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...

Answer to 21:
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.
b)
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)
Answer to 23:
Individual demand in segment A: q= 1- (1/100)p and individual demand in segment B: q = (1/2)-(1/100)P
Cost function: C = 600+20q, marginal cost (MC) = dC/dq = 20
(a)
Total market demand: Q = 100qA+ 200qB = 100[1- (1/100)p] + 200[(1/2)-(1/100)P] = 100-p+100-2p = 200-
3p
So...