Could you calculate the revenue-maximizing quantity and price?
From the scenario, assuming Katrina's Candies is operating in the monopolistically competitive market structure and faces the following weekly demand and short-run cost functions:
VC = 20Q+0.006665 Q2 with MC=20 + 0.01333Q and FC = $5,000
P = 50-0.01Q and MR = 50-0.02Q
*Where price is in $ and Q is in kilograms. All answers should be rounded to the nearest whole number.
Algebraically, determine what price Katrina's Candies should charge in order for the company to maximize profit in the short run. Determine the quantity that would be produced at this price and the maximum profit possible.
Answer:
P = 50-0.01Q........demand curve
Profit is maximized at a point where MR = MC i.e.
50-0.02Q = 20 + 0.01333Q or
30 = 0.03333Q, implies profit maximizing quantity (Qm) = 30/0.03333 = 900 approx.
And profit maximizing price (Pm) = 50-0.01*900 = $41 [using demand curve]
So maximum profit = total revenue - total cost = P*Q - FC - VC = 41*900 - 5000 - 20*900-0.006665*(900^2) = $8501.35