1. Use the following information to answer the questions below. Please note that output of good X is measured in 100’s on the x axis, i.e. if you find Q = 10 then output is 10 × 100 = 1, 000 units. You must have a diagram to support you answers.

• Domestic Demand: P = 200 − 2Q
• Domestic Supply: P = 40 + 2Q
• Domestic Supply and Imports: P = 2Q
(a) Solve for equilibrium price and output in Autarky.
(b) Find the value of the consumer and producer surpluses in Autarky.
(c) Solve for equilibrium price when the country imports good X from abroad. How many units will be imported?
(d) Find the new values of the consumer and producer surpluses.
(e) Suppose the government imposes a $10 specific tariff on all imports of good X. What is the new price? How many units will consumers demand? How many units will be supplied by domestic producers? What is the value of the revenue collected by government.
2. Assume that Mexico places a tariff of 10% on all imported TVs. Mexico produces its own TVs but imports TV components valued at 50% of the cost of producing TVs. Use this information to answer the following:
(a) Find the ERP for each of the following tariffs on imported components; 5%, 10% and 15%.
(b) Repeat the exercise above assuming that the value of imported components is now 70% of production costs. Compared to the answers you got in part a, what can you say about the amount of protection that domestic producers receive when the tariffs on components change and when imported components as a percentage of production costs change, e.g. given a 10% tariff on components compare the ERPs when a = 50% and a = 70%. Draw conclusions based on what you have seen.

1. (a) To find the equilibrium price and output in autarky, we need to set the domestic demand equal to the domestic supply:

Domestic Demand: P = 200 - 2Q
Domestic Supply: P = 40 + 2Q

Setting these two equations equal to each other, we have:
200 - 2Q = 40 + 2Q

Solving for Q, we get:
4Q = 160
Q = 40

To find the equilibrium price, we substitute the value of Q into either the demand or supply equation. Let's use the supply equation:
P = 40 + 2Q
P = 40 + 2(40)
P = 40 + 80
P = 120

Therefore, the equilibrium price in autarky is P = 120 and the equilibrium output is Q = 40.

(b) Consumer surplus is the difference between the maximum price consumers are willing to pay and the price they actually pay. To find consumer surplus, we need to calculate the area below the demand curve and above the equilibrium price.

Consumer Surplus = 0.5 * (200 - P) * Q
Consumer Surplus = 0.5 * (200 - 120) * 40
Consumer Surplus = 0.5 * 80 * 40
Consumer Surplus = 1600

Producer surplus is the difference between the price producers receive and the minimum price they are willing to accept. To find producer surplus, we need to calculate the area above the supply curve and below the equilibrium price.

Producer Surplus = 0.5 * (P - 40) * Q
Producer Surplus = 0.5 * (120 - 40) * 40
Producer Surplus = 0.5 * 80 * 40
Producer Surplus = 1600

Therefore, the value of consumer surplus in autarky is 1600 and the value of producer surplus is also 1600.

(c) To find the equilibrium price when the country imports good X from abroad, we sum the domestic supply and imports:

Domestic Supply and Imports: P = 2Q

To find the equilibrium price, we substitute the value of Q into the supply and import equation:
P = 2(40)
P = 80

To find the number of units imported, we substitute the equilibrium price into the domestic supply and imports equation:
80 = 2Q
Q = 40

Therefore, the equilibrium price when the country imports good X from abroad is P = 80 and the number of units imported is Q = 40.

(d) To find the new values of consumer and producer surpluses, we need to calculate the areas below the demand curve and above the new equilibrium price (P = 80) for consumer surplus, and above the supply curve and below the new equilibrium price for producer surplus.

Consumer Surplus = 0.5 * (200 - P) * Q
Consumer Surplus = 0.5 * (200 - 80) * 40
Consumer Surplus = 0.5 * 120 * 40
Consumer Surplus = 2400

Producer Surplus = 0.5 * (P - 40) * Q
Producer Surplus = 0.5 * (80 - 40) * 40
Producer Surplus = 0.5 * 40 * 40
Producer Surplus = 800

Therefore, the new value of consumer surplus is 2400 and the new value of producer surplus is 800.

(e) If the government imposes a $10 specific tariff on all imports of good X, the new price will be the sum of the equilibrium price (P = 80) and the tariff ($10):

New Price = 80 + 10
New Price = 90

To find the number of units consumers demand, we substitute the new price into the demand equation:
P = 200 - 2Q
90 = 200 - 2Q
2Q = 110
Q = 55

To find the number of units supplied by domestic producers, we substitute the new price into the supply equation:
P = 40 + 2Q
90 = 40 + 2Q
2Q = 50
Q = 25

The value of the revenue collected by the government is equal to the tariff per unit multiplied by the quantity imported:
Revenue = Tariff * Quantity Imported
Revenue = $10 * 30 (assuming 30 units are imported)
Revenue = $300

Therefore, the new price is $90, consumers demand 55 units, domestic producers supply 25 units, and the government collects $300 in revenue from the tariff.