Question

Given the following demand function and total cost function as:

Q = 250-5P and TC = 0.5Q² + 5Q + 125 

Calculate the equilibrium price, Equilibrium Quantity and the total profit

A. under perfectly competitive market structure

B. Under monopolistic competitive market

Answer 1

A. Under perfectly competitive market structure in equilibrium D = MC, so:

$MC = TC'(Q) = Q + 5,$

50 - 0.2Q = Q + 5,

Q = 37.5 units,

$P = 50 - 0.2*37.5 = 42.5.$

B. Under monopolistic competitive market in equilibrium MR = MC, so:

$MR = TR'(Q) = 50 - 0.4Q,$

50 - 0.4Q = Q + 5,

Q = 32.14 units,

$P = 50 - 0.2*32.14 = 43.57.$