9781118041581

Marginal Revenue

Marginal revenueis the amount of additional revenue that comes with a unit

increase in output and sales. The marginal revenue (MR) of an increase in unit

sales from Q 0 to Q 1 is

For instance, the MR earned by increasing sales from 2.0 to 2.1 lots is

where 268.8 is the revenue from selling 2.1 lots and 260.0 is the revenue from

selling 2.0 lots. The graphic depiction of the MR between two quantities is given

by the slope of the line segment joining the two points on the revenue graph.

In turn, marginal revenue ata given sales quantity has as its graphic counter-

part the slope of the tangent line touching the revenue graph. To calculate the

marginal revenue at a given sales output, we start with the revenue expression

(Equation 2.3), R 170Q 20Q^2 , and take the derivative with respect to quantity:

[2.8]

We can use this formula to compute MR at any particular sales quantity. For

example, marginal revenue at Q 3 is MR  170 (40)(3) $50 thousand;

that is, at this sales quantity, a small increase in sales increases revenue at the

rate of $50,000 per additional lot sold.

A SIMPLIFYING FACT Recall that the firm’s market-clearing price is given by

Equation 2.2:

Note the close similarity between the MR expression in Equation 2.8 and the

firm’s selling price in Equation 2.2. This similarity is no coincidence. The fol-

lowing result holds:

For any linear (i.e., straight-line) demand curve with an inverse demand equation

of the form P a bQ, the resulting marginal revenue is MR a 2bQ.

In short, the MR equation has the same intercept and twice the slope as the

firm’s price equation.^5

P 170 20Q.

MR 170 40Q.

[268.8260.0]/[2.12.0]$88 thousand per lot.

¢R/¢Q[R 1 R 0 ]/[Q 1 Q 0 ]

Marginal revenue[Change in Revenue]/[Change in Output]

44 Chapter 2 Optimal Decisions Using Marginal Analysis

(^5) If P a bQ, it follows that R PQ aQ bQ (^2). Taking the derivative with respect to Q, we
find that MR dR/dQ a 2bQ. This confirms the result described.
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