Question

Problem VI A-B: Apple used to produce two different versions of the Iphone, Iphone 5s and Iphone 5c. Assume the cost of production is zero. There are two types of consumers on the market, knowledgeable consumers and kids. Knowledgeable consumers value the Iphone 5s at $220 for its superior technology and the Iphone 5c at only $120. Kids don’t know that much about technology and they like colors a lot so their valuations are $110 for the Iphone 5s and $100 for the Iphone 5c. Apple is designing a pricing strategy to sell the Iphone.

a) Apple is considering a price discrimination strategy to sell the Iphone 5s to knowledgeable customers and the Iphone 5c to kids for two different prices. Write down the individual rationality and incentive compatibility constraints for the two types of customers. Find the optimal prices.

b) Assume there are N total consumers and the proportion of knowledgeable consumers is ?. That means there are ?N knowledgable consumers and (1 ? ?)N kids on the market. Write the profit function of Apple if the price discrimination mechanism is put into action.

Please answer this question in complete detail as I don't understand this subject too well. Thank you

Answer 1

Apple is a monopolist firm. So it practices discretionary pricing strategy. In the above part (a) It has segregated the market as the knowledgeable consumers and kids. It follows a price discrimination strategy wherein the knowledgeable consumers will be ready to pay the price as high as $ 220 for 5s as the demand for the product is inelastic or less elastic. On the other hand optimal price for the kids to buy 5c will also be high. As the demand for the product is inelastic and apple is a monopolist so kids will be willing to buy the product at any price irrespective of the feasibility. Also a monopolist firm will try to maximise the profits so it will take the advantage of the price discrimination strategy which will help the firm earn its revenue and expand.   

(B)since the firm is practising price discrimination policy it will charge $ 220 for 5s from knowledgeable customers and $ 120 for 5c from kids so total revenue will be calculated as price into quantity i.e $220* ?N + $ 120* 1. ?? And we have learned from above that production cost is 0 so profit will be calculated as TR-TCWhich here will give the following profit function $220* ?N+ $120*1?? N