In: Economics
Example 4:
Suppose that the monopolist faces a demand curve for its widgets as q = 9 - 0.2p. The firm’s marginal revenue and cost functions are: MR(q) = 45 – 10q and MC(q) = 15 + 5q. The firm’s total cost function is C(q) = 2.5q2 + 15q + 3.
q = 9 - 0.2p
0.2p = 9 - q
p = 45 - 5q
TR = pq
TR = (45 - 5q)q
TR = 45q - 5q2
dTR/dq = 45 - 10q
MR = 45 - 10q
C(q) = 2.5q2 + 15q + 3
MC = 5q + 15
a)
Profit Maximising condition
MR = MC
45 - 10q = 5q + 15
45 - 15 = 5q + 10q
30 = 15q
q = 2
Therefore the firm should sell 2 widgets to maximise its profit.
b)
p = 45 - 5q
p = 45 - 5(2)
p = 45 - 10
p = 35
So the firm should charge $ 35 to maximise its profit.
c)
TR = pq
TR = 35(2)
TR = 70
The firm will earn $70 in total sale or total revenue.
d)
Total profit = TR - C(q)
= pq - 2.5q2 - 15q - 3
= 35(2) - 2.5(2)2 - 15(2) - 3
= 70 - 10 - 30 - 3
= 27
The firm will earn $ 27 in total profits.