Intermediate Microeconomics a) What is the pre-tax equilibrium price and quantit

Question

Intermediate Microeconomics

a) What is the pre-tax equilibrium price and quantity of salmon?
b) What is the post-tax equilibrium price and quantity of salmon?
c) What is the tax burden on producers?

a) What is the competitive equilibrium price and quantity?
b) What is the monopolist price and quantity for Sandra?
c) What are the gains to being a monopolist for Sandra?

a) Suppose both firms play a Cournot game, what is the price and quantity charged by both firms?
b) Suppose both firms compete over price, what is the price and quantity charged by both firms?
c) Suppose BBC Inc. announces his quantity first, and then ABC Inc. observes and announces second
(Stackelberg). What will be the price and quantity charged by both firms?

Explanation / Answer

Ques1.

Qd = 80-5P

Qs = 90+0.75P

This implies, 80-5P = 90+0.75P

This gives price in negative. Hence, equation is wrong for either of demand or supply.

New supply curve: 90+0.75(P+3) = 92.25+0.75P

Equilibrium: Qd = Qs

This implies, 80-5P = 92.25+0.75P

Again, price comes out to be negative.

Ques2.

For a monopoly, equilibrium is achieved when MR = MC

In this case, TC = 2Q. Therefore, MC = 2

Therefore, P = (27/q3)^1/8

or, TR = PQ = (27Q^5)^1/8

Therefore, MR = 27^1/8 . (5/8)Q^(-3/8)

Set this equal to MC = 2 to get equilibrium qty and P

Therefore, P = Q^-7

So, TR = PQ = Q^-6

MR = (-6)Q^-7

Set this equal to MC = 2 to get equilibrium qty and P

So, P = 20/3-Q/3

TR = PQ = 20Q/3

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