# Penn State University Eco 433

· 案例展示

This problem set is due on Sept 21, 2020 at midnight. Answers must be clearly written or typed, scanned
and then uploaded to CANVAS. You may use a free app like Genius Scan to scan your answers.
Q1. Consider the following unit labor requirements:

 Shoes Wine Italy 6 hrs per unit 4 hrs per unit Spain 8 hrs per unit 4 hrs per unit
1. Why is there a basis for trade? (2 marks)
2. Which good should each country export under free trade? Why? (2 marks)
3. The international terms of trade (relative prices) must lie between _______ and _______ (1
mark)
Q2. Consider the following economic environment
• 2 countries i = f1; 2g
• 2 tradable consumption goods j = f1; 2g ; xij denotes consumption of good j in country i.
• Endowments: Non-tradable factor of production (labor). 100 units in each country.
• Technology:
– Let yij denote production of good j in country i
– Let lij denote the labor used in production of good j in country i
– Production functions are then given by:
– Country 1: y11 = l11 2 ; y12 = l12 4
– Country 2: y21 = l21; y22 = l22
• Consumer preferences: U (xi1; xi2) = min (xi1; xi2) for country i = 1; 2
• Market arrangement: perfect competition
1. Draw country 1’s PPF and find graphically the autarky equilibrium production and consumtpion. (5
marks)
2. Draw the world PPF and carefully label your diagram (10 marks)
3. Is there complete specialization in the free trade equilibrium? Explain why or why not? What is the
world equilibrium relative price of the two goods (4 marks)
4. What would be the effect on welfare un each of the two countries under free trade of a reduction in
country 2’s unit labor requirements in good 2 from a22 = 1 to a22 = 1 2? (6 marks)
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Q3. “Wages in China are less than 5% of wages in the United States. Therefore, free trade between the U.S.
and China will destroy American jobs and lead to all goods being produced in China.” Evaluate the validity
of this statement using the Ricardian model (20 marks)
Q4. Consider a world with two countries i 2 f1; 2g; each inhabited by Li consumers. Suppose that each
country has the technology to produce a continuum g 2 [0; 1] of goods. Let αi (g) be the unit labor cost of
producing good g 2 [0; 1] in country i 2 f1; 2g. Normalize the wage in country 2 to one and let w denote the
relative wage in country 1.
1. Suppose that α1 (g) = g2 and α2 (g) = g. If the equilibrium wage is w = 2, which country would
produce which goods? (5 marks)
2. Suppose consumers have Cobb-Douglas preferences with equal demand shifters for all goods, i.e.:
Ui = ˆ01 log Ci (g) dg:
Solve for the equiblirium quantity consumed of a good g by a consumer in i as a function of the goods
price pi (g) and the total income in country i, Yi. (10 marks)
3. Suppose L1 = 1 and L2 = 2, unit labor costs are as in 4(1) and preferences are as in 4(2). Find the
equilibrium relative wage, incomes in the two countries and pattern of specialization. [15 marks]
4. Suppose the population of country 1 doubled to L1 = 2. Show using both math and a figure how
equilibrium wages would change. Would the equilibrium pattern of specialization change? [20 marks]
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