Question

Assume the market demand for wheat may be written as Q = 45 - 2p + 0.3Y + 1pb where Y refers to income and pb refers to the price of barley. Assuming that wheat and barley both sell for $1, and income is $20, calculate the price elasticity, cross price elasticity and income elasticity for wheat.

Answer 1

Market demand is as follows -

Q = 45 - 2p + 0.3Y + 1pb

p = 1

pb = 1

Y = 20

Q = 45 - (2*1) + (0.3*20) + (1*1)

Q = 45 - 2 + 6 + 1

Q = 50

Price Elasticity

Calculate -

= dQ/dp = d(45 - 2p + 0.3Y + 1pb)/dp = -2

Calculate the price elasticity -

Price elasticity = * (p/Q)

Price elasticity = (-2) * (1/50)

Price elasticity = -0.04

The Price Elasticity is -0.04

Cross Price Elasticity

Calculate -

= dQ/dpb = d(45 - 2p + 0.3Y + 1pb)/dpb = 1

Calculate the cross price elasticity -

Cross price elasticity = * (pb/Q)

Cross price elasticity = 1 * (1/50)

Cross price elasticity = 0.02

The cross price elasticity is 0.02

Income elasticity

Calculate -

= dQ/dY = d(45 - 2p + 0.3Y + 1pb)/dY = 0.3

Calculate the income elasticity -

Income elasticity = * (Y/Q)

Income elasticity = 0.3 * (20/50)

Income elasticity = 0.12

The income elasticity is 0.12