Industrial Organisation And Competition Policy

Question 1

What is the Bertrand unique Nash equilibrium in pure strategies in competition with market power and why?

Answer 1

• The unique Nash equilibrium in pure strategies (with prices being chosen from a continuous interval) is {c, c}. Pricing at marginal cost.
• The Bertrand paradox. The competitive outcome arises with only two firms.
• Why is {c, c} an equilibrium? Suppose, given P2 = c, firm 1 sets P1 > P2. It still earns 0. Suppose instead P1 < P2 = c. Then 1 makes a loss. Payoff for 1 when P1 = c is at least as high as with any other price. Same reasoning applies for 2.
• Why is the equilibrium unique? Sketched answer: suppose there’s another equilibrium at a different common price. If P1 = P2 > c then a firm benefits by undercutting. If P1 = P2 < c then a firm benefits by raising its price to avoid a loss.

Question 2

what is the difference between vertically and horizontally differentiated products?

Answer 2

vertically differentiated products vary in quality and horizontally differentiated products vary on dimensions other than quality and are not perfect substitutes

Question 3

Bertrand model with horizontally differentiated products?

Answer 3

Q1(p1, p2) =a − bp1 + gp2;
Q2(p1, p2) =a − bp2 + gp1

b>0 because demand for a good is decreasing in its price
g>0 because goods are substitutes
b>g so that if both prices rise by the same amount demand falls

Question 4

why does price in oligopoly exceed exceed marginal cost whilst it doesn’t when products are identical

Answer 4

▶ Product differentiation gives each firm some market power
▶ Starting with price equal to c, an increase in price does not drive that firm’s demand to zero: it now sells a positive quantity at a positive profit margin
▶ The “Bertrand Paradox” is a knife-edge result that depends on the assumption that goods are perfect substitutes
▶ But while profits and prices are higher than in competitive markets, they are still lower than in monopoly
▶ Some profit gets “competed away”

Question 5

What happens if firm 1 has a lower marginal cost in Cournot?

Answer 5

▶ Suppose firm 1 has a lower marginal cost
▶ 1’s best response shifts out
▶ Direct effect: Firm 1 produces more (horizontal shift in BR1)
▶ Strategic effect: Firm 2 produces less, inducing 1 to increase output even further
▶ The strategic effect is positive because outputs are strategic substitutes

Question 6

How does the number of firms affect whether collusion is sustainable?

Answer 6

• Infinitely-repeated Bertrand oligopoly game
• n firms, identical constant marginal costs, no fixed costs, identical products, no capacity constraints
• Π(pm) > 0 is the industry profit when all firms set the collusive price pm
• Payoffs: collusion Π (𝑝𝑚)/𝑛 ; deviation Π (𝑝𝑚) ; punishment 0. Discount factor: δ = 1/(1 + r), r > 0

collusion sustainable with grim trigger strategies if δ> (n-1)/n = 1 - 1/n

if frequency of sale is different this is different - harder to maintain collusion when frequency of sales less frequent. also harder to maintain collusion if cheating less easily detectable

Question 7

What is a vertical and horizontal merger?

Answer 7

Horizontal merger: Merger between companies that operate in the same part of the supply chain
Vertical merger: Merger between companies that operate in different parts of the supply chain

Question 8

What do the Lerner index and Herfindahl index measure?

Answer 8

The Lerner index, L = (P−MC)/P , measures market power

The Herfindahl index, the
sum of the squared market shares, H = Σis^2i, measures
concentration.

A merger leads to an increase in H

Question 9

What is the diversion effect

Answer 9

▶ Firms A, B, C , . . . , Z set prices to maximize profits
▶ Each trades off the benefit of a higher profit margin against the loss of sales
▶ If A and B merge, what happens to their prices?
▶ If A raises its price a little, it loses some demand
▶ The demand that goes to its remaining rivals C , . . . , Z is lost
▶ But the demand that is diverted to B contributes to the joint profits of A and B
▶ So A, and B, will want to raise their prices
▶ The greater the diversion of demand to B the more the merged firm will want to raise pA
▶ Best responses are upward-sloping, so others will also raise their prices
▶ A merger is very likely to be profitable
▶ Firm A will want to increase its price in a merger with B if:
B’s pre-merger margin × Diversion RatioAB > Fall in MCA
▶ Take-away: the larger the existing market share of the partner, the greater the price-increasing effect of the merger