Question

1. A laptop manufacturer produces ‘𝑥’ sets per week at total cost of

𝑅𝑠. (2𝑥/25+ 3𝑥 + 100). He is a monopolist and the demand for his product

is: 𝑥 = 75 − 3𝑝, where 𝑝 is the price in rupees per set. Shoe that the

maximum revenue is obtained when about 30 sets are produced per week.

What is the monopoly price?

Answer 1

The maximum revenue TR is obtained when $TR'(x) = MR = (p×x)' = 25 - 2x/3 = 0.$

The monopoly price and quantity are:

MR = MC,

25 - 2x/3 = 2x/25 + 3,

56/75 x = 22,

x = 29.46 units,

p = 25 - 29.46/3 = 15.18.