Answer :
Answer:
1) [tex]\frac{d\pi (q) }{dq} = 40 - 20 - 20q = 0[/tex]
2) variable cost would be = 20 + 10 = 30, revenue = 40 , -100
3) Q = 1
Explanation:
The firm's profit function is given as
[tex]pi (q) = R(q) = C(q) = 40q - (110 + 20q + 10q^2).[/tex]
1) The positive output level that maximizes the firm's profit
can be expressed as the derivative of the given function
= [tex]\frac{d\pi (q) }{dq} = 40 - 20 - 20q = 0[/tex]
2) The firm's revenue, variable cost and profit
variable cost = 20 + 10q ( from the given function )
when q = 1 variable cost would be = 20 + 10 = 30
TR = 40q = revenue ( from given function)
when q = 1 then revenue = 40
hence variable cost is less than Revenue ( firm should operate in short run)
profit = Revenue - total cost = 40 - 140 = -100
3) The output level at which the firms profit is maximized is
q = 1