Question

You are the manager of a shoe producer. Your company specializes in basketball shoes and a cleaning product for basketball shoes. While the shoes bring in more revenue ($500,000 per year), the cleaning product is a strong seller as well ($150,000 of revenue per year). You are considering a 2% decrease in the price of your company's basketball shoes. Assume that the shoes have an own price elasticity of demand of -1.8 and the shoes and cleaning product have a cross-price elasticity of demand of -1.4. How much do you estimate your company's total revenue to change if you go forward with the proposed 2% shoe price decrease?

Answer 1

We see that shoes and shoe cleaning product, both are complementary goods.

Present Revenue from Shoes = $500000
Proposed decrease in shoe prices = - 2%
Ed of shoes = - 1.8
Resulting increase in quantity of shoes sold = - 2% * -1.8 = 3.6%
Revised revenue from shoes sale = $500000 * (100% - 2%) * (100% + 3.6%)
Processed to = $500000 * 0.98 * 1.036
Revised revenue from shoes sale = $507640
Increase in revenue from sale of shoes = $507640 - $500000 = $7640 (Figure A)

Present revenue from shoe cleaning product = $150000
Cross-price elasticity of demand between shoes and cleaning product = -1.4
(Remember that there is no proposal for change in prics of shoe cleaning product)
Increase in quantity of shoes sold = 3.6% (we calculated it in the first part above)
If cross price elasticity is -1.4, then:
Increase in quantity of cleaning product sold wll be = 3.6% * 1.4 = 5.04%
Revised revenue from cleaning product = $150000 * (1 + 5.04%)
Processed to = $150000 * 1.0504
Revised revenue from cleaning product = $157560
Increase in revenue from sale of cleaning product = $157560 - $150000 = $7560 (Figure B)

Increase in total revenue = Figure A + Figure B = $7640 + $7560
Increase in total revenue = $15200