Question

a cycle manufacturer produces X cycles per week at a cost of x2/25+3x+100. He is a monopolist and the demand for his market is x=75-3p where p is the price in rupees per cycle. Show thay the maximum net revenue is obtained when about 30 cycles are produced per week. what is the monopoly price

Answer 1

The maximum net revenue is obtained when MR = MC, so:

x = 75 - 3p, p = 25 - x/3,

$MR = TR'(x) = 25 - 2/3x,$

$MC = TC'(x) = 0.08x + 3,$

$25 - 2/3x = 0.08x + 3,$

0.41x = 22,

x = 53.7.

p = 25 - 53.7/3 = 7.11.