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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.

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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 + 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)

Suppose a uniform pricing monopolist's price equation is P(Q) = 120 − Q; the uniform pricing monopolist's marginal revenue is MR(Q) =120 − 2Q; the uniform pricing mo- nopolist's total cost is C(Q) = Q2+40+40Q+150; and the uniform pricing monopolist's marginal cost is MC(Q) = 2Q + 40.

a) Solve for the pro t-maximizing (or loss minimizing) quantity (Q*). (b) Solve for the pro t-maximizing (or loss minimizing) price (P*).

(c) Should the uniform pricing monopolist produce Q*? Explain. (d) Does the uniform pricing monopolist make a pro t? Explain.

(e) How much pro t (or loss) does the uniform pricing monopolist make?

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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