A monopolistic firm faces the following demand curve. Q = 8000 -10 P This monopo
ID: 2496466 • Letter: A
Question
A monopolistic firm faces the following demand curve.
Q = 8000 -10 P
This monopoly's cost function has been estimated as follows:
TC = 480,000 + 40 Q
a. What price should this monopoly charge to maximize its profit?
b. What would be its equilibrium profit?
c. What price should it charge if it were to maximize its revenue?
d. What would be its profit if it maximized its revenue?
e. If this monopoly were to behave like a competitive firm, what price should it charge and what quantity should it produce?
f. Would this monopolist still make an economic profit if it were to behave like a competitive firm?
g. What is the break-even quantity of this monopoly?
Explanation / Answer
Demand curve: Q = 8000 – 10P
Inverse demand function, 10P =8000 – Q
=> P = (8000-Q) / 10
=> P = 800 – (Q/10)
Total Revenue = price x Quantity = P x Q
=> TR = (800 – (Q/10)) x Q
=> TR = 800Q – (Q2/10)
We can calculate Marginal revenue as derivative of Total revenue,
So MR = d (TR)/dQ
=> MR = d (800Q – (Q2/10))/dQ
=> MR = 800 – (2Q/10)
=> MR = 800 – (Q/5)
Total Cost: TC = 480,000 + 40Q
We can calculate Marginal cost as derivative of Total cost,
Marginal cost = d (TC) / dQ
= d (480,000 + 40Q) / dQ
= 40
For monopolist, to find the maximizing profit quantity, the MR = MC
=> 800 – (Q/5) = 40
=> Q/5 = 800-40
=> Q = 760 x 5
=> Q = 3800
a)
Now we can use this quantity in demand curve to find the profit maximization price,
=> Q = 8000 – 10P
=> 3800 = 8000 – 10P
=> 10P = 8000 – 3800
=> P = 4200 / 10
=> P = 420
So the price = 420
b) Profit = Total Revenue – Total Cost
= 800Q – (Q2/10) – (480,000 + 40Q)
= 800Q – (Q2 / 10) – 480,000 – 40Q
= 760Q – (Q2 / 10) – 480,000
Now for equilibrium profit, we need to put the profit maximization quantity already found in the above profit equation, Q = 3800
=> Equilibrium profit = 760Q – (Q2 / 10) – 480,000
= (760 x 3800) – (38002 / 10) - 480,000
= 2,888,000 – 1,444,000 - 480,000
= 964,000
c) To maximize the revenue, when MR=MC, for that quantity meeting the Demand line will provide the price,
It is same as the profit maximization price = 3800 (Already calculated in question a)
d) With the price 3800, the profit is 964,000 (Already calculated in question b)
e) If this monopoly were to behave like a competitive firm, then for profit maximization,
MR = MC = Price
As Marginal Cost (MC) = 40, the price should be 40.
With this price the quantity = 3800 (Already calculated before question a)
f) Total profit = Total Revenue – Total Cost
= P x Q – (480,000 + 40Q)
= 40 x 3800 – 480,000 – (40 x 3800)
= 152000 – 480000 - 152000
= -480,000
So the monopoly will make loss if it will behave like a Competitive firm
g) The break-even quantity should be 3800
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