Question

A market is dominated by a price leader and also contains a competitive sector. The
leader chooses the price and the competitive sector simply chooses the same price as the leader.
Market demand is given by
p = 2000 - Y
where Y is the total output of the industry. This output is given by Y = yL + yF, where yL is the output of
leader and yF is the output of the competitive sector. The leader has the total cost function
cL (yL) = 14 yL, while the competitive sector has the total cost function cF (yF) = 20 yF^2
.
a) Find the supply function of the competitive sector.
b) Find the leader's residual demand.
c) Find the inverse residual demand of the leader.
d) Find the choice the leader will make to maximize his profit (hint: find his output).
e) Find the equilibrium price.
f) Find the output of the competitive sector.

Answer 1

Solution

Give that :

p=2000-Y

Y is industry output where Y=yL+yF

(a).

Market demand function =

P= 2000-Y

Supply function =

Y= 2000- P

Supply function would be the inverse of the other function .

(B).

Residual demand of the leader would be

Demand of the good less the supply of the good demanded in the market .

Residual demand= yl + yf - 14yl

= Yf - 13yl

C).

The inverse reidual demand for the funtion would be

= 1 - yf - 13yl

(D).

The leader would make a choice to produce more goods by keeping the prices low so that there is an increased demand of the good so that the profits could be maximised.

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