Question

If demand for the price searching-firm (e.g. monopoly) is q=20-p and total cost is 2+4q^2.
A)Compute the marginal revenue function. To check it what is marginal revenue from selling 4 units of output?

B)What is the profit for this price searching firm?

Answer 1

Answer : A) Given,

q = 20 - p

=> p = 20 - q

TR (Total Revenue) = p*q = (20 - q) * q = 20q - q^2

MR (Marginal Revenue) = TR / q = 20 - 2q

Therefore, here the marginal revenue function is,

MR = 20 - 2q.

Now if q = 4 units then

MR = 20 - (2 * 4)

=> MR = 12

Therefore, when q = 4 then the marginal revenue is MR = 12.

B) Given,

TC (Total Cost) = 2 + 4q^2

MC (Marginal Cost) = TC / q = 8q

For price searching firm the profit maximizing condition is MR = MC. So,

20 - 2q = 8q

=> 20 = 8q + 2q

=> 20 = 10q

=> q = 20 / 10

=> q = 2

From demand function we get,

q = 20 - p

=> 2 = 20 - p

=> p = 20 - 2

=> p = 18

TR = p*q = 18 * 2 = 36

TC = 2 + 4 * (2)^2

=> TC = 18

Profit = TR - TC = 36 - 18 = 18

Therefore, here the price searching firm's profit level is 18.