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Assume quantities need not be integers. Market demand is MWTP=80-Q. Each firm in a constant-cost industry...

Assume quantities need not be integers. Market demand is MWTP=80-Q. Each firm in a constant-cost industry has total costs TC(q)=45+40q+5q^{2} and marginal costs are MC(q)=40+10q. If there are currently 10 firms in the market, what is short-run equilibrium price? Enter a number only, no $ sign.

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Answer

the individual firm supply curve is the MC curve

MC=40+10q

P=40+10q

converting to normal form

10q=40+P

q=-4+0.1P

the market supply is

Q=q*10=40+P

Q=-40+P

converting to the inverse supply of market

P=Q+40

equating with demand

80-Q=Q+40

2Q=40

Q=20 units

P=80-20=60

the price is $60

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