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Finding Equilibrium Price and Output

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Question: Consider a competitive market served by many domestic and foreign firms. The domestic demand for these firm's product is Qd=500-1.5P. The supply function of the domestic firms is Qsd=50+.5P, while that of the foreign firms is Qsf=250.

A) Determine the equilibrium price and quantity under free trade.
B) Determine the equilibrium price and quantity when foreign firms are constrained by a 100-unit quota.
C) Are domestic consumers better or worse off as a result of free trade?
D) Are domestic producers better or worse off as a result of the quota?

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First, we map the demand curve and the supply curve. (Please view attachment for this)

Demand: Qd=500-1.5P
- When P = 0, Qd = 500
- When Qd =0 , P = 500/1.5 = 333.333
This is a linear function, thus a straight line with a -2/3 slope (ie. the inverse of 1.5).

Domestic Qsd=50+.5P
When P = 0, Qsd = 50
This is a linear function. If you play with it you get that it is: 1/2P=Qsd-50
Which means that the slope is 2.

That of the foreign firms is Qsf=250. They will supply ...

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