TU Wien:International Trade Theory and Policy VO (Stehrer)/Exercises

Topic 1: Imports, Tariffs, and Quotas

Exercise 1: Autarky vs. Free Trade Equilibrium

Focus: Calculating autarky equilibrium, import levels, and welfare gains.

Problem: Consider a domestic market for widgets with the following demand and supply schedules:

• Demand: $q^{D}=100-2p$
• Supply: $q^{S}=-20+2p$

Questions:

1. Calculate Autarky: Find the autarky equilibrium price ($p^{a}$) and quantity ($q^{a}$) where domestic demand equals domestic supply.
2. Free Trade: The country opens up to trade. The world market price is $p^{w}=20$. Assume the country is "small" and cannot influence world prices. Calculate the new domestic quantity demanded ($q^{D}$) and domestic quantity supplied ($q^{S}$).
3. Imports: Calculate the volume of imports ($m$).
4. Welfare: Using the formula $\Delta W={\frac {1}{2}}\cdot m\cdot \Delta p$ (where $\Delta p=p^{a}-p^{w}$), calculate the total welfare gain from trade.

Angebot und Nachfrage Diagramm hier einfügen. Markiere p_a, p_w und das Importvolumen

Angebot und Nachfrage Diagramm hier einfügen. Markiere p_a, p_w und das Importvolumen

Solution Exercise 1

1. Autarky: $100-2p=-20+2p\Rightarrow 120=4p\Rightarrow p^{a}=30$. Substituting back: $q^{a}=40$.
2. Free Trade: At $p^{w}=20$: $q^{D}=100-2(20)=60$. $q^{S}=-20+2(20)=20$.
3. Imports: $m=60-20=40$.
4. Welfare: $\Delta p=30-20=10$. $\Delta W={\frac {1}{2}}\cdot 40\cdot 10=200$.

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Exercise 2: The Welfare Effects of an Import Tariff

Focus: Calculating the impact of tariffs on price, imports, government revenue, and deadweight loss.

Problem: Continuing from a similar market structure, assume a country has the following curves:

• Demand: $q^{D}=50-p$
• Supply: $q^{S}=-10+p$
• World Price: $p^{w}=10$

Questions:

1. Free Trade Baseline: At the free trade price of $p^{w}=10$, calculate the initial imports ($m_{initial}$).
2. Tariff Imposition: The government introduces a tariff $t=10$ per unit. This raises the domestic price to $p=p^{w}+t$. Calculate the new domestic quantity demanded, new domestic quantity supplied, and the new level of imports ($m_{new}$).
3. Tariff Income: Calculate the revenue collected by the government ($T=m_{new}\cdot t$).
4. Welfare Loss: Calculate the net welfare loss caused by the tariff. Formula: $\Delta W={\frac {1}{2}}\cdot \Delta m\cdot t$.

Datei:Placeholder Ex2 TariffWelfare.jpg

[DIAGRAMM PLATZHALTER: Zeige den Wohlfahrtsverlust (Harberger Dreiecke) und die Staatseinnahmen.]

Solution Exercise 2

1. Baseline: At $p=10$: $q^{D}=40,q^{S}=0$. Imports $m_{initial}=40$.
2. Tariff: New Price $p=10+10=20$.
   • $q^{D}=50-20=30$.
   • $q^{S}=-10+20=10$.
   • $m_{new}=30-10=20$.
3. Income: $T=20\cdot 10=200$.
4. Loss: $\Delta m=20-40=-20$. $\Delta W={\frac {1}{2}}\cdot (-20)\cdot 10=-100$ (Net welfare loss of 100).

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Exercise 3: Conceptual - Elasticity and Producer Rent

Topic: Understanding how supply elasticity affects producer rent losses.

Problem: Compare two different industries in a country that is about to open up to trade (where World Price < Autarky Price).

• Industry A has a completely inelastic supply curve (vertical).
• Industry B has a completely elastic supply curve (horizontal).

Questions:

1. In Industry A, when the price drops to the world price, what happens to the domestic quantity supplied? Does the producer rent decrease significantly or minimally?
2. In Industry B, when the price drops to the world price, what happens to the domestic quantity supplied? What is the loss in producer rent?

Solution Exercise 3

1. Industry A (Inelastic): Quantity supplied remains constant. Producer rent suffers a large loss because they sell the same amount at a lower price.
2. Industry B (Elastic): Domestic firms exit the market (quantity supplied drops to zero). There is no loss in producer rent because producer rent was already zero in autarky (Revenue = Variable Costs).

Topic 2: Exports and Subsidies

Exercise 1: Welfare Distribution in Exports

Topic: Winners and Losers under Free Trade (Small Country)

Problem: Consider a domestic market for Wheat with the following functions:

• Demand: $q^{D}=80-2p$
• Supply: $q^{S}=-20+2p$

Questions:

1. Autarky: Calculate the autarky price ($p^{a}$) and quantity ($q^{a}$).
2. Free Trade: The world market price is $p^{w}=30$. Determine the new domestic Quantity Demanded, Quantity Supplied, and Exports ($x$).
3. Welfare Distribution:
   • Calculate the change in Consumer Rent ($\Delta CR$).
   • Calculate the change in Producer Rent ($\Delta PR$).
   • Show that the Net Welfare Gain ($\Delta W$) equals the area of the "gains from trade" triangle.

Datei:Placeholder Topic2 Ex1.jpg

[DIAGRAMM PLATZHALTER: Export-Markt Gleichgewicht, Gewinn-Dreieck hervorheben.]

Solution Exercise 1

1. Autarky: $80-2p=-20+2p\rightarrow p^{a}=25,q^{a}=30$.
2. Free Trade ($p^{w}=30$):
   • $q^{D}=20,q^{S}=40$. Exports $x=20$.
3. Welfare:
   • $\Delta CR=-125$ (Loss).
   • $\Delta PR=+175$ (Gain).
   • $\Delta W=+50$.

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Exercise 2: Export Subsidy (Constant World Price)

Topic: Subsidy costs and efficiency loss (Deadweight Loss)

Problem: Use the same market ($q^{D}=80-2p$, $q^{S}=-20+2p$). Initial Free Trade with $p^{w}=30$. Government introduces an Export Subsidy of $s=5$.

Questions:

1. Price & Quantity: Calculate new producer price, consumer price, and export level ($x_{new}$).
2. Budget Impact: Calculate total subsidy cost ($s\cdot x_{new}$).
3. Welfare Analysis: Calculate the Net Welfare Loss using $\Delta W=0.5\cdot \Delta x\cdot (-s)$.

Datei:Placeholder Topic2 Ex2.jpg

[DIAGRAMM PLATZHALTER: Exportsubvention, Dreiecke für Wohlfahrtsverlust (b und d) markieren.]

Solution Exercise 2

1. New State: Price = 35. $q^{D}=10,q^{S}=50$. Exports $x_{new}=40$.
2. Cost: $5\cdot 40=200$.
3. Net Welfare Loss: $\Delta x=20$. Loss = $0.5\cdot 20\cdot (-5)=-50$.

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Exercise 3: Export Subsidy with Terms of Trade Effect

Topic: Large Country case (Declining World Price)

Problem:

• Initial World Price: $p_{0}^{w}=30$
• Export Subsidy: $s=5$
• World Price Reaction: Falls to $p_{1}^{w}=28$.

Questions:

1. Domestic Price: What is the new price domestic producers receive?
2. Welfare Components: Why is the welfare loss larger in this scenario compared to the small country case?

Solution Exercise 3

1. Domestic Price: $28+5=33$.
2. Net Effect: Larger loss because of the Terms of Trade loss. The subsidy lowers the world price, effectively subsidizing foreign consumers.

Topic 3: Strategic Trade Policy

Exercise 1: Reaction Curves & Unilateral Subsidy

Topic: Graphical derivation and "Profit Shifting".

Problem: Boeing (A) and Airbus (B) compete in quantities.

• Demand: $P=100-(q_{A}+q_{B})$
• Marginal Costs: $c_{A}=c_{B}=10$

Questions:

1. Initial Equilibrium: Derive the reaction function for Airbus ($R^{A}$) and calculate the Cournot-Nash equilibrium.
2. Unilateral Subsidy: Country A gives a subsidy $s=5$. How does $R^{A}$ shift? Explain the mechanism.
3. Profit Analysis: Explain "Profit Shifting" in this context.

Datei:Placeholder Topic3 Ex1.jpg

[DIAGRAMM PLATZHALTER: Reaktionskurven (qA auf x-Achse, qB auf y-Achse). Zeige Verschiebung von RA nach rechts.]

Solution Exercise 1

1. Reaction: $q_{A}=45-0.5q_{B}$. Intersection at $(30,30)$.
2. Subsidy: New MC = 5. $R^{A}$ shifts outward. Boeing produces more; Airbus responds by producing less.
3. Profit: Boeing gains market share and profit; Airbus loses profit.

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Exercise 2: The Prisoner's Dilemma (Bilateral Subsidies)

Topic: Strategic interaction and Welfare Analysis.

Problem: Country B retaliates with its own subsidy $s_{B}=5$.

Questions:

1. Graph: Show the shift of $R^{B}$. Where is the new equilibrium?
2. Welfare Matrix: Explain why countries subsidize even if the (Sub, Sub) payoff is worse than (Free, Free).
3. Third Country Effect: What happens to the consumers in the third market?

Solution Exercise 2

1. Graph: Both curves shift out. Higher total quantity, lower price.
2. Dilemma: Subsidizing is a dominant strategy (Nash Equilibrium), leading to a Prisoner's Dilemma outcome.
3. Third Country: Consumers win due to significantly lower prices.

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Exercise 3: Optimal Subsidy & Total Welfare

Problem: Calculate optimal subsidy $s^{*}$ for $a=100,c=10$ using $s^{*}=(a-c)/4$.

Solution Exercise 3

1. $s^{*}=22.5$.
2. The subsidy is positive because the marginal gain from shifting profit initially outweighs the subsidy cost.

Topic 4: The Ricardian Model

Exercise 1: Constructing the Autarky Equilibrium

Problem: Country with $h=200$. Productivity: Wine $\varphi _{1}=0.5$, Cloth $\varphi _{2}=2.0$.

Questions:

1. Calculate labor coefficients ($a_{l1},a_{l2}$).
2. Write the PPF equation.
3. Calculate MRT and explain opportunity cost.
4. If wage $w=10$, calculate autarky prices.

Datei:Placeholder Topic4 Ex1.jpg

[DIAGRAMM PLATZHALTER: PPF Diagramm. Achsenabschnitte 100 (Wein) und 400 (Tuch).]

Solution Exercise 1

1. $a_{l1}=2,a_{l2}=0.5$.
2. PPF: $x_{2}=400-4x_{1}$.
3. MRT = -4. Opportunity cost of 1 Wine is 4 Cloth.
4. Prices: $p_{1}=20,p_{2}=5$.

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Exercise 2: General Equilibrium with Demand

Problem: Consumers spend 50% on each good (Cobb-Douglas). $h=200,w=10$.

Questions:

1. Calculate Nominal GDP.
2. Calculate physical demand for Wine and Cloth.

Solution Exercise 2

1. GDP = 2000.
2. Demand: Wine = 50, Cloth = 200.

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Exercise 3: Comparative Statics (Technical Progress)

Problem: Wine productivity doubles to $\varphi _{1}'=1.0$.

Questions:

1. New Prices?
2. How does the PPF shift?
3. Effect on Real Income?

Solution Exercise 3

1. $p_{1}$ falls to 10. $p_{2}$ stays 5.
2. PPF rotates out along the Wine axis (max Wine = 200).
3. Real Income increases (purchasing power for wine doubles).

Topic 5: Specific Factors Model

Exercise 1: Labor Allocation & The "Bathtub" Diagram

Problem: Labor $h=100$. Specific factors: Land (Wine), Capital (Cloth). $MPL_{1}=20-0.2l_{1}$, $MPL_{2}=10-0.1l_{2}$. Prices: $p_{1}=1,p_{2}=2$.

Questions:

1. Calculate equilibrium labor allocation ($l_{1},l_{2}$) and wage $w$.
2. Draw the Bathtub diagram.
3. Explain diminishing returns.

Datei:Placeholder Topic5 Ex1.jpg

[DIAGRAMM PLATZHALTER: Arbeitsmarkt-Diagramm (Badewanne). Schnittpunkt der Wertgrenzprodukt-Kurven.]

Solution Exercise 1

1. $l_{1}=50,l_{2}=50$. Wage $w=10$.

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Exercise 2: Winners and Losers

Problem: Price of Wine doubles ($p_{1}=2$). Wage rises to $w'=18$.

Questions:

1. Labor: Calculate real wage changes ($w/p_{1},w/p_{2}$). Are they better off?
2. Land Owners (Specific to Wine): Are they winners or losers?
3. Capital Owners (Specific to Cloth): Are they winners or losers?

Solution Exercise 2

1. Labor: Ambiguous. Real wage in Cloth rises (9), in Wine falls (9 < 10).
2. Land: Winners (Price up + Productivity up).
3. Capital: Losers (Price constant + Productivity down due to lost labor).

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Exercise 3: Capital Accumulation

Problem: Capital stock increases (Specific to Industry 2). Prices constant.

Questions:

1. Which curve shifts in the diagram?
2. Effect on Labor allocation and Output?

Solution Exercise 3

1. $p_{2}\cdot MPL_{2}$ shifts up.
2. Labor moves to Industry 2. Output of Industry 2 rises; Output of Industry 1 falls.

Topic 6: Heckscher-Ohlin Model

Exercise 1: Factor Intensity

Problem: Microchips (1) are Capital Intensive. T-Shirts (2) are Labor Intensive.

Questions:

1. Define inequality for input coefficients.
2. If $w/r$ rises, what happens to $k/l$ in both sectors?

Datei:Placeholder Topic6 Ex1.jpg

[DIAGRAMM PLATZHALTER: Verhältnis von Faktorpreisen zu Faktorintensitäten.]

Solution Exercise 1

1. $a_{1,k}/a_{1,l}>a_{2,k}/a_{2,l}$.
2. $k/l$ rises in both sectors (Substitution effect).

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Exercise 2: Stolper-Samuelson

Problem: Country exports Labor-intensive good. Price of Labor-intensive good rises.

Questions:

1. What happens to $w/r$?
2. Effect on Real Wage and Real Rental Rate?

Solution Exercise 2

1. $w/r$ increases.
2. Real Wage: Increases (Workers win). Real Rental: Decreases (Capital owners lose).

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Exercise 3: Factor Price Insensitivity

Problem: Small Open Economy. Labor endowment increases by 20%. Prices fixed.

Questions:

1. Do wages fall?
2. How does the economy adjust?

Solution Exercise 3

1. Wages do not fall (Factor Price Insensitivity).
2. Rybczynski Effect: Output of Labor-intensive sector expands; Capital-intensive sector contracts.

MOCK EXAM 1

Exercise 1: Strategic Trade Policy (Oligopoly)

Setup:

• Inverse Demand: $P=120-(q_{USA}+q_{China})$
• MC: $c_{USA}=20,c_{China}=20$.

Questions:

1. Reaction Functions: Derive $R_{USA}$.
2. Equilibrium: Calculate Cournot-Nash quantities.
3. Unilateral Subsidy: Subsidy $s=10$ for USA. Calculate new quantities.
4. Profit: Calculate change in USA profit (excluding subsidy).

Datei:Placeholder Exam Ex1.jpg

[DIAGRAMM PLATZHALTER: Reaktionskurven-Verschiebung durch Subvention.]

Solution Exam Ex 1

1. $q_{USA}=50-0.5q_{China}$.
2. $q=33.3$.
3. New $q_{USA}=40,q_{China}=30$.
4. Profit increases from ~1111 to 1200.

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Exercise 2: The Specific Factors Model

Setup: Agria exports Corn. $P_{Corn}$ rises 20%. $P_{Electronics}$ constant.

Questions:

1. Labor Market: Draw the diagram shift. Does wage rise more or less than 20%?
2. Real Income: Analyze Real Wage changes.
3. Specific Factors: Explain Real Rental Rate changes for Land and Capital.

Datei:Placeholder Exam Ex2.jpg

[DIAGRAMM PLATZHALTER: Spezifische Faktoren Arbeitsmarkt Shift.]

Solution Exam Ex 2

1. Wage rises by less than 20% (diminishing returns).
2. Real wage falls in terms of Corn, rises in terms of Electronics.
3. Land: Real return rises. Capital: Real return falls.

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Exercise 3: Tariffs & Welfare

Setup: Small country. $D=100-P$, $S=2P-20$. World Price $P^{W}=30$. Tariff $t=10$.

Questions:

1. Free Trade: Calculate Imports.
2. Tariff: Calculate new Imports.
3. Welfare: Calculate Production and Consumption Distortion losses.

Datei:Placeholder Exam Ex3.jpg

[DIAGRAMM PLATZHALTER: Wohlfahrtsverlust durch Zoll.]

Solution Exam Ex 3

1. Free Trade Imports = 30.
2. Tariff Price = 40. Imports = 0.
3. Loss = 150. (Production Loss 100 + Consumption Loss 50).

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