## Marginal Revenue Curves

We saw in the last section that marginal revenue is given by

We will find it useful to plot these marginal revenue curves. First, note that when quantity is zero, marginal revenue is just equal to the price. For the first unit of the good sold, the extra revenue you get is just the price. But after that, the marginal revenue will be less than the price, since Ap/Aq is negative.

Think about it. If you decide to sell one more unit of output, you will have to decrease the price. But this reduction in price reduces the revenue you receive on all the units of output that you were selling already. Thus the extra revenue you receive will be less than the price that you get for selling the extra unit.

Let's consider the special case of the linear (inverse) demand curve:

Here it is easy to see that the slope of the inverse demand curve is constant:

Thus the formula for marginal revenue becomes

This marginal revenue curve is depicted in Figure 15.7A. The marginal revenue curve has the same vertical intercept as the demand curve, but has twice the slope. Marginal revenue is negative when q > a/2b. The quantity a/26 is the quantity at which the elasticity is equal to â€”1. At any larger

Marginal revenue. (A) Marginal revenue for a linear demand curve. (B) Marginal revenue for a constant elasticity demand curve.

quantity demand will be inelastic, which implies that marginal revenue is negative.

The constant elasticity demand curve provides another special case of the marginal revenue curve. (See Figure 15.7B.) If the elasticity of demand is constant at e(q) = e, then the marginal revenue curve will have the form

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