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Calculating profit maximizing price and output level

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A high-end lamp monopolist operates in the Mid-West where the demand for lamps is given by Q1=200-P1. Producing one lamp costs 10 per unit.

(a) Derive the profit maximizing price and the profits at this price.

(b)What is the demand elasticity at this price?

Suppose now that the monopolist has the opportunity to expand to the East Coast.This would entail launching an advertising campaign at a cost of 1000,a one time expense. The demand on the East Coast is given by Q2 =160-3P2.The per-unit cost of selling lamps on the East Coast is identical to the cost of selling them in the Midwest.Suppose first that,because he is thinking of selling from his website,the monopolist must charge the same price in both markets .

(c) What is the total demand when the monopolist charges a price P?

(d) Derive the profit maximizing price and the profits at this price in the case where
the monopolist must charge the same price in both markets.Would you recommend the monopolist to expand to this market?
Now suppose that the monopolist will sell through a network of distributors,and can charge different prices on the East Coast and in the Mid West .

(e)What price would the monopolist charge in the Mid-West?What price would the
monopolist charge in the East?What are the total profits?Would yo recommend the monopolist to expand in this case?

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Solution Preview

(a) Derive the profit maximizing price and the profits at this price.

Q1=200-P1
On rearranging, we get
P1=200-Q1

Total Revenue in Mid West=TR1=P1*Q1=(200-Q1)*Q1=200Q1-Q1^2
Marginal Revenue in Mid West=MR1=d(TR1)/dQ1=200-2Q1

A monopolist will set its output level such that MR1=MC to maximize profits.
Put MR1=MC
200-2Q1=10
2Q1=190
Q1=95
P1=200-Q1=200-95=$105

Total Revenue=105*95=$9975
Total Cost=10*95=$950

Profits=Total Revenue-Total Cost=9975-950=$9025

(b)What is the demand elasticity at this price?
Q1=200-P1
dQ1/dP1=-1

He have calculated that P1=$105 and Q1=95

Price elasticity of demand=(dQ1/dP1)*(P1/Q1)=-1*(105/95)=-1.05

Suppose now that the monopolist has the opportunity to expand to the East Coast.This would entail launching an advertising ...

Solution Summary

Solution describes the steps to calculate profit maximizing output and price in the given case.

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See Also This Related BrainMass Solution

Calculating profit maximizing output level and price

Suppose a company has just introduced a new line of ceramic insulators for which it has received patent protection, effectively granting the company monopoly status in the industry. The company's revenue and cost relations are given as:

TR = $300Q - $0.001Q2

TC = $9,000,000 + $20Q + $0.0004Q2

where TR is total revenue, Q is output, and TC is total cost.

a) As a monopolist, calculate this firm's optimal output (Q) and price per unit (P).
b) Calculate the level of total profit at this output level and also the value of per unit profit at this output level.

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