Question

the inverse demand for its product is given P=80-2Q; total costs for this monopolist are estimated to be C(Q)=100+20Q+Q^2; consider a competitive economy; determine the competitive output and price

Answer 1

Demand : P = 80-2Q

Total revenue = TR = P×Q = 80Q-2Q²

Total cost = TC = C(Q) = 100+20Q+Q²

Since it is perfect compitition, the profits are maximized where MR=MC

Or, where, P=MC

This is derived by maximizing the Profit function i.e. TR-TC with respect to Q.

Here, MC = = 20 + 2Q

Thus, By the profit maximizing condition,

20 + 2Q = 80 - 2Q

Or, 4Q = 60

Or, Q = 15

Thus, Q=15 is the competitive output

Putting Q = 15 in the inverse demand function, we get:

P = 80 - 2(15) = 80 - 30 = 50

Thus, competitive price = $50.