Switching Costs

Suppose there is a new mobile service provider who is hoping to take some subscribers away from an incumbent in a market with switching cost. The incumbent charges $p per month, and incurs a cost of c per subscriber. These numbers are the same for the new entrant. Assume there is no difference in quality of the service provided by the two firms. Also assume that once a consumer switches, s/he stays forever with the service provider.

Let us use the following notation:

p is the monthly payment made by a subscriber

c is the cost of serving one subscriber

s is the switching cost of a subscriber (the monetary value of inconvenience in switching)

g is the amount of “goodies” (e.g., cash back, free phones, etc.) provided by the new entrant

r is the monthly discount or interest rate (e.g., 1%)

A subscriber has to decide whether to switch to the new service provider. S/he will switch only if (p - g) + s + p/r < p + p/r

(p - g) is what s/he pays now, and s/he also incurs a switching cost s. From second month onward, s/he pays p, the present value of which is p/r. Note that p + p/r is what is costs to stay with the current provider.

The minimum g (goodies) that will make the subscriber indifferent between switching to the new provider and staying with the current provider can be found by making the net present value of what it will cost with the new service provider = net present value of what it will cost to stay with the current service provider.

That is p – gmin + s + p/r = p + p/r ……… (1)

This means gmin = s. That is, the new service provider must at least cover the switching cost of the subscriber to make him/her switch.

However, what does the new service provider gain financially by making the subscriber switch?

The new service provider gets (p – c) – g + (p – c)/r from one subscriber. But since we know that the minimum value of g is s (from the above equation), we can write the maximum net present value that the service provider gets from a subscriber:

(p – c) – s + (p – c)/r

Unfortunately for the new service provider, if there is a lot of competition, then the above net present value should tend toward zero. The idea is that with many competitors, if one competitor reduces the price p, then others will follow suit, followed by more rounds of price cuts. Thus we have

(p – c) – s + (p – c)/r = 0 (in the case of heavy competition) ………. (2)

There are two ways to interpret the above equation by rearranging terms:

p = c + s/(1 + 1/r) which is saying that the price should be equal to the marginal cost c plus a markup that is proportional to the switching cost of the subscriber.

Another way to interpret