Market Demand Curve is the Average Revenue Curve

The market demand curve shows the quantities that consumers as a whole are willing to buy at different prices. At a high price $p_0$ consumers buy the small quantity $q_0$; at a lower price $p_1$ they buy the larger quantity $q_1$. In short, the quantity demanded is a decreasing function of price.

For the monopoly firm the same relationship reads in reverse. The firm can sell a larger quantity only at a lower price, and if it brings a smaller quantity to market it can sell at a higher price. Thus, for the monopolist, price depends on the quantity sold — price is a decreasing function of quantity. Since the firm is assumed to know the market demand curve perfectly, choosing the price is the same as choosing the quantity: to sell at $p_0$ it produces $q_0$, and to sell $q_1$ it must accept the lower price $p_1$. We express this by saying that the monopoly firm faces the market demand curve, which is downward sloping (this is Fig. 6.1 in the textbook).

The contrast with perfect competition is sharp: there, the firm could sell as much as it liked at the same price. Because that is not true for a monopolist, we must look carefully at the revenue the firm receives. We do this through a schedule, a graph, and a simple straight-line demand equation.

A worked demand function

Let the demand function be

where $q$ is the quantity sold and $p$ is the price in rupees. Written with price on the left,

Substituting values of $q$ from 0 to 13 gives prices from 10 down to 3.5. The total revenue is $TR = p \times q$, the average revenue is $AR = \dfrac{TR}{q}$, and the marginal revenue $MR$ (introduced fully in the next section) is the change in $TR$ from selling one more unit. These are set out in Table 6.1.

Table 6.1: Prices and Revenue

Plotting the $p$ values against $q$ gives the solid straight demand line $D$. The total revenue is not a straight line; mathematically,

This is a quadratic in which the squared term has a negative coefficient, so its graph is an inverted vertical parabola (the TR curve of Fig. 6.2). As quantity rises, $TR$ increases to a maximum of Rs 50 at 10 units and then declines.

Why average revenue equals price

The revenue received per unit sold is the average revenue, $AR = \dfrac{TR}{q}$. In Table 6.1 the $AR$ column is identical to the $p$ column — and this is exactly what we should expect, because

$AR = \frac{TR}{q} = \frac{p \times q}{q} = p.$ …