15. You are a seller of ski supplies and face three kinds of skiers: advanced, i

Question

15. You are a seller of ski supplies and face three kinds of skiers: advanced, intermediate, and beginner. You sell two goods, skis and bindings, at zero marginal cost. The following table depicts the willingness to pay for each consumer. Skis indin 350 400 kpinmer 100 i. If you cannot tell consumers apart, what are the profit maximizing prices and ii. If you cannot tell consumers apart, what are the profit maximizing prices and iii. If you cannot tell consumers apart, find a way to achieve a profit greater than iv. Suppose you can tell who is a beginner and who is not. What is the maximal v. What is your profit when you can tell all consumers apart and how is it achieved? ensuing profit if selling the goods separately? ensuing profit if selling only bundles? $1500. What is the highest attainable profit and how do you achieve it? achievable profit and how is it achieved?

Explanation / Answer

Before I begin, let me explain 2 terms. Willigness to pay is the price till which a consumer is sure to buy the good. Consumer's surplus is the surplus of willingness to pay over the existing price in the market. Till the market has consumer's surplus, the firms have opportunity to earn more profits by increasing the price. Here there is no cost to the firm as MC is zero. whatever is charged as price is the profit.

i) There are 3 types of customer and if you cannot tell them apart, then you cannot charge different people differently. Hence you have to charge a common price. You can charge 100 for skiswhereby all the skiers will buy or you can charge the average willingness to pay - (350+250+100)/3 = 233.33 but a beginner will not buy at 233.33 Or you can charge at 250 where you are sure that 2 categories of skiers will buy. Hence the profit maximising price would be at 250 for skis where we are sure advanced and intermediate skiers will buy. The profit would be maximum at 500(250*2) as there is no marginal cost. It is not multiplied by 3 as a beginner will not buy it. Now the bindings can be charged at the lowest willingness to pay - 250 each and the profit will be 250*3 equals 750.

ii) Say a bundle has 1 ski and 1 binding. Then, add what each category has as willingness to pay - Advanced has 350+250 = 600 Intermediate is 250+350 = 600 Beginner is 100+400 = 500. Now in this case, average for a bundle is 566.66 but this is higher than the beginner's bundle and we are not sure if they will buy the product. Hence the bundle should be placed at 500 where we are sure that all the skiers will buy the bundle. The profit will be 500*3 = 1500.

iii) The total consumer's surplus in the market is 350+250+350+250+100+400 = 1700 If we charge a price for the bundle greater than 500, then the beginner category will not purchase and the profit will reduce. If the price individually is set above 250 for skis and 250 for bindings also it will reduce the profit. Hence 1500 is the maximum possible profits.

iv) If you can say who is a beginner, then you can have 2 slabs for the bundle. One bundle can be at 500 for the beginners alone and another bundle for 600 for others. This way, all the consumer's surplus wil be converted into profits. The profits will be at 1700.

v) If you can tell all the customers apart, then you can charge the goods separately. Each good can be charged at the willingness to pay level and all the consumers surplus will be converted into profits.

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