30. Correct. The answer is true.
To maximize profits, the price discriminating monopolist would produce when MR
= MC. For a perfectly price discriminating monopolist
P = 50-0.25Q =
MR = 50 - 0.25
or the
demand curve.
50 - 0.25Q =
2.5Q,
Q = 50/2.75 =
18.18.
Substituting Q into demand
curve, P = 50 - 0.25*18.18 = $45.45.
Total profits for this
monopolist are the total area under the demand curve minus the total area under
the marginal cost curve. In general notation, profits would be the integral of
the demand curve from 0 to 18.18 minus the integral of the marginal cost curve
from 0 to 18.18 or
∫018.18 (50-0.25q)dq - ∫018.18 (2.5Q)dq
The integral of the demand curve
is
50q - 0.125q2|018.18 = 50*18.18 -
0.125*(18.18)2 - (50*0 - 0.125*(0)2 = 867.7.
The integral of the marginal
cost curve is
1.25* q2 |018.18 = 18.182*1.25
- 02*1.25 = 413.14.
Total profits for the perfectly
discriminating monopolist are
π
= 867.7 - 413.14 = 454.56.