In a certain town, the market for a particular product has a single dominant fir
ID: 1194806 • Letter: I
Question
In a certain town, the market for a particular product has a single dominant firm that behaves as a price setter, a competitive fringe comprised of many firms that behave as price takers. The dominant firm sets the price and the competitive fringe follows. There is no shortage or surplus in the market, i.e the market always clears. The market demand and the competitive fringe supply are given as follows:
QM= 140,000 - 32,000P
QF= 60,000 + 8,000P
Where QM= market quantity demanded, and QF= the supply of the competitive fringe.
The dominant firm has an estimated total cost to be:
TC= 5 + 0.025QD2
Where QD= the demand of (quantity produced by) the dominant firm.
A. Determine the profit maximizing level of output for the dominant firm. (* you have to first determine the demand faced byt the dominant firm).
B. What price does the dominant firm set?
C. Determine the dominant firms profit.
D. How much output does the competitive fringe produce?
E. What is the total industry output?
Explanation / Answer
(A). QM = DF + QD
So, QD = QM - DF
= 140,000 - 32,000P - 60,000 - 8,000P
QD = 80,000 - 40,000P ( Denand function for dominant firm)
The inverse demand function for dominant firm is: P = 2 - 0.000025Q
TR = P x Q = 2Q - 0.000025Q2
MR = 2 - 0.00005Q
TC = 5 + 0.025Q2
MC = 0.05Q
profit maximization level of output can be determined when
MR =MC
2 - 0.00005Q = 0.05Q
0,05005Q =2
Q = 39.96 units ( it can be round to 40 units)
(B) P = 2 - 0.000025Q = 2 - 0.000025 x 40 = $1.99 ( it can be round to $2)
(C) Dominant firms profit = TR -TC = (2 x 40) - (5 + 0.025 x 402) = 80 - 40 = $40
(D) QF= 60,000 + 8,000 x 2 = 76,000
(E) 76,000 units ( which is produced only by fringe producers)