Question

given market demand Q=100-P if the market supply function for the smaller firms is given by S=0.5P. And the cost function of the dominant firms is TC=10+40QD, where QD= output of the dominant firm. a) Find the market price and output of the dominant firm at equilibrium. b) Find the output level to be supplied by the smaller firms.

Answer 1

$a)$

Market price and output of the dominant firm:

At equilibrium: market demand = market supply

Therefore,

100 – P = 0.5P

100 = 0.5P + P

100 = 1.5P

$P=\frac{100}{1.5} = 66.67$

Given P=66.67, we equate for Q

Q = 100 – P

Q = 100 – 66.67

Q = 33.33

Therefore, the market price is 66.67 and the market quantity for the dominant firm is 33.33units

$b)$

Output level to be supplied by the smaller firms:

Smaller firms will supply output at the equilibrium price

The Equilibrium price, $P= 66.67$ and the smaller firms supply function is,

$S=0.5P$

Therefore,

 $S=0.5(66.67) = 33.33 units$

Thus, smaller firms will supply an output level of 33.33 units.