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A monopolist with total cost function T C = 30Q + Q^2 is facing a market demand given by P = 150 Q.

a) What is the optimal quantity and price the monopolist will set on this market? (Q=30, P=120)

b) What quantity and price would this firm set if it was to behave competitively? (Q=40, P=110)

c) Calculate the price elasticity of demand at the monopoly price and quantity point. Does the Lerner price formula hold? (-4)

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Kritika Krishnakumar
Kritika KrishnakumarLv10
28 Sep 2019

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Related questions

A monopolist with total cost function T C = 30Q + Q2 is facing a market demand given by P = 150 - Q. a) What is the optimal quantity and price the monopolist will set on this market? (Q=30, P=120) b) What quantity and price would this firm set if it was to behave competitively? (Q=40, P=110) c) Calculate the price elasticity of demand.

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?

Consider a single firm facing inverse demand function
p=100-10q
where q is the quantity of the good produced and p is the price for the good.
The firm has a linear cost function C(q)=10q.

Suppose now two firms are facing inverse demand function
p = 100 - 10Q
where Q=q_1 + q _ 2 is the total quantity of the good produced and p is the price for the good.
Each firm has linear cost function C(q) = 10q .

Compare the monopoly price in Q1, call it p^M, to the competitive equilibrium price in Q2, call it p^CE,
What is p^M - p^CE

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