91Ó°ÊÓ

• 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, $\frac{â–³Q}{â–³P}=\frac{-6}{3}=-2$, 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:

$\frac{â–³Q}{â–³P}=\frac{2}{3}$, 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 $\frac{â–³Q}{â–³P}=-2$ as calculated above.

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

The elasticity of demand will be 0.82.

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

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

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 $\frac{â–³Q}{â–³P}=\frac{2}{3}$ as calculated above.

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

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:

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

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).