Question

2. Suppose a designer shoe company knowns their inverse-demand curve for each individual is
P = 500-100Q and that their cost function is C(Q) = 100Q. That is, the marginal cost to produce a pair of shoes is $100.

a. The company is considering using an advanced pricing technique to raise revenue, and is considering a buy one get on 25% off promotion.

i. What type of pricing scheme is this?

ii. What price should be charged for the first pair of shoes and what price should be charged for the second pair (remember, 25% off the first pair)? How much profit will the company make? Compare this to part a. Have they increased their profit?

iii. Illustrate graphically the profit from the pricing scheme in part b on the diagram below. Be sure to label all relevant points.

Answer 1

The wording of the question is slightly confusing. I am assuming that the promitional offer is buy one get 25% off on second pair of shoes. I will solve the question accordingly. If thats not the case, let me know in the comment what the promotional offer is and I will update the answer accordingly.

i. What type of pricing scheme is this?- It is bundle pricing scheme.

ii. What price should be charged for the first pair of shoes and what price should be charged for the second pair (remember, 25% off the first pair)?

It is given that the inverse-demand curve for each individual is
P = 500-100Q.

To sell 2 shoes to someone, the price per shoe should be

P=500-100*2=300.

So for 2 shoes, the customer will pay 600.

Let us assume that the price of first shoe is X. Then the price of second should e .75X (25% off). The total price, as we already know, is 600. So, we get

X+.75X=600

OR X= 342.8571. Hence the price of the first shoe should be 342.8571, ~343. Profit is 343-100=243.

The price of the second shoe should be .75*342.8571= 257.1429 OR ~257. Profit is 257-100=157.

Total Profit=243+157=400.

Compare this to part a. Have they increased their profit?- If they had sold the shoes together without promotion, the customer wouldve paid 600, with profit being 600-2*100=400. So, no they havent increased their profit. It has remained the same.

Part iii needs a diagram which is missing.