Answer to Question #176623 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

a) The market price and output of the dominant firm at equilibrium are:

MR = TR'(Q) = 100 - 2Q,

MC = TC'(QD) = 40,

MR = MC,

100 - 2Q = 40,

Q = 30 units,

P = 100 - 30 = 70.

b) The output level to be supplied by the smaller firms is:

Q = S,

100 - P = 0.5P,

P = 66.67,

Q = 33.33 units.