Question

A natural spring supplies a local business with their drinking water and is particularly popular, the owner thinks that there are two types of customers for her product - high volume and low volume consumers. An economist estimated that the high volume annual consumption equals Qh = 24 − 0.3P , where P is the price of a bottle of spring water. Alternatively, the low volume annual consumption equates to Ql = 10 − 0.1P . The marginal and average total cost to the firm for providing a bottle of water is $20. (a) If the owner could tell a high volume from a low volume consumer, what price should she charge each type and how much would each type consume? (b) How much profit would the firm generate? The sales manager has a hard time telling the difference between the high volume consumer and the low volume consumer, so she decides to use second- degree price discrimination (quantity discounts) to make different types of consumer self-select into the most profitable pricing scheme. The firm sets prices normally per bottle, but also offers a quantity discount for those willing to buy large quantity in advance. The owner hope that high volume consumers will self-select into the discounted plan, and that low volume con- sumers will still choose to buy individual bottles as required. (c) What price should the firm set for individual bottles and why? (d) If the firm wishes to maximise profit, what price and minimum quantity should it establish for the discounted plan? (e) Which plan will generate the greatest consumer surplus for high volume consumers, the by-the-bottle or the discount plan? Illustrate your answer by showing and measuring the areas of surplus on high volume consumers inverse demand curves. (f) Which plan will generate the greatest consumer surplus for low volume consumers, the by-the-bottle or the discount plan? Illustrate your answer by showing the areas of surplus on low volume consumers inverse demand curves.

Answer 1