(a)
Revenue (R) = P x q = 100q - 3q2
Cost (C) = 8 + 2q2
Profit (Z) = R - C
Z = 100q - 3q2 - 8 - 2q2
Z = 100q - 5q2 - 8
(b)
Profit is maximized when dZ/dq = 0
dZ/dq = 100 - 10q = 0
10q = 100
q = 10
R = (100 x 10) - (3 x 10 x 10) = 1000 - 300 = 700
C = 8 + (2 x 10 x 10) = 8 + 200 = 208
Z = 700 - 208 = 492
(c)
The minimum price is the minimum point of AVC, where MC intersects AVC.
AVC = TVC/q = 2q2/q = 2q
MC = dC/dq = 4q
Equating,
2q = 4q
This holds true when q = 0.
Minimum price = AVC = 2 x 0 = 0
Exercise 1. Your firm produces basketballs. The inverse demand function for your basketballs is given by: P = 100 – 3q....
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Show work please A monopolist's inverse demand function is P= 150 – 3Q. The company produces output at two facilities; the marginal cost of producing at facility 1 is MC1(Q1) = 6Q1, and the marginal cost of producing at facility 2 is MC2(Q2) = 2Q2: a. Provide the equation for the monopolist's marginal revenue function. (Hint: Recall that Q1 + Q2 = Q.) MR(Q) = 150-C6 Q4-06 Q2 b. Determine the profit-maximizing level of output for each facility. Output for...
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The OUTPUT is already answered BUT STILL NEED PROFITS FOR EACH FIRM. please don’t forget to answer profits for part 1!!! Two firms compete as a duopoly. The demand they face is P 100-3Q. The cost function for each firm is C(Q) = 4Q. Determine output, and profits for each firm in a Cournot oligopoly 2 If firms collude, determine output and profit for each firm. 3. If firm 1 cheats on the collusion in item 2, determine output and...
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