US import demand for French perfumes is given by P = 90 - 3Q, where P is the perfume price ($), Q is the number of imported perfume bottles (in millions) demanded by US consumers. International supply of French perfumes (in dollars and in million bottles) is given by: P = 10 + 2Q. If the US government imposes a $10 import tariff on French perfumes entering the US market, what would be the deadweight loss for the world as a whole in the perfume market? Assume that these are the only two countries in the world.
Draw a graph to explain.
Hint: Draw supply and demand curves. From the producers' point of view, tariff appears as a cost that must be paid to the government. This means that the supply curve of perfumes will shift up by $10.
To determine the deadweight loss in the perfume market after the imposition of an import tariff, we need to consider the changes in supply and demand.
1. Start by drawing the initial supply and demand curves on a graph, with quantity (Q) on the x-axis and price (P) on the y-axis. The supply curve is given by P = 10 + 2Q, and the demand curve is given by P = 90 - 3Q.
2. Plot the supply curve. The supply curve is upward sloping, indicating that as the quantity of imported perfumes increases, the price also increases. Using the equation P = 10 + 2Q, you can plot the points on the graph and connect them to form the supply curve.
3. Plot the demand curve. The demand curve is downward sloping, indicating that as the price of perfumes decreases, the quantity demanded increases. Using the equation P = 90 - 3Q, you can plot the points on the graph and connect them to form the demand curve.
4. Determine the initial equilibrium price and quantity. This occurs at the intersection of the supply and demand curves. To find this point, set the equations for supply and demand equal to each other: 10 + 2Q = 90 - 3Q. Solve for Q to find the equilibrium quantity, and then substitute it back into either the supply or demand equation to find the equilibrium price.
5. With the imposition of a $10 import tariff, the effective price for imported perfumes would increase by $10. This means the supply curve shifts upward by $10, creating a new supply curve parallel to the original supply curve but at a higher price level. The new supply curve can be plotted by adding $10 to the equation for the original supply curve: P = 20 + 2Q.
6. Identify the new equilibrium price and quantity. The new equilibrium occurs at the intersection of the new supply curve (P = 20 + 2Q) and the initial demand curve (P = 90 - 3Q). Set these equations equal to each other and solve for Q to find the new equilibrium quantity. Substitute this value back into either the new supply or initial demand equation to find the new equilibrium price.
7. The deadweight loss can be calculated as the difference between the initial equilibrium quantity and the new equilibrium quantity, multiplied by half of the difference between the initial and new equilibrium prices. Deadweight loss represents the inefficiency or loss of economic welfare caused by the tariff.
Remember to label the axes with the price and quantity units and provide a clear legend for the different curves on the graph.
By following these steps and plotting the necessary curves on a graph, you can visually explain and determine the deadweight loss in the perfume market after the imposition of the import tariff.
To find the deadweight loss in the perfume market, we need to analyze the impact of the import tariff on the supply and demand for French perfumes. Let's start by drawing the initial supply and demand curves.
The initial demand curve for French perfumes in the US market is given by P = 90 - 3Q, where P is the perfume price ($) and Q is the quantity of imported perfume bottles demanded by US consumers (in millions).
The initial supply curve for French perfumes in the international market is given by P = 10 + 2Q, where P is the perfume price ($) and Q is the quantity of imported perfume bottles (in millions) supplied by French producers.
Let's plot these initial supply and demand curves on a graph.
Price ($)
|
100 -| D
|
90 -|
|
80 -|
|
70 -|
|
60 -|
| S
50 -|
|
40 -|
|
30 -|
|
20 -|
|
10 -|___________________
0 Quantity (Millions)
On the graph, the demand curve (D) slopes downwards as price increases, indicating that as the price of perfumes decreases, the demand for them increases. The supply curve (S) slopes upwards as price increases, indicating that as the price of perfumes increases, the supply of them also increases.
Now, let's analyze the impact of the $10 import tariff imposed by the US government. The tariff acts as a cost to the importers, making the supply curve shift up by $10. This means that the new supply curve will be P = 20 + 2Q.
Let's plot the new supply curve on the graph.
Price ($)
|
100 -| D
|
90 -|
|
80 -|
|
70 -|
|
60 -|
| S (With tariff)
50 -|
|
40 -|
|
30 -|
|
20 -| S (Initial)
|
10 -|___________________
0 Quantity (Millions)
The new supply curve (S with tariff) is parallel to the initial supply curve (S) but is located $10 higher on the price axis, reflecting the additional cost imposed by the tariff.
Now, to find the deadweight loss, we need to determine the quantity of perfumes demanded and supplied before and after the tariff. We can do this by equating the demand and supply equations to find the equilibrium quantity and price both before and after the tariff.
Before the tariff, the equilibrium quantity (Q1) and price (P1) are found by setting the initial supply and demand equal to each other:
90 - 3Q1 = 10 + 2Q1
Solving this equation, we find Q1 = 20 million bottles and P1 = $50.
After the tariff, the equilibrium quantity (Q2) and price (P2) are found by setting the new supply and demand equal to each other:
90 - 3Q2 = 20 + 2Q2
Solving this equation, we find Q2 = 18 million bottles and P2 = $54.
Now, let's calculate the deadweight loss. Deadweight loss represents the loss of consumer and producer surplus that occurs due to the reduction in trade caused by the tariff.
Deadweight loss = 0.5 * (Q1 - Q2) * (P1 - P2)
Plugging in the values:
Deadweight loss = 0.5 * (20 - 18) * ($50 - $54)
= 0.5 * 2 * (-$4)
= -$4 (Note: The negative value indicates a loss)
Therefore, the deadweight loss for the world as a whole in the perfume market due to the tariff is $4 million.