Question

The demand for company X's product is given by Q_x = 12 – 3P_x + 4P_y. Suppose good X sells for $3.00 per unit and good Y sells for RM1.50 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 i and iii change if the price of X dropped to RM2.50 per unit?

Answer 1

Demand for X is given as

Qx = 12 - 3.Px + 4.Py

Here, we get,

dQx/dPx = -3

dQx/dPy = 4

Good X sells for RM3 and good Y sells for RM1.50.

Hence, Px = 3 and Py = 1.5. Putting these in demand function we get,

Qx = 12 - 3×3 + 4×1.5

or, Qx = 9

Let's answer the following questions one by one.

(i) The cross price elasticity of demand between X and Y is

Exy = (dQx/dPy).(Py/Qx)

or, Exy = (4)×(1.5/9)

or, Exy = 0.67

The cross price elasticity of demand between X and Y is 0.67.

(ii) If cross price elasticity is positive, then X and Y are substitutes.

And, if cross price elasticity is negative, then X and Y are complements.

Here, Exy = 0.67 > 0

Hence, goods X and Y are substitutes.

(iii) The own price elasticity of demand of demand is

Exx = (dQx/dPx).(Px/Qx)

or, Exx = (-3)×(3/9)

or, Ex = (-1)

The own price elasticity of demand is (-1).

(iv) If price of good X drops to RM2.50 per unit, then,

Px' = 2.5 and Py = 1.5

Hence, Qx = 12 - 3×2.5 + 4×1.5

or, Qx = 10.5

Hence, cross price elasticity of demand between X and Y is

Exy' = (dQx/dPy).(Py/Qx)

or, Exy' = (4)×(1.5/10.5)

or, Exy' = 0.57

Cross price elasticity of demand will fall to 0.57.

And, own price elasticity of demand is

Exx = (dQx/dPx).(Px/Qx)

or, Exx = (-3)×(2.5/10.5)

or, Exx = -0.71

Own price elasticity of demand will fall to (-0.71).

Hope the solutions are clear to you my friend.