 3 would be willing to pay to enter the market and then compete in a Cournot game with total cost equal to firm 1?
Problem 2.
Two firms produce a homogeneous product. Inverse demand is P(Q) = D − Q. Firm 1 has a constant marginal cost of c1 and firm 2 has a constant marginal cost of c2 .
Assume that D > c2 > c1 > 0.
a) Solve for the competitive equilibrium price and output level for each firm.
b) Solve for the Cournot equilibrium price and output level for each firm.
c) What is the total deadweight loss arising from Cournot competition in this market?
d) Productive inefficiency refers to the extra costs to produce a given amount relative to the lowest cost method of producing that amount. How much of this loss is due to productive inefficiency rather than market power?
Problem 3.
N=2 video broadcasting websites, You and Twi, must decide the number of minutes of ads to be displayed for every video that the user elects to watch. One ad-minute is worth 0.01 (this is the revenue that platforms collect from advertisers).
Let ty be the number of ad-minutes per video set by You, and tT the number of ad-minutes per video set by Twi. Streaming one video costs You Cy = 0.02, while it costs Twi CT = 0.03.
There are 100 million potential users, and each watches videos according to the following demand curves:
qy(ty,tT) = 10 − 2ty + tT
qT(ty,tT) = 10 − 2tT + ty
a- What is the “cross-ad-minute” elasticity between You and Twi? That is, how many users switch from You to Twi (and viceversa) if ty (tT ) increases?
b- Suppose, for now, that You and Twi enter an (illegal) agreement by which they set
ty = tT = t. Derive the total number of videos watched in the market as a function of t.
c- Derive the profits for each website as a function of t. (Hint: if the number of per-user videos streamed is qi (ti, t−i) the revenues per-user are 0.01ti × qi (ti, t−i) , since each ad-minute is worth 0.01 .)
d- Now let the two platforms compete by each setting their number of ad-minutes:
i. What is the best reply of You? What is the best reply of Twi?
ii. Find the Nash Equilibrium of the game.
iii. How many total users choose You and how many total users choose Twi?
iv. [EXTRA] Would you expect consumers to be better off if platforms were
offering a flat-fee to experience the websites without ads? (No math needed, discuss!)
Problem 4 (extra, can be challenging)
Consider a simple Bertrand market in which N=3 firms compete by setting prices. As long as they can purchase for less than 20, 10 million consumers select to buy the good from the cheapest firm, and breakindifferences at random with equal probabilities if more than one firm set the lowest price.
a- The three firms have equal marginal costs c1 = c2 = c3 = 5. Derive the demand and payoff function of each firm i as a function of the prices in the market.
b- What is the set of non-dominated strategies (or prices) for each firm?
c- Derive the Nash Equilibrium of this game.
d- How do total consumer surplus, welfare, and profits in the market change relatively to a- above if firm 1 becomes more efficient, and specifically if c1 = 2 < c2 = c3 = 5?
e- How does total consumer surplus, welfare, and profits in the market change if
relatively tod- above, while firm 1 becomes more efficient, firms 2 and 3 experience a cost-increase (e.g. inputs become harder to procure) so that c1 = 2 < c2 = c3 = 7?
f- In parts a,d,e, is there any deadweight loss due to productive inefficiency (see
Problem 2 for a definition)? Is there any deadweight loss due to market power? Is there any decrease in consumer surplus due to market power? Discuss.