L9: Models of Oligopoly

Question 1

stackelberg oligopoly

Answer 1

similar to cournot but sequential game where one firm chooses quantity before the other

Question 2

cournot duopoly vs. stackelberg

Answer 2

firm 1 produces more when they can move first in stackelberg
- total quantities are bigger in sequential rather than simultaneous game

being leader lets firm 1 ‘sculpt’ the outcome
- makes them better off and hurts firm 2

industry is more competitive since it supplies more quantity and price is lower in stackelberg

firm 1 has to be able to commit to its quantity or else we’re back to simultaneous cournot

Question 3

bertrand oligopoly

Answer 3

firms choose prices instead of quantities

with homogenous products, consumers buy from the lowest-priced firm

equilibrium where firms end up profit pricing at MC and the model converges to perfect competition

Question 4

bertrand equilibrium

Answer 4

if p2 > c, firm 1 never sets p1 > p2

p1 = p2 > c is not an equilibrium either
- firm 1 can just drop price slightly to get more of the market
- unilateral deviation makes one firm better off

p1 = p2 = c is an equilibrium
- no profit for either firm as a nash equilibrium

Question 5

comparing models

Answer 5

bertrand paradox where you achieve perfect competition and profit goes to 0

bertrand predicts lower prices, higher quantity and lower profits than Cournot
- price is highest in monopoly, lower in cournot and lowest with bertrand where they are equal MC
- outcome is lowest with monopoly, goes up with cournot and is maximised at bertrand
- profits are the highest under the monopoly, lower with cournot and 0 in bertrand

Question 6

variants of bertrand

Answer 6

cost heterogeneity so a firm can sustain profits

capacity constraints
- one firm cannot serve the whole market

differentiated products
- products are not perfect substitutes

consumer search
- effective competition is weaker than the number of rivals

Question 7

bertrand with cost heterogeneity

Answer 7

if c1 < c2, no equilibrium at p > c2

once p = c2 - e, firm 2 cannot decrease below this
- firm 1 will set a price right below the marginal cost of firm 2

equilibrium in this case involves profits for firm 1

Question 8

bertrand with capacity constraints

Answer 8

MC is 0 when firm is producing below capacity, but goes up to infinity if firms want to produce over fixed capacity

firms compete by simultaneously announcing prices and the buy purchases from the firm quoting the lowest price
- if they have the same price, buyer splits purchases equally
- if the low-price firm has insufficient capacity to satisfy demand, buyer purchases residual from high-price firm

Question 9

small capacity case in bertrand with capacity constraints

Answer 9

v is the maximum price consumers are willing to pay
- pure strategy nash equilibrium with p1 = p2 = v and profit1 = profit2 = vK (maximum capacity)

firms are both making profit since they have limited capacity so they are not competing and undercutting each other
- no incentive to undercut if that decreases sales

capacity constraints lead to profits, enough to depart from the bertrand paradox

Question 10

large capacity case in bertrand with capacity constraints

Answer 10

rule out any case where prices are slightly differen
- the firm with the lowest price will increase price by a big to gain more of the market

also rule out p1 = p2 > 0
- either firm can increase profits y slightly undercutting the other

also rule out p1 = p2 = 0
- either firm can earn positive profits by setting p = v
- better to deviate and go up to v to get residual demand

no static pure strategy equilibrium, only mixed strategy equilibrium

dynamic equilibrium that leads to Edgeworth cycles
- one firm raises price quickly, then the other follows dynamically
- then cut prices slowly until getting to MC, repeat