Question

2. A market (or industry) demand curve is described by Q = 600 – 0.5 PThe monopolist firm’s cost function isTC = 8,550 + 20Q

a.Find the profit-maximizing quantity and price.

b. If the monopoly is dissolved and then the market becomes perfectly competitive, how much more quantity will be produced?

Answer 1

Answer 2

(a)

In order to maximize profit a monopolist produces that quantity at which MR = MC.

where MC = Marginal cost = d(TC)/dQ = 20 and MR = d(TR)/dQ = d(P*Q)/dQ , TR = Total Revenue.

Here Q = 600 - 0.5P => P = 1200 - 2Q => MR= d(TR)/dQ = d(P*Q)/dQ = 1200 - 4Q.

Thus MR = MC => 1200 - 4Q = 20 => Q = 1180/4 = 295.

Hence Profit Maximizing Quantity = 295.

Thus, P = 1200 - 2*295 = 610

Hence Profit maximizing price = 610

(b)

In order to maximize profit a perfect competitive produces that quantity at which P = MC.

where MC = Marginal cost = d(TC)/dQ = 20.

Here Q = 600 - 0.5P => P = 1200 - 2Q

Thus P = MC => 1200 - 2Q = 20 => Q = 1180/2 = 590..

Hence Profit Maximizing Quantity = 590.

Hence, If the monopoly is dissolved and then the market becomes perfectly competitive then increase in number of quantity = 590 - 295 = 295.