Question

There are two firms in a market with marginal cost functions given by MC1(q) = 1/3q MC2(q) = q . Market demand is given by D(p) = 20 − 2p . (a) Obtain the competitive equilibrium output and price. Calculate consumer surplus and each firm’s producer surplus. (b) Derive the monopoly price when only firm 1 operates. Calculate consumer surplus and each firm’s producer surplus. (c) Derive the monopoly price when only firm 2 operates. (d) Now assume that a monopolist owns two plants with marginal costs MC1(q), MC2(q) given above. Obtain the monopoly price and output.

Answer 1

The student's question involves finding competitive equilibrium, consumer surplus, producer surplus in a perfectly competitive market, and determining monopoly pricing and output when one firm operates and when a monopolist operates two plants with different marginal costs.

Step-by-step explanation:

Finding the Equilibrium in Different Market Structures

The student's question pertains to finding the competitive equilibrium output and price, consumer surplus, producer surplus under perfect competition, and monopoly pricing and output when one firm operates or when a monopolist operates two plants with different marginal costs.

Competitive Equilibrium Output and Price

In a competitive market, firms will produce up to the point where the market demand equals the sum of the marginal costs of both firms (MC1 + MC2). To find this competitive equilibrium, we set the sum of the MC functions equal to the inverse demand function.

Monopoly Output and Pricing

For the monopoly scenarios, the firm (whether it be Firm 1 or Firm 2 alone, or a monopolist operating both plants) will produce where marginal revenue (MR) equals marginal cost (MC). This is known as profit maximization condition for a monopolist. Once the profit-maximizing quantity is determined, the price is derived from the demand curve.

For firm 1 as a monopolist, we would set MR equal to MC1, solve for the quantity, and then find the monopoly price from the demand curve at that quantity. For firm 2 as a monopolist, similar steps are followed with MC2. When a monopolist operates both plants, the total MR is equated to the sum of MC1 and MC2 to find the monopoly output and price.

Consumer and Producer Surplus

Consumer surplus is the difference between what consumers are willing to pay and what they actually pay, while producer surplus for each firm is the difference between the market price and the marginal cost of production.