workbook!

[Devika]

27.9 (0) Consider a market with one large firm and many small firms.

The supply curve of the small firms taken together is
S(p) = 100 +p:

The demand curve for the product is
D(p) = 200 −p:

The cost function for the one large firm is
c(y) = 25y

(a) Suppose that the large firm is forced to operate at a zero level of
output. What will be the equilibrium price? 50. What will be the
equilibrium quantity? 150.

(b) Suppose now that the large firm attempts to exploit its market power
and set a profit-maximizing price. In order to model this we assume that
customers always go first to the competitive firms and buy as much as
they are able to and then go to the large firm. In this situation, the
equilibrium price will be $37.50. The quantity supplied by the
large rm will be 25. and the equilibrium quantity supplied by the
competitive rms will be 137.5.

(c) What will be the large firm's profits? $312.50.

(d) Finally suppose that the large rm could force the competitive firms
out of the business and behave as a real monopolist. What will be the
equilibrium price? 225/2. What will be the equilibrium quantity?
175=2. What will be the large firm's profits? (175/2) squared

Please explain part b,c and d. Answers are written next to the questions!

Thank you!

[srawan]

b-let q = quantity produced by large firm
suuply =demand
100+p+q=200-p
p=100-q/2

large firm profit= (100-q/2)*q-25q
just optimize get q = 25,just plug in p=100-q/2

for d part- large firm profit= (200-q)*q-25q
just diff. w r. to q =0
q=175/2
...........rest follows from this

[Devika]

Wow, that was easy! I was trying to fit in the price leadership model! x_x

Thank you so much! :)

[srawan]

initially i also thought about price leadership model
but then this is it
language understanding -we all face this problem while problem solving

[Devika]

Agreed.

Thank you once again :)