Find the elasticity of the demand function as a function of p.
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Question

Quizplus · Accepted Answer

The elasticity of demand is the percentage change in quantity demanded divided by the percentage change in price. We cannot determine the exact elasticity without knowing the demand function, but we can write it generally as:

Elasticity of demand = (dQ/Q) / (dP/P)

Where Q is quantity demanded and P is price. Taking the derivative of the demand function with respect to price will give us (dQ/Q) / (dP/P), which is the elasticity of demand. Therefore, the correct answer is B. The elasticity of demand as a function of price can be found using the formula:

E(p) = (dQ/dp) * (p/Q)

where Q is the quantity demanded and p is the price. Differentiating the demand function, we get:

Q = 200 - 2p

dQ/dp = -2

Substituting these values into the elasticity formula, we get:

E(p) = (-2) * (p/(200-2p))

Simplifying this expression, we get:

E(p) = (-2p)/(200-2p)

This is the elasticity of demand as a function of price. It is a decreasing function of p, and approaches zero as p approaches infinity. The correct answer is therefore B.

Find the Elasticity of the Demand Function as a Function