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:

PRICE	U.S. SUPPLY (MILLIONS)	U.S. (DEMAND) (MILLIONS)
3	2	34
6	4	28
9	6	22
12	8	16
15	10	10
18	12	4

1. What is the equation for demand? What is the equation for supply?

2. At a price of \)9, what is the price elasticity of demand? What is it at a price of \(12?

3. What is the price elasticity of supply at \)9? At $12?

4. In a free market, what will be the U.S. price and level of fiber imports?

• The demand curve equation is represented by Q = a + bP, where Q is the quantity demand, P is the price in the market; a is the intercept, b is the slope of the demand curve, i.e., change in quantity demanded by the change in price.

The quantity falls by 6 million pounds as the price increase by $3. Thus, $\frac{△Q}{△P}=\frac{-6}{3}=-2$, the slope of the demand curve is -2, i.e., b = -2. To get the value of a, substitute any value of Q and P in the demand curve from the given table. For example, consider Q = 34, and P = $3. Therefore, the value of a will be:

34 = a - 2(3)

34 = a - 6

a = 34 +6

a = 40

The value of a will be 40. The demand curve will be Q = 40 - 2P.

• The supply curve equation is represented by Q = c + dP, where Q is the quantity supply, P is the price in the market, c is the intercept, d is the slope of the supply curve, i.e., change in quantity supplied by the change in price. If the quantity rises by 2 million pounds as the price increase by $3, the slope will be:

$\frac{△Q}{△P}=\frac{2}{3}$, the slope of the demand curve is 2/3, i.e., d = 2/3.

To get the value of c, substitute any value of Q and P in the supply curve equation from the given table. For example, consider Q = 2, and P = $3. Therefore, the value of a will be:

2 = c +2/3(3)

2 = a + 2

a = 2-2

a = 0

The value of c will be 0. The supply curve will be $Q=\frac{2}{3}P$.

The price elasticity demand when the price is $9 is calculated below:

The slope of the demand curve, i.e., rate of change, will be $\frac{△Q}{△P}=-2$ as calculated above.

$$\begin{gathered} E_D=\frac{△Q}{△P}\times \frac{P}{Q} \\ \frac{△Q}{△P}=-2 \\ {E}_D=-2\times \frac{9}{22} \\ =-0.82 \\ \left|E_D\right|=0.82 \end{gathered}$$

The elasticity of demand will be 0.82.

The price elasticity demand when the price is $12 is calculated below:

$$\begin{gathered} E_D=\frac{△Q}{△P}\times \frac{P}{Q} \\ \frac{△Q}{△P}=-2 \\ {E}_D=-2\times \frac{12}{16} \\ =-1.5 \\ \left|E_D\right|=1.5 \end{gathered}$$

The elasticity of demand will be 1.5.

The price elasticity supply is calculated when the price is $9 and quantity is 6 million pounds below:

The slope of the supply curve, i.e., rate of change, will be $\frac{△Q}{△P}=\frac{2}{3}$ as calculated above.

$$\begin{gathered} E_S=\frac{△Q}{△P}\times \frac{P}{Q} \\ \frac{△Q}{△P}=\frac{2}{3} \\ {E}_S=\frac{2}{3}\times \frac{9}{6} \\ =1 \end{gathered}$$

The elasticity of supply will be 1.

The price elasticity supply is calculated when the price is $12 and quantity is 8 million pounds below:

$$\begin{gathered} E_S=\frac{△Q}{△P}\times \frac{P}{Q} \\ \frac{△Q}{△P}=\frac{2}{3} \\ {E}_S=\frac{2}{3}\times \frac{12}{8} \\ =1 \end{gathered}$$

The elasticity of supply will be 1.

The U.S. price will be the world price in the free market, i.e., $9 per pound. At $9, the U.S. supply is 6 million pounds, and demand is 22 million pounds. The import quantity will be 16 million pounds (=22 – 6).