Q.A monopolist faces the demand function $P = 100 - Q$ and has a total cost function $TC = 20Q$. Find the profit-maximising price and output.

Under monopoly a single seller with no close substitutes and blocked entry is a price maker facing a falling AR curve, with MR lying below AR. The monopolist maximises profit at the output where MC = MR (with MC cutting MR from below) and charges the price shown by the demand (AR) curve at that output, allowing super-normal profit to persist even in the long run.

Meaning of monopoly

Monopoly means a single seller. It is a market situation in which there is only one producer or seller of a commodity that has no close substitutes, and there are strong barriers preventing the entry of new firms. The monopolist controls the entire supply and so is a price maker rather than a price taker.

Features

• Single seller, many buyers.
• No close substitutes for the product.
• Strong barriers to entry (legal, natural or technical).
• The firm is the industry.
• The monopolist can fix either the price or the quantity, but not both independently.

Revenue curves

Because the monopolist faces the whole market demand, the average revenue (AR) curve slopes downward from left to right. To sell more the price must be lowered on all units, so the marginal revenue (MR) curve lies below the AR curve.

Price-output determination (equilibrium)

The monopolist aims to maximise profit. Profit is greatest at the output where:

1. Marginal Cost = Marginal Revenue (MC = MR), and
2. The MC curve cuts the MR curve from below.

Having chosen that profit-maximising output, the monopolist charges the price corresponding to that output on the AR (demand) curve. Since the AR curve lies above the MR curve, the price (AR) is higher than MR, and usually higher than marginal cost.

Profit position

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