If price falls from 6 to 4 on a linear demand curve, total revenue will remain unchanged.

• A. TR will decrease.
• B. TR will increase.
• C. Quantity demanded will increase by more than 100 percent.
• D. TR will remain unchanged.

Answer: (D)

On a linear demand curve, total revenue is the product of price and quantity, and because quantity is a linear function of price (Q = a - bP), total revenue as a function of price is TR(P) = aP - bP^2. This is a downward-opening parabola with its maximum where elasticity equals 1, at P* = a/(2b). A useful property of a parabola is symmetry around its vertex: prices that are equally far from P* give the same TR.

Here, the two price points 6 and 4 are equally distant from 5. If the revenue-maximizing price is 5, then TR at 6 and at 4 will be the same, so total revenue remains unchanged when price falls from 6 to 4. Algebraically, TR(6) = 6(a - 6b) and TR(4) = 4(a - 4b); these are equal when a = 10b, which also means P* = a/(2b) = 5. In short, the statement holds because total revenue on a linear demand curve is symmetric around the unit-elastic (revenue-maximizing) price.