Question

1. The demand for company X's product is given by

Qxd = 12 – 3Px + 4Py,

Suppose good X sells for $3 per unit & good Y sells for $1 per unit.

1. Calculate the cross-price elasticity of demand between goods X and Y at the given prices.
2. Are goods X and Y substitutes or complements?
3. What is the own price elasticity of demand at these prices?
4. How would your answers to parts a and c change if the price of X dropped to $2 per unit?

Answer 1

(a) Formula:

Cross price elasticity = (dQ_x/dP_y)(P_y/Q_x)

Here P_x = $3 & P_y = $1

=> Q_x = 12 – 3*3 + 4*1 = 7 and dQ_x/dP_y = 4

=> Cross Price elasticity = 4(1/7) = 4/7 = 0.55

(b) X and Y are substitute goods If increase in Price of 1 results in increase in demand of other and X and Y are complementary goods if increase in Price of one results in decrease in demand of other.

Here Cross price elasticity is positive, this means that increase in price of Y will result in increase in demand of X. Hence here, X and Y are substitute goods.

(c)

Formula:

Own price elasticity = (dQ_x/dP_x)(P_x/Q_x)

Here P_x = $3 & P_y = $1

=> Q_x = 12 – 3*3 + 4*1 = 7 and dQ_x/dP_x = -3

=> Own Price elasticity = -3(3/7) = -9/7 = (-)1.28

(d)

(a) Formula:

Cross price elasticity = (dQ_x/dP_y)(P_y/Q_x)

Here P_x = $2 & P_y = $1

=> Q_x = 12 – 2*3 + 4*1 = 10 and dQ_x/dP_y = 4

=> Cross Price elasticity = 4(1/10) = 4/10 = 0.4

Hence Cross price elasticity will decrease If price of X reduces from $3 to $2

Formula:

Own price elasticity = (dQ_x/dP_x)(P_x/Q_x)

Here P_x = $2 & P_y = $1

=> Q_x = 12 – 2*3 + 4*1 = 10 and dQ_x/dP_x = -3

=> Own Price elasticity = -3(2/7) = -9/7 = (-)0.85.

Hence X will become less own Price elastic If price of X reduces from $3 to $2.