Question

Three pizza places share market for pizzas in a small city.

Demand for pizzas is given by Q(p)=4200 - 200p where p - price of pizza and Q is total number of pizzas. Marginal cost of production of pizza is $3 for chain A, $4 for chain B and $5 for chain C. Each has a fixed cost of $3000/week. Due to a combination of economic downtown and local lost of population in the city, the chains find themselves with enough capacity to serve all the demand for pizza even at low prices. a) which model of oligopolistic competition is most appropriate to analyze this market b) according to answer in (a) what will be equilibrium price of pizza in this city c) Suppose you are manager of chain B, what could you do to get out of scenario (b) and increase profit. Can you give examples of strategies that you can adopt to accomplish this?

Answer 1

Annswer (a)

The Cournot model of oligopoly applies here the main reason behind it lies in the fact that where

(a) the three firms produce homogeneous goods i.e. PIZZA

(b) they compete simultaneously on output and market share.

(c) they expect their rivals to not change their output in response to any change that the make.

Cournot equilibrium is the output level at which each firm in the oligopoly maximizes its profit given the output level of all other firms. No firm can gain from changing its output level away from Cournot equilibrium because the response of other firms will wipe out any additional profit.

Answer (b)

Demand curve Q=4000 - 200P

Under complete collusion, with the firms of equal size so that Q = 3q , each individual firm's demand curve is

Q= 4000- 200p

0.005Q = 20- p , p= 20 - 0.005Q

P= 20- 0.005(q1 + q2 + q3)  is the demand function for three firm carnot model

Also given MC1 = $3, MC2=$4, MC3= $ 5

Total Revenue for the first firm =Price x Quantity

= [20- 0.005(q1 + q2 + q3)] q1

= 20q1 - 0.005(q1)^2 - 0.005 q1.q2- 0.005q1.q3

MR is the derivative of Total revenue w.r.t q1 thus we have

MR= 20 - 0.01 q1- 0.005q2 - 0.005 q3

For equilibrium MR=MC

20 - 0.01q1-0.005q2-0.005q3=3

17 - 0.005q2 - 0.005q3 = 0.01q1

1700- 0.5 q2 - 0.05 q3= q1

similarly we calculate for q2= 1700- 0.5 q1 - 0.05 q3 and q3= 1700- 0.5 q2 - 0.05 q1 . Substituting q1,q2 and q3 among themselves and Putting all the equation

P= 20- 0.005(q1 + q2 + q3) we will get the value of equilibrium price.

Answer c: Since all the producer produces similar type of product than any body can get better outcome by increasing the outcome rather than an increase in the price.A better strategy will be to try to bring some innovation to the product if possible and come out of the model and become a price leader. The first mover had a chance to get the added advantage and become the market leader. If he remain in the same model any producer had the chance of increasing the production so it might no be a good move.