Question

Bubbly Beer (BB) is a monopoly manufacturer and distributor because of a government-granted monopoly. They make of a special kind of champagne-inspired beer that they call French Beer (FB). The annual market demand for FB is P = 205 - Q. The total cost function is C = 100 + 5Q + Q2 . 

a) (15) Using calculus, derive the profit maximizing quantity of FB released on to the market, the monopolistic price in equilibrium, total revenues, total costs, and profit for BB under its monopoly power. 

b) (10) Assume that the government plans to revoke BB’s monopoly grant in one year. Entry costs are small, and you expect the market will become perfectly competitive. (Assume that marginal costs for BB are the same as the competitive market supply curve.) What is the new equilibrium quantity under perfect competition? Equilibrium price?

Answer 1

The annual market demand for FB is P=205-Q
then, total revenue TR = P*Q = 205Q - Q²

and marginal revenue MR = dTR/dQ = 205-2Q

Total cost function C = 100+5Q+Q²

then, marginal cost MC = dC/dQ = 5+2Q

A) Now, for profit maximization in the monopoly market,
MR = MC

or, 205-2Q = 5+2Q

or, 4Q = 200

or, Q = 50 units

and P = 205-Q = 205-50 = $155

B) Now, when the firm is in perfectly competitive market,

P = MC

or, 205-Q= 5+2Q

or, 3Q=200

or, Q=66.67 units

and P=5+2Q = 5+(2*66.67) = $138.34