# 21. (Monopoly under Various Objectives) Pororo and Crong are co-owners of the media company supplying a 3D animation toolkit as a monopoly. Their company has the total cost function C= 3,200 -I- q2...

21. (Monopoly under Various Objectives) Pororo and Crong are co-owners of the media company supplying a 3D animation toolkit as a monopoly. Their company has the total cost function C= 3,200 -I- q2 and the market demand is given by Q= 200 — p. (a) Pororo wants to sell as many toolkits as possible without losing money. What would be his choice of price and output? Explain. (b) Crong wants the company to bring in as much revenue as possible. What would be his choice of price and output? Explain.

## Solution

Robert answered on Dec 20 2021
C = 3200+q^2
Q = 200-p, implies p= 200-Q
a)
C = 3200+q^2, implies marginal cost (MC) = dC/dq = 2q
Since pororo wants to sell maximum possible toolkits without losing money, it would operate at a point
where price equals the marginal cost i.e.
200-q = 2q, implies optimum output q = 66.67
And price P = 200-66.67 = 133.33
And the profit = P*q-C = 133.33*66.67-3200-66.67^(2) = \$1244.222
This kind of pricing would ensure that firms sell the maximum possible toolkits without losing money.
)
Total revenue (TR) = P*q = 200q-q^2
For maximum, dTR/dq = 0 i.e. 200-2q = 0 implies optimum choice of output q = 100
And optimum choice of price P = 200-100 = 100 (from the demand function)