The color copy machine market is dominated by a large firm with significant prod
ID: 1212368 • Letter: T
Question
The color copy machine market is dominated by a large firm with significant production capacity. The market demand for color copy machines is:
Q = 4300 - 5 P
The dominant firm has projected the supply by the small firms in the market to be:
Qs = - 700 + 3 P
I. Write the demand curve faced by the dominant firm.
II. What price should the leader charge to drive all the small firms out of the market?
III. Write the marginal revenue function of the dominant firm.
IV. Assuming the leader's cost function is:
TC = 6000 + 175 Q + 1/32 Q2,
determine the following:
a. The price
b. The total quantity demanded (purchased)
c. The leader's share of the market
d. The small firms' share of the market
e. The leader's profit
f. Assuming the consolidated fixed cost of the small firms is $25000, determine the small firms' consolidated profits.
Explanation / Answer
I. The market demand for color copy machines minus the dominant firm's projected supply by small firms will give us the market demand function for dominant firm.Which is
Qd= 4300-5P-(-700+3P)
=>Qd= 5000-8P
III) Given Q = 4300-5P
=>P = 860-Q/5
Now Total revenue(TR) = Price * Quantity
So TR = (860-Q/5) * Q
=> TR = 860Q - Q2/5
Differentiate TR with respect to Quantity We have Marginal Revenue (MR).
MR = 860-0.4Q
IV(B)TC = 6000 + 175 Q + 1/32 Q2
Now to find Price and output first we have to find Marginal Cost (MC) which is nothing but Differentiating TC with respect to Quantity (Q).
So MC = 175+Q/16
Now setting MR= MC
we have 860-0.4Q=175+Q/16
=> Q = 685/0.4625
=> Q = 1481 (Approx)
IV(A)Now put Q in
Q = 4300-5P
We have
P = (4300-1481)/5
=>P = 564(Approx)
IV(C) Now put P = 564 in Qs= -700 + 3P
so, Qs= 992 and 1481-992 = 489
market share = (489/1481) *100= 33.02%
IV(D) Therefore small firms share = 66.98%
IV(E) Leader's Profit = (1481-992)*564 = $275796