Question

If, in a monopoly market, the demand function for a product is p = 140 − 0.10x and the revenue function is R = px, where x is the number of units sold and p is the price per unit, what price will maximize revenue?

Answer 1

The revenue here is given as:

R = px = (140 - 0.1x)*x = 140x - 0.1x²

Differentiating it with respect to x, we get here:

$\frac{\mathrm{d} R}{\mathrm{d} x} = 140 - 0.2x$

Differentiating it again with respect to x, we get here:

$\frac{\mathrm{d}^2 R}{\mathrm{d} x^2} = - 0.2 < 0$

Therefore we would get maximum value of R for dR / dx = 0

Therefore, we have here:

140 - 0.2x = 0

x = 140/0.2 = 700

Therefore the price that will maximize the revenue is computed as:

P = 140 - 0.1x = 140 - 0.1*700 = 70

Therefore 70 is the required price here.