Suppose demand for good A is given by: QS = 500-10 PA + 2Pa + 0.71 where PA is t

Question

Suppose demand for good A is given by: QS = 500-10 PA + 2Pa + 0.71 where PA is the price of good A, PB is the price of some other good B, and I is income Assume that PA is currently $10, PB is currently S5, and I is currently S100. What is the elasticity of demand for good A with respect to the price of good A at the current situation? a) b) What is the cross-price elasticity of the demand for good A with respect to the price of good B at the current situation? c) What is the income elasticity of demand for good A at the current situation?

Explanation / Answer

Qd = 500 - 10PA + 2PB + 0.1I

= 500 - 10(10) + 2(5) + 0.7(100)

= 500 - 100 + 10 + 70

= 480

a) Ed = (dQ/dP) *P/Q ......(1)

dQ/dP = - 10

Substituting values in equation (1)

= -10 (10) /480

= 0.20

b)

Cross elasticity of Demand = dQ/dPB * PB/Q

= 2*(5/480)

= 0.020

C)

Income Elasticity = dQ/dI * I/Q

= dQ/dI = 0.7

= 0.7 * 100/480

= 70/480

= 0.14

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