Question

3) Suppose the number of users (i.e. total quantity demanded) for a new online messaging service (NOMS) is:
?=?−?+??? ?h????∈(0,1),?? ???h????????????????????,????h??????. a) Interpret the parameter ?. What strategies can NOMS use to affect ??
1
b)Suppose?=100, ?=2, ????h??????????????????????????? ???h???=? ,andthe
marginal cost per user is 0. What is the profit maximising price? (1 mark)

Answer 1

a)

The number of users for a new online messaging service is given by,

n = M - p - y ne , where y(0,1)

Here, ne: Expected network size

p: price

Here, y is the sensitivity that measures the change in the number of users due to the change in the expected network size. And the sensitivity lies between 0 and 1.

The NOMS can change the price i.e p to affect the sensitivity i.e y. The changes in the income i.e M can also affect the sensitivity i.e y.

b)

When M=100 and y=2 then the equation for the number of users become,

n = 200 - p -2 ne

And the users accurately anticipated so, ne=n. And the equation becomes

n = 200 - p - 2n

=> p =200 -2n - n

=> p = 200-3n

The marginal cost is zero. so, the profit function is given by

= p.n -0 = (200-3n)n = 200n - 3n²

Now, max

At F.O.C,

=> 200 -6n = 0

=> 6n= 200

=> n = 200/6

Therefore, price p = 200 - 3*200/6 = 200-100 = 100

Therefore p =100 is the profit maximising price.