1. Ajax, Inc. is a monopolist. The estimated demand function for its product is
ID: 1178053 • Letter: 1
Question
1. Ajax, Inc. is a monopolist. The estimated demand function for its product is
Qd = 120 %u2013 0.8P + 12Y + 4A
Where Qd denotes quantity demanded, P denotes price, Y denotes personal income (in thousands of dollars), and A denotes advertising expenditures in hundreds of dollars.
Ajax%u2019s marginal cost function is given as
MC = 21 + 4Q
Assume Y equals 3 and A equals 3 and fixed costs equal $1000
a. What is the inverse demand function? (The equation demand equation in the form
P = a %u2013 bQd)?
b. What is the profit maximizing price and quantity of output for Ajax, assuming it is an unregulated monopoly? What are its profits?
c. If fixed costs increase to $1200, what will happen to equilibrium price and quantity?
Explanation / Answer
Ajax, Inc. is a monopolist. The estimated demand function for its product is
Qd = 120 %u2013 0.8P + 12Y + 4A
Where Qd denotes quantity demanded, P denotes price, Y denotes personal income (in thousands of dollars), and A denotes advertising expenditures in hundreds of dollars.
Ajax%u2019s marginal cost function is given as
MC = 21 + 4Q
Assume Y equals 3 and A equals 3 and fixed costs equal $1000
a. What is the inverse demand function? (The equation demand equation in the form
P = a %u2013 bQd)?
Qd = 120 %u2013 0.8P + 12Y + 4A
0.8P = Qd - 120 + 12Y + 4A
P = (1/0.8)[Qd - 120 + 12Y + 4A]
b. What is the profit maximizing price and quantity of output for Ajax, assuming it is an unregulated monopoly? What are its profits?
MC = 21 + 4Q
C = 21Q + 2Q^2 + c
c = fixed costs = $1000
Minimizing cost would be:
dC/dQ = 21 + 4Q
Q = -21/4 = 5 units
Hence, profit maximizing Quantity = 5 units
profit maximizing price = (1/0.8)[Qd - 120 + 12Y + 4A] = (1/0.8) (5 - 120 + 12x3 + 4x3) = $83.75
Profits = Revenue - Cost
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