In Exercise 4 in Chapter 2 (page 84), we examined a vegetable fiber traded in a competitive world market and imported into the United States at a world price of \(9 per pound. U.S. domestic supply and demand for various price levels are shown in the following table.

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

Answer the following questions about the U.S. market:

a. Confirm that the demand curve is given by QD = 40 - 2P, and that the supply curve is given by QS = 2/3P.

b. Confirm that if there were no restrictions on trade, the United States would import 16 million pounds.

c. If the United States imposes a tariff of \)3 per pound, what will be the U.S. price and level of imports? How much revenue will the government earn from the tariff? How large is the deadweight loss?

d. If the United States has no tariff but imposes an import quota of 8 million pounds, what will be the U.S. domestic price? What is the cost of this quota for U.S. consumers of fiber? What is the gain for U.S. producers?

If the value of demanded quantity coincides with the demand values given in the table after putting different price levels, then the equation is correct for the demand schedule. The same goes for the given supply curve equation.

The demand equation is QD = 40 - 2P. The value of QD for price levels 3,6,9,12,15, and 18 is calculated below:

For price $3, the value of QD is 40 - 2×3 = 34

For price $6, the value of QD is 40 - 2×6 = 28

For price $9, the value of QD is 40 - 2×9 = 22

For price $12, the value of QD is 40 - 2×12 = 16

For price $15, the value of QD is 40 - 2×15 = 10

For price $18, the value of QD is 40 - 2×18 = 4

The values of QD coincide with the values given in the table for the demand schedule. Thus, the equation is true for the demand curve.

A similar process is applied to check for the supply equation QS = 2/3P.

For price $3, the value of QS is 2/3×3 = 2

For price $6, the value of QS is 2/3×6 = 4

For price $9, the value of QS is 2/3×9 = 6

For price $12, the value of QS is 2/3×12 = 8

For price $15, the value of QS is 2/3×15 = 10

For price $18, the value of QS is 2/3×18 = 12

The values of QS coincide with the values given in the table for the supply schedule. Thus, the equation is true for the supply curve.

The world price of fiber is $9. In the absence of any import restrictions, the price of fiber in the U.S. market would be the same. The demanded quantity is 22 million pounds of fiber at this price level, but the U.S. market is supplying only 6 million pounds of fiber. The demand exceeds the supplied quantity.

U.S. market will import fiver to cover the excess demand. The difference between the demanded quantity and supplied quantity is the quantity imported by the U.S market.

$$\begin{gathered} Import=DemandedQuantity-SuppliedQuantity \\ =22-6 \\ =16 \end{gathered}$$

The value of the imported quantity is 16 million pounds.

A $3 per pound tariff on imported quantity will increase the price of the vegetable fiber by $3 in the U.S market. Hence, the price of the vegetable fiber after the imposition of tariff would be $12 per pound.

At this price level, the supplied quantity is 8 pounds, and demanded quantity is 16 pounds as in the market. The supply has increased, and demand has decreased after the imposition of tariffs. The new level import is calculated below:

$$\begin{gathered} NewImport=DemandedQuantity-SuppliedQuantity \\ =16-8 \\ =8 \end{gathered}$$

The new import level is 8 million pounds of vegetable fiber.

Government revenue: The government will earn revenue equal to the product of quantity imported and the amount of tariff on each quantity. Thus, the government revenue will be:

$$\begin{gathered} Governmentrevenue=Quantityimported\left(millionpounds\right)\times Tariff\left(\$\right) \\ =8millionpounds\times 3 \\ =24millionpounds \end{gathered}$$

The value of the deadweight loss: The deadweight loss is the loss to the society created due to the tariff imposed by the government. It is calculated by multiplying the difference between the prices (P2 - P1) and quantities (Q1 – Q2) of the pre-tariff and post-tariff situations. The deadweight loss is calculated below:

$$\begin{gathered} DWL=\left(P_2-P_1\right)\left(Q_1-Q_2\right) \\ =\left(12-9\right)\left(8-6\right) \\ =3\times 2 \\ =6 \end{gathered}$$

The tariff policy created a deadweight loss of $6 million pounds to society.

In the absence of any restriction, the U.S. market was importing 16 million pounds of vegetable fiber. The quota will limit the quantity of vegetables imported into the U.S. market to 8 million pounds since the import quantity is the shortage of goods in the U.S. market. It provides the equation for quota as:

Import = Quantity demanded (QD) –Quantity supplied (QS). Putting the values of import, QD, and QS, the new price after the quota policy is calculated below:

$$\begin{gathered} Import=QD-QS \\ 8=\left(40-2P\right)-\left(\frac{2}{3}P\right) \\ 40-8=2P+\frac{2}{3}P \\ P=12 \end{gathered}$$

After implementing the quota policy, the new U.S. domestic price of fiber will be $12 per pound.

Cost on consumers: In the absence of any import restrictions, U.S. consumers could purchase the vegetable fiber at the world price of $9. The quota policy increased the price of fiber to $12. Thus, the cost on consumers is the difference between the new price (P₂) and the previous price (P₁).

$$\begin{gathered} CostonConsumers=\left(P_2-P_1\right) \\ =\left(12-9\right) \\ =3 \end{gathered}$$

The cost on consumers is $3 per pound of vegetable fiber.

Gain for U.S. producers: The gain to producers is the product of the increase in price level and the quantity after the quota implementation. The new price level is $12 per pound, and the quantity supplied at this price level is 8 million pounds. The gain for producers is:

$$\begin{gathered} GainforU.S.producers=IncreaseinPrice\times InreaseinQuantitysupplied \\ =\$3\times 2millionpounds \\ =\$6millionpounds \end{gathered}$$