John Riley UCLA Case Study 14 April 2016 KIWI ROAMING

Transcription

1 John Riley UCLA Case Study 14 April 2016 KIWI ROAMING Telecom NZ was awarded a patent for software that will allow any tourist visiting New Zealand connect up with the Telecom cell phone network This will work regardless of where the phone was purchased Many visitors had been paying high Roaming Fees while in New Zealand Telecom hoped to provide a service that will serve the needs of these visitors more cheaply It created an App that visitors could download to a smart phone for a small fee Once downloaded, a customer can click on the KIWI ROAMING app (see above) The customer is then able to call any New Zealand numbers or anyone else with the KIWI ROAMING service

2 In the first year, roaming time was sold at a price per unit of p Based on the data from this year, the marketing department believes that there are two distinct markets The first group are economy travelers, the second are luxury travelers The marketing department estimates that the demand price function for a typical customer in each class is as follows: p q and p2 2 q Telecom s marginal cost of providing the service is c The demand price functions are depicted below As an economist, you know that a good measure of the benefit of consuming q units is the area under the demand curve 1 Then with a price ˆp The total benefit to an economy customer is the sum of the three shaded area in the left figure and the total benefit to a luxury customer is the corresponding sum in the right figure Figure 11: Customer benefit and profit on each plan 1 See the Appendix 2

3 Profit is for customer class i is ( pˆ c) q i This is the dotted area The solid shaded area is the total variable cost per customer The vertically shade area is therefore the net benefit to the customer After the first year, Telecom reports sizeable profits But there is an internal debate going on in the marketing department about offering a two plans Plan 1 will offer the same number of minutes per week q 1 that economy customers are currently using for a fixed weekly fee Plan 2 will offer the same number of minutes q 2 that luxury customers are purchasing for a fixed weekly fee of r 2 The rate will be set so that economy customers are (almost) indifferent as to whether or not to purchases plan 1 The fee is then set to equal the total benefit to the customer (the sum of the solid, dotted and vertically shaded areas in the left figure) The profit is therefore the sum of the dotted and vertically shaded areas Figure 12: Profit on each plan 3

4 It is also possible to increase profit from a luxury customer If she chooses plan 1, she also pays, that is, the sum of the solid, dotted and vertically shaded areas A luxury consumer s benefit is the area under her demand price function Therefore her net gain if she chooses plan 1 is the diamond patterned area Now consider plan 2 A luxury customer s total benefit is the sum of all the shaded areas Such a customer cannot be charged this much because she can switch to plan 1 and have a net gain equal to the diamond patterned area Telecom can however extract all the other customer benefit by setting a weekly fee r 2 equal to the sum of the dotted and solid areas The latter is the total variable cost Thus the profit is the dotted area Comparing the dotted areas in Figure 11 and 12, it is clear that Telecom can significantly increase profit by offering two plan each with a fixed use allowance and a fixed weekly cost Telecom hires you as a consultant to review the proposal to switch to two plans with usage ceilings and a fixed payment per week You are to offer a recommendation on whether to switch to the new pair of plans, stay with the current plan, or do something else Here are some ideas on how you might do your analysis 1 Would Telecom make more money by increasing the minutes per week (and the total weekly fee on plan 2? 2 Suppose that the minute allowance in the economy plan is increased by q Depict the increase in profit on plan 1 3 There is a catch Adding minutes to plan 1 makes plan 1 more attractive to those purchasing plan 2 Depict this increase in net gain to luxury customers if they switch 4 Is there a trade-off between the increased profit on plan 1 and the loss in profit on plan 2? 4

5 Appendix: Consumer demand and consumer benefit A consumer s benefit from consuming q units of a product is Bq ( ) His marginal benefit from consuming an additional unit is MB( q) B ( q) Typically, the bigger th consumption level, the lower is the marginal benefit The figure below depicts marginal benefit for the special linear case MB( q) B ( q) a bq Figure 11: Customer benefit If the price is p and the consumer purchase q units, the net gain is N( q) B( q) pq The consumer then chooses qp ( ) to solve Max{ N( q) B( q) pq} q Note that N ( q) B ( q) p MB( q) p Therefore to maximize her net gain, the consumer chooses qp ( ) such that p MB( q( p)) 5

6 Marginal benefit is the derivative of total benefit Thus to get q formula for total benefit we need to find a function equal to the marginal benefit This is easy for the linear case Note that the derivative of 1 2 aq 2 bq K Since there is no benefit when B() q aq bq This is the area under the curve p a bq In the non-linear case, is a bq q 0 it follows that q B( q) MB( x) dx p( x) dx 0 0 q 6