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Profits in monopoly and perfectly competitive environment

Consider a market in which the demand curve is given by:
P = 500 - 12Q
Average and marginal cost are both a constant of 20.

a.What is the perfectly competitive price?
b.What is the elasticity of market demand at the competitive price?
c.If the market is perfectly competitive, what is the elasticity of demand facing an individual firm at the market price?
d.What are profits at the perfectly competitive price?
e.What is the monopoly price?
f.What are profits at the monopoly price?
g.Suppose marginal cost increases to 25 as a result of the imposition of a tax. What happens to the monopoly and competitive price and output?
h.Compare the % change in monopoly output as a result of the cost change with the % change in output under perfect competition as a result of the cost change? What accounts for any difference you observe?

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Solution:

a. What is the perfectly competitive price?

For a perfectly competitive market price=marginal cost=$20

b. What is the elasticity of market demand at the competitive price?

P=500-12Q
Q=(500-P)/12
dQ/dP=-1/12

Q at P=20 is given by
Q=(500-20)/12=40
Elasticity of demand at P=20 is given by
Ep=(dQ/dP)*(P/Q)=(-1/12)*(20/40)= -0.04167

c. If the market is perfectly competitive, what is the elasticity of demand facing an individual firm at the market price?
Price ...

Solution Summary

Solution describes the steps for calculating profit for a firm under the assumption if it is operating in perfectly competitive environment and if it is operating in monopoly environment.

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