Consider a world with two countries i {1,2}; each inhabited by L, consumers. Suppose that each...

 

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Consider a world with two countries i {1,2}; each inhabited by L, consumers. Suppose that each country has the technology to produce a continuum g € [0, 1] of goods. Let a, (g) be the unit labor cost of producing good g € [0, 1] in country i E {1,2}. Normalize the wage in country 2 to one and let w denote the relative wage in country 1. 1. Suppose that a₁ (g) = g² and a₂ (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.: U₁ log C₁ (g) dg. Solve for the equiblirium quantity consumed of a good g by a consumer in i as a function of the goods price p. (9) and the total income in country i, Y,. (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] Consider a world with two countries i {1,2}; each inhabited by L, consumers. Suppose that each country has the technology to produce a continuum g € [0, 1] of goods. Let a, (g) be the unit labor cost of producing good g € [0, 1] in country i E {1,2}. Normalize the wage in country 2 to one and let w denote the relative wage in country 1. 1. Suppose that a₁ (g) = g² and a₂ (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.: U₁ log C₁ (g) dg. Solve for the equiblirium quantity consumed of a good g by a consumer in i as a function of the goods price p. (9) and the total income in country i, Y,. (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]