1. A profit maximizing monopolist faces a demand function given by Q(p)=70-p. Th
ID: 1202771 • Letter: 1
Question
1. A profit maximizing monopolist faces a demand function given by Q(p)=70-p. The cost function is C(q)=5q. Suppose that the government introduces a tax of $10 per unit of output. As a result of the tax, the monopolist will? (increase the price to what?)
2. A price-discriminating monopolist with a constant marginal cost sells in two separate markets such that the goods from one market cannot be resold in the other. The profit maximizing price in market 1 is 4 and in market 2 is 8. If the price elasticity of demand in market 1 is -1.5, what is the price elasticity of demand in market 2?
Explanation / Answer
1)Q(p)=70-p
p=70-q
TR=P.q
=70q-q2
MR=70-2q
C(q)=5q
MC=5
tax=$10 per unit
For a profit maximizing monopolist
MC=MR
70-2q=5
2q=65
q=32.5
p=70-q
=70-32.5
=37.5
For a profit maximizing monopolist with taxes
MR(y) = MC(y) + t
70-2q=5+10
2q=70-15
q=55/2=27.5
p=70-q
=70-27.5
=42.5
Increase in price=42.5-37.5=5
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