Question

The domestic supply and demand curves for hula beans are as follows:

Supply: P = 50 + Q

Demand: P = 200 - 2Q

where P is the price in cents per pound and Q is the quantity in millions of pounds. The U.S. is a small producer in the world hula bean market, where the current price (which will not be affected by anything we do) is 60 cents per pound. Congress is considering a tariff of 40 cents per pound. Find the domestic price of hula beans that will result if the tariff is imposed. Also compute the dollar gain or loss to domestic consumers, domestic producers, and government revenue from the tariff.

Short answer

• After the imposition of the tariff, the domestic price will be 100 cents or $1 per pound for hula beans.

• The domestic consumers will lose. The loss will be equal to $8 million.

• The domestic producers will gain. The gain will be equal to 16 million.

• The government revenue will be zero.

Step-by-step solution

Step 1. Determining the U.S. domestic price after the imposition of tariff policy

The price of hula beans in the U.S market before the imposition of the tariff was 60 cents per pound. The government is imposing a tariff of 40 cents on it. The new price of the hula beans in the U.S. domestic market will be the sum of the previous price and tariff amount. It is calculated below:

$$\begin{gathered} NewDomesticprice=PreviousPrice+TariffAmount \\ =\left(60+40\right) \\ =100cents \end{gathered}$$

The U.S. domestic price after the imposition of tariff policy is 100 cents or $1.

Gain or loss to domestic consumers

The demand equation for the hula beans is:

The quantity demanded by consumers at the old price (60 cents) is:

$$\begin{gathered} P=200-2Q \\ 2Q=200-P \\ Q=100-\frac{P}{2} \end{gathered}$$

The quantity demanded by consumers at the new price level of 100 cents after the imposition of tariff policy is:

$$\begin{gathered} OldDemandedQuantity,Q1=100-\frac{60}{2} \\ =100-30 \\ =70 \end{gathered}$$

The new demanded quantity is 50 million pounds at the new price level.

$$\begin{gathered} NewDemndedQuantity,Q2=100-\frac{100}{2} \\ =100-50 \\ =50 \end{gathered}$$

The tariff increased the price of hula beans in the U.S. market. This has caused consumers to decrease the level of quantity demanded by them. Hence, the policy is creating loss to the consumers.

The extent of loss to domestic consumers is calculated by multiplying the decrease in quantity demanded with the tariff price. It is calculated below:

$$\begin{gathered} Losstoconsumers\left(millions\right)=\left(Q1-Q2\right)\times TariffPrice \\ =\left(70-50\right) \\ =800cents \\ =\$8 \end{gathered}$$

Loss to domestic consumers after the imposition of tariff is $8 million.

Step 3. Gain or loss to domestic producers

The tariff increased the price of hula beans in the U.S. market. The producers will increase their production level at a higher price.

The supply equation for hula beans is:

$$\begin{gathered} P=50+Q \\ Q=P-50 \end{gathered}$$

The quantity supplied at the old price (60 cents) is:

$$\begin{gathered} OldSuppliedQuantity,S1=60-50 \\ =10 \end{gathered}$$

The suppliers will supply 10 million pounds at the old price level of 60 cents.

The new supplied quantity is calculated at the new price level of 100 cents after the imposition of tariff policy:

$$\begin{gathered} NewSuppliedQuantity,S2=P-50 \\ =100-50 \\ 50 \end{gathered}$$

The new supplied quantity is 50 million pounds at the new price level.

Since the supplied quantity has increased from 10 million pounds to 50 million pounds, the producers have increased the level of quantity supplied. Hence, they gain from the tariff policy.

The extent of gain to domestic producers is calculated by multiplying the increase in quantity supplied with the tariff price. It is calculated below:

$$\begin{gathered} GaintoProducers\left(millions\right)=\left(S2-S1\right)\times TarrifPrice \\ =\left(50-10\right)\times 40cents \\ =1600cents \\ =\$16 \end{gathered}$$

Gain to domestic producers after the imposition of tariff is $16 million.

Step 4. Determining the government revenue from tariff

The government will earn revenue from each quantity of imported hula beans at the new price level of 100 cents. The revenue will be equal to the imported quantity and tariff price. The value of imports would be the difference between the quantity demand and quantity supplied at this price level.

The quantity demanded at the new price level of 100 cents is 50 million pounds.

The quantity supplied at the new price level of 100 cents is 50 million pounds.

The value of demanded quantity and supplied quantity is the same. The difference between them will be zero. Thus, there will be no import at the new price level. The government revenue is the product of imports and tariff amounts. A zero value of import will lead to zero government revenue.

Hence, the government will earn no revenue after the imposition of the price level.