The demand for personal computers has been estimated to be Q = 500,000 - 700P + 200I - 500S.Assume that per capita income I is $13,000 and the average price of software S is $400.When the price of personal computers is P = $3,000,the price elasticity of demand is:
A) -2.625.
B) -7.0.
C) -1.0.
D) -21.0.
E) -4.25.

Question

Quizplus · Accepted Answer

The price elasticity of demand (PED) is calculated using the formula: PED = (dQ/dP) * (P/Q), where dQ/dP is the derivative of the demand function with respect to price, P is the price, and Q is the quantity demanded. From the given demand function Q = 500,000 - 700P + 200I - 500S, the derivative dQ/dP = -700. Substituting P = $3,000, I = $13,000, and S = $400 into the demand function gives Q = 500,000 - 700(3,000) + 200(13,000) - 500(400) = 500,000 - 2,100,000 + 2,600,000 - 200,000 = 800,000. Therefore, PED = (-700) * (3,000 / 800,000) = -2.625.

The Demand for Personal Computers Has Been Estimated to Be