#### Market Structure II and Oligopoly

Market Structure:

Oligopoly:

1. Spectrum of market structure:

Most markets are neither perfectly competitive nor monopolistic but they may fall somewhere in between along the spectrum. Typical market will have more than one seller of the same or similar products, but not enough to justify the assumption that sellers simply take prices as given. Thus, each firm will have an individual, downward sloping demand curve and is said to have “some level” of monopoly power.

2. Oligopoly:

Oligopoly is from the Greek word “oligospolein” meaning “few to sell.” as well as it is reflecting the interdependence between firms which means oligopoly or imperfectly competitive firm must take account of its rival’s actions in making its own pricing decisions. So studies of oligopoly can give us good information about competitions among firms strategic reaction or decision making process and trend of market shares of firms.

The most modern approach is to model such firms as choosing “strategies” or playing “games” with one another. This approach is called as game theory.

3. Early Generalized Model:

Assumptions:

• N firms producing homogeneous and standardized products.
• Input market is absolutely competitive.
• No entry is authorized.

From these assumptions, we can derive several things;

a) Inverse demand function is expressed as:

p = f (Q) .......(i)

Where market quantity is:

b) Profit of each firm will be π i = p (Q) .qi − ci (qi ), i = 1, 2, L...., N         (ii)

c) FOC of profit maximization is:

cf) dQ/ dqi mean that a change in product of i-th firm can affect the change in total product or change in products of other firms.

d) We require to know the value of dQ/dqi . Rewriting this we are able to get:

C.V (Conjectural Variation):

Therefore equation (iv) is now dQ/dqi = 1+λi  .................................... (v)

(This is the most important factor in Oligopoly. We can figure out different types of oligopoly as λ changes)

Putting aside the discussion about λi we need to derive the generalized result by assuming that ci (cost structure) and λi are constant across individual firms. Consequently

e) From (iii) and (v), we can get p MCi = − qi (dp/dQ) (1+λ)

(ki is market share of i-th firm. ε is price elasticity of market demand)

From (vi), assuming that every firm has the same size, then ki = 1 N.

f) So Lerner Index or monopoly power can be determined by N, ε , and λ .

Example: In perfect competition, p MCi = (QN → ∞ and ε = ∞)

In monopoly, N = 1, λ = 0 . So,( p -M Ci)/ p = 1/ε
For more generalized case, we can relax the assumption that λ is constant. So, assuming that λi and ki can vary among the firms, then we get:

g) Let’s think about the industry (But, assume that MC = AC) Rewriting equation (ii), we can get:

πi = p (Q). q i −c ′i( q i). q i, =1, 2, L,... N     ...........(ix)

Let Π denote the industry profit or aggregate profits then:

h) From (viii), multiplying by qi on both sides and summing up from 1 through N, we get:

From equation (x) and (xi),

where HHI= (Herfindahl-Hirschmann Index)

i) From (xii), l.h.s is called Industrial Rate of Return, which can reflect the performance of the industry.

j) If MCi , ki , and λ i are constant, HHI =

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