Answer to Question #176622 in Microeconomics for daniel

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

Solution:

a.). Market price and output of the dominant firm:

At equilibrium: market demand = market supply

100 – P = 0.5P

100 = 0.5P + P

100 = 1.5P

P = $\frac{100}{1.5} = 67$

P = 67

Equate for Q:

Q = 100 – P

Q = 100 – 67

Q = 33

Market price = 67

Market quantity for the dominant firm = 33units

 

b.). Output level to be supplied by the smaller firms:

Smaller firms will supply output at the equilibrium price

Equilibrium price = 67

Smaller firms supply function: S = 0.5P

 = 0.5(67) = 33 units

Smaller firms will supply an output level of = 33 units