A vegetable fiber is traded in a competitive world market, and the world price i

Question

A vegetable fiber is traded in a competitive world market, and the world price is $9 per pound. Unlimited quantities are available for import into the United States at this price. The U.S. domestic supply and demand for various price levels are shown as follows:

U.S. Supply U.S. Demand
Price (Million Lbs.) (Million Lbs.)
3 2 34
6 4 28
9 6 22
12 8 16
15 10 10
18 12 4


a)What is the equation for demand?
b)What is the equation for supply?
c)At a price of $9, what is the price elasticity of demand?
d)What is it at a price of $12?
e)What is the price elasticity of supply at $9?
f)At $12?
g)In a free market, what will be the U.S. price and level of fiber imports?

Explanation / Answer

You can run a simple linear regression (OLS) on the data to find the intercept and slope. A) D = 40-2P B) S = 3P/2 It's good to confirm that the demand equation is downward sloping and the supply equation is upward sloping. C) At P=9, D=22. The price elasticity is calculated as follows: E=L*(P/Q), where L is the slope of the demand curve. So, E=-2*(9/22)=-0.81. D) At P=12, D=16 E=-2*(12/16)=-1.5 E) At P=9, S=6. Remember to use the slope of supply, not demand. E=(3/2)*(9/6)=2.25. F) At P=12, S=8 E=(3/2)*(12/8)=2.25 G) If the world price is $9, then the US price will be $9. At this level, D=22 and S=6. So, the imports will be 22-6=16.

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