Question

A department store has 700 pairs of purple Capri stretch pants that it must sell in the next four weeks. The store manager knows that demand by week for the next four weeks will be linear each week, with the following price-response functions:

Week 1: d1(p1) =1,000 -100p1

Week 2: d2(p2) =800 -100p2

Week 3: d3(p3) = 700 - 100p3

Week 4: d4(p4) =600 -100 p4.

What is the optimum price the retailer should charge per pair if she only sets ONE price for ALL four weeks? What is her corresponding revenue?

Answer 1

We know that the demand for 4 weeks is as below and price for all 4 weeks should be same. If the price is denoted as p, we have the total demand for 4 weeks as below

Demand = 1000 -100p + 800 -100p + 700 - 100p + 600 -100 p = 3100 - 400p

We know that there are 700 pairs available which need to be sold. Hence we have to equate the above demand to 700 and solve for p. Hence we have

3100 - 400p = 700

3100 - 700 = 400p

400p = 2400

p = 2400/400 = 6

Hence the optimum price she should set is 6.

We know that revenue is given as the product of demand and price. As the total demand would be 700 and price is 6, the total revenue is 700*6 = 4200