Suppose the market demand function is given by: Q = 100 - 2P , where Q: total qu

Question

Suppose the market demand function is given by: Q = 100 - 2P , where Q: total quantity, P: market price. And in this market there are two firms with MC=AV= $10. Find each of the following: 1. Perfect competition price, quantity, and consumer surplus? 2. Monopoly price, quantity, consumer surplus, profit, and welfare loss? 3. Cournot price, quantity, consumer surplus , each firm`s profit, and welfare loss? 4. Stackelberg price, quantity, consumer surplus, each firm`s profit, and welfare loss? 5. Collusion quantity, profit from collusion?

Explanation / Answer

Perfect Competition

P=MC

Q = 100 - 2P or 2P = 100 -Q or P = 50 - 0.5Q

50 - 0.5Q = 10

0.5Q = 40

Q = 80

P = 10

Consumer Surplus = 0.5*(50-10)*80 = 1600

TR = 50Q - 0.5Q^2

TC = 10Q

Profit = TR - TC = 50Q - 0.5Q^2 - 10Q

= 50*80-0.5*80*80-10*80

= 0(Long run equilibrium)

Monopoly

P = 50 - 0.5Q

TR = P*Q = 50Q - 0.5Q^2

MR=dTR/dQ = 50 - Q

MC = 10

MR=MC, the condition for equilibrium

50-Q = 10

Q = 40

P = 50 - 0.5*40 = 30

Consumer Surplus = 0.5*(50-30)*40 = 400

Profit = TR - TC = 50Q - 0.5Q^2 - 10Q

= 50*40-0.5*40*40-10*40

=800

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