School

Simon Fraser UniversityDepartment

Business AdministrationCourse Code

BUS 207Professor

Karen RuckmanLecture

8This

**preview**shows pages 1-3. to view the full**9 pages of the document.**Oligopoly

• Market structure where there is a relatively small # of firms competing in a market & there are

some entrance barriers

• Key feature: firms recognize their mutual interdependence

o Know their decisions will affect their rivals & vice versa

o ∴ competitors must determine how rival will respond to their actions

o This problem = realized by the game theory

Models that Recognize Interdependence of D-M:

• Cournot

o 2 firms make simultaneous decisions about how much of a homogenous G to produce

• Bertrand

o 2 firms make simultaneous decisions about the price of a homogenous G

• Stackelberg

o 2 firms make sequential decisions about how much of a homogenous G to produce

Cournot Model

• Assumptions:

o Equal size w/same costs

▪ TC1 = TC2 = cq1 = cq2

▪ 2 firms of equal size, same costs/G produced (homogenous; substitutable)

o Homogenous products

▪ E.g. farmers, vaccinations, anything grown/takes long to manufacture

o Market D curve is downward sloping

▪ P = a – Q = a – (q1 + q2) = a – q1 – q2

▪ Each firm knows the shape of the market D curve ∴ can predict P based on

different total industry Q

o Simultaneous choice of output

o Each firm chooses output by choosing the best response to rival actions

▪ Chooses w/o knowing what the other has chosen

• Problem = solved by: assuming each firm chooses profit maximizing Q by choosing the best

response to rival actions

• Each firm maximizes profits based on an assumed Q that the other firm will produce:

o Fi ’s pofit aiizig 1:

▪ TR = p*q = (a – q1 – q2) * q1

▪ MR = a – 2q1 – q2

▪ C = c*q1

▪ MC = c

▪ MR = MC

• a – 2q1 – q2 = c

find more resources at oneclass.com

find more resources at oneclass.com

Only pages 1-3 are available for preview. Some parts have been intentionally blurred.

• q1 = (a - q2 – c)/2

o Fi ’s pofit aiizig 2:

▪ q2 = q1 = q1 = (a – q1 – c)/2

Graphs and Calculations

• Firm 1 current sees itself as a monopoly but then assumes Firm 2 will produce the same Q

o ∴ must share industry (market) D so DF1 ↓ and q1 ↓ and MR1 ↑

• Reatio f’s slope doads / he 2 = 0, F1has entire market

o As q1 ↑, q2 ↓

▪ But, q1 ↓ by less than what q2 produces

▪ q2 produces more than what q1 ↓ by

o If q2 = 0, then q1 = (a – c)/2

o If q2 = 0, then q2 = (a – c)/2

o Meaning, q1 goes down by q2/2

• Equilibrium Q where both firms maximize profits = q2 = 1/3(a-c)

o Occurs where neither player has incentive to deviate b/c chosen a strategy that

maximizes profits, given the strategy of the other firm (Nash Equi)

• Market:

o Q = q1 + q2

▪ = 2 * 1/3(a – c)

o P = a – Q

▪ = a - 2 * 1/3(a – c)

▪ = 1/3a + 2/3c

• Recall that relative to PC firm, M will restrict Q to ↑ P

• Given the same D & C structures, Cournot duopoly = P/Q combo that is between a PC & M

o W/o collusion, restricts Q to level that ↑ P above competitive P ∴ allows firms to earn

above-formal profits

▪ But profit ≠ as high as M profit

• Assuming: P = a – c and Tc = c*Q, profit-maximizing Qs:

o PC: Q = a – c

▪ b/c c = a – Q

▪ Solve for Q

o M: Q = 1/2(a – c)

▪ b/c TR = a – Q so MR = a – 2Q

▪ MC = c

▪ MR = MC a – 2Q = c

▪ Solve for Q

o CD: Q = 2/3(a – c)

• Copaig the fatios fo PC, M, ad CD, PC > CD > M hee h CD is i etee

• Comparing PC & CD: (a – c) vs 2/3(a – c)

o In general, the output of an n-firm industry behaving as a CD is:

▪ Q = (n/n+1)(a - c)

find more resources at oneclass.com

find more resources at oneclass.com

Only pages 1-3 are available for preview. Some parts have been intentionally blurred.

o Industry Q & P thus depend on the number of firms more firms = more firm output

requires to profit maximize and ↓ P

▪ So, CD will restrict output below competitive level & will earn above-normal

profit

▪ Also notice how as n gets larger (approaches infinity), n/n+1 approaches 1 aka

gets closer to an industry that behaves as a PC b/c lose oligopoly power

• Profit margins in crease as more firms enter the market

o (P – C)/profit margin = H

▪ H = Herfindahl index sum of squared market share of each firm in industry

• Measure of industry concentration

• If all firms had equal market share, 1/n = H

▪ What H tells us:

• H is large (1) then the market is more concentrated and margins are

high M

• H is small (0) then the market is less concentrated and margins are low

PC

Bertrand Duopoly

• Firms produce a homogenous product but compete on P

o ∴ Equi P & industry Q = same as under PC

o Outcome occurs b/c best response to any P chosen by competitor is a lower P ∴ let’s

you take the whole market

• So, every firm will choose the lowest possible P (according to MC)

o In the end, each firm ears 0 profit b/c keep over/under-cutting e/o equalizes profit and

losses to 0

• Limits of Bertrand:

o When firms = capacity-constrained (limited in size) b/c ≠ steal the whole market by

under-cutting rivals

▪ P competition is limited

• Limits effectiveness b/c ≠ steal the whole market (as the model

assumes)

▪ Meanwhile, excess capacity = encourages P competition

▪ E.g. seasons for vacationing: peak or quiet

• @ peak = compete w/installed capacity b/c cannot serve all of market

(travellers)

• @ quiet = airlines have planes that take off even when empty; have to

sell seats @ lower P

o When products = differentiated b/ fis ≠ steal the etie aket ↓ P sie soe

customers will prefer to pay a higher P for a product they prefer

▪ So, product differentiation = ↑ market power for each firm and ↓ P

competition

• ≠ fully capture the nature of P comp

find more resources at oneclass.com

find more resources at oneclass.com

###### You're Reading a Preview

Unlock to view full version