Question

Suppose the demand curve for a firm is Q=50 - 0.125P, where Q measures units of output and P is the price per unit. Complete the following:

a.Derive the firm's marginal revenue curve.

b. What is the value of marginal revenue at 10 units of output?

c. Graph the firm's demand and marginal revenue curve.

Answer 1

Answer : a) Q = 50 - 0.125P

=> 0.125P = 50 - Q

=> P = (50 - Q) / 0.125

=> P = 400 - 8Q

TR (Total Revenue) = P * Q = (400 - 8Q) * Q

=> TR = 400Q - 8Q^2

MR (Marginal Revenue) = TR / Q = 400 - 16Q

Therefore, here the marginal revenue curve is,

MR = 400 - 16Q

b) When Q = 10 units,

MR = 400 - (16 * 10)

=> MR = $240

Therefore, here the value of marginal revenue is $240.

c) For demand curve we have to take Q = 0 to demand function. So, the intercept of price axis is,

P = 400 - (8 * 0)

=> P = 400

For the intercept of demand curve on quantity axis we have to take P = 0 to demand function. So, the intercept of demand curve on quantity axis is,

Q = 50 - (0.125 * 0)

=> Q = 50

Now for marginal revenue curve the intercept on price axis is same as demand intercept. But the marginal revenue intercept on quantity axis is half of the demand intercept.

The demand curve and marginal revenue curve are shown in the following picture's diagram.