Question

Your firm sells two products, product Gamma and product Theta. The cross price elasticity of Gamma with respect to the price of Theta is +1.5. The own price elasticity of Gamma is -0.5. The own price elasticity of Theta is -1.5.
Currently: the price of Gamma is $20 and the price of Theta is $40.
The quantity sold of Gamma is 100, and the quantity sold of Theta is 200.

Assume the price of Theta increases to $48. Nothing else changes. What will be unit sales of Theta?

A 140
B 170
C 230
D 260
E cannot be calculated

Answer 1

We summerize the information as

• CPE of Gamma -Theta is +1.5 (substitutes)
• OPE of Gamma is -0.5.
• OPE of Theta is -1.5.
• Presently the price of Gamma is $20 and quantity sold is 100.
• Presently the price of Theta is $40 and quantity sold of Theta is 200.

Assume the price of Theta increases to $48. This implies a % change of (48 - 40)*100/40 = 20%. Hence according to own price elasticity, -1.5 = % change in Q/% change in P

-1.5 = % change in Q/20%

= -30%

This shows that quantity demanded/sold of Theta falls by 30% from 200, which is 200 - 30%*200 = 140.

Option A is correct.