Suppose that at the equilibrium price and quantity,the marginal revenue is −$15 and the price elasticity of demand for a linear demand function is −0.75.Then we know that the equilibrium price is:
A) −$5.
B) $45.
C) −$45.
D) $5.

Question

Quizplus · Accepted Answer

We know that for a linear demand function, elasticity is equal to the slope of the demand curve multiplied by the price level over quantity. Thus, we have:

-0.75 = (slope of the demand function) x (P/Q)

Since we know that at the equilibrium point, MR = MC and MR = P(1 + 1/E), we can use the information that MR = -$15 to solve for the equilibrium price:

-$15 = P(1 + 1/-0.75)
-$15 = P(1 - 4/3)
-$15 = P(1/3)
P = -$45

However, we know that price cannot be negative, so we need to take the absolute value of P, which gives us $45 as the equilibrium price. Thus, the correct answer is B.

Suppose That at the Equilibrium Price and Quantity,the Marginal Revenue