Question

Pym Industry is a manufacturer of petrochemical products. The firm's research efforts have
resulted in the development of a new auto fuel injector cleaner that is considerably more
effective than other products on the market. Another firm, Stark Industry, independently
developed a very similar product that is as effective as the Pym’s formula. To avoid a lengthy
court battle over conflicting patent claims, the two firms have decided to cross-license each
other's patents and proceed with production. It is unlikely that other petrochemical companies
will be able to duplicate the product, making the market a duopoly for the foreseeable future.
Pym estimates the demand curve given below for the new cleaner. Marginal cost is estimated
to be a constant $2 per bottle.
Q = 300,000 - 25,000P.
where P = dollars per bottle and Q = monthly sales in bottles
a) Pym and Stark have very similar operating strategies. Consequently, the management of
Pym believes that the Cournot model is appropriate for analyzing the market, provided
that both firms enter at the same time. Calculate Pym’s profit-maximizing output and
price according to this model
b) Pym’s productive capacity and technical expertise could allow them to enter the market
several months before Stark’s. Choose an appropriate model and analyze the impact of
Pym being first into the market. Should Pym hurry to enter first?

Answer 1

a)

pyms price and quantity as Py , Qy and starks Ps and Qs

Q = 300,000 - 25,000p

P = 12 - 0.00004Q TRy= Py· Qy

TRy= (12 - 0.00004Q)Qy Q = Qy+ Qs

TRy= [12 - 0.00004(Qy+ Qs)]Qy

TRy= 12Qy- 0.00004Qy

12- 0.00004QyQs

MRy= 12 - 0.00008Qy- 0.00004Qs

assume MRy= MC

12 - 0.00008Qy- 0.00004QS= 2

0.00008Qy- 0.00004Qs = -10

Qy= 125,000 - 0.5Qs

the same way, Qs= 125,000 - 0.5Qy

Substitute for QS: Qy= 62,500 + 0.25Qy

Qy= 62 500/0.75,.= 83,333

Q = Qy+ Qs

Q = 83,333 + 83,333 = 166,666

P = 12 - 6.67 = 5.33

P = $5.33

total bottles sold

166,666

b)

Stackelberg model can used in this situation

pym and stark determines its output, which Stark then takes as given.

pyms total revenue function is given as: TRy= 12Qy- 0.00004Qy² - 0.00004QyQs

Stark reaction function Qs= 125,000 - 0.5Qycan be substituted into TRy

  Stark will take pym output as given. TRy= 12Qy- 0.00004Qy²- 0.00004Qy(125,000 - .5Qy)

TRy= 12Qy- 0.00004Qy²- 5Qy+ 0.00002Qy²

TRy= 7Qy- 0.00002Qy²

MRy= 7 - 0.00004Qy

MRy= MC ; 7 - 0.00004Qy= 2

-0.00004Qy= -5

Qy= 125,000

get QS substitute with Qy into

reaction function QS= 125,000 - 0.5Qy

QS= 125,000 - 0.5(125,000)

QS= 62,500

Q = Qy+ Qs

Q = 125,000 + 62,500

Q = 187,500

P = 12 - 0.0004(187,500)

P = 12 - 7.5 = $4.50

Pym gets a larger share of the market by entering first.