A firm exist as a monopoly in the industry and has the following functions of revenue and cost.
TR = 300q -2q²
TC = 2q³ - 20q² + 60q +60
Find the level of output at which the firm will maximize the profits.
To maximize profits, we need to find the level of output where marginal revenue (MR) equals marginal cost (MC).
First, we need to find the total revenue function by taking the derivative of the total revenue function:
TR = 300q - 2q^2
MR = dTR/dq = 300 - 4q
Next, we need to find the total cost function by taking the derivative of the total cost function:
TC = 2q^3 - 20q^2 + 60q + 60
MC = dTC/dq = 6q^2 - 40q + 60
Now, we set MR equal to MC and solve for q:
300 - 4q = 6q^2 - 40q + 60
6q^2 - 36q - 240 = 0
q^2 - 6q - 40 = 0
(q - 10)(q + 4) = 0
q = 10 or q = -4
Since output cannot be negative, the level of output at which the firm will maximize profits is q = 10.