About the ricardian model with increasing returns

Question

Assignment:

Question 1. This question is about the Ricardian model with increasing returns. There are two countries in this model, Colombia (Home) and Italy (Foreign). There are two goods in this model, coffee beans and espresso machines. Both countries are identical in terms of production technology and population. Coffee bean production exhibits constant returns to scale,

a_c = a*_c = 1/400

Espresso machine manufacturing exhibits increasing returns to scale. In particular, unit labor productivity depends on the quantity of labor employed.

a_e = h(L_e) = 1/L²c

Finally, the population of each country is given by, L ^col = L ^ita = 50

a. Suppose both countries are initially in autarky, and that labor is allocated so that the marginal product of labor is the same in both sectors. How much labor is allocated to each sector and how much of each good is produced? (Remember the countries are identical)

b. Now suppose that these countries open to trade, and espresso machine production is concentrated in Colombia. In particular, the free trade level of q_q^col, is equal to the sum of autarky production of espresso machines in the two countries. The remaining labor is allocated to coffee production.

• How much of each good does each country produce?

• How does the wage in each country, relative to the price of each good compare to its value in autarky?

• What is the value of the relative wage between these two countries?

Question 2. This question is about changes in technology and the effect it has on the terms of trade. This economy consists of three countries; United States, Mexico, and Canada. Each country can produce two goods, an agricultural good and a manufacturing good. Production functions are constant returns to scale in labor. Unit labor requirements are given by,

a^usaa = 1, a^usam = 1

a^mexa = 1,a^mexm= 2

a^cana = 1,a^canm= 4

The labor forces in each country, L^usa = 329, L^mex = 129, L^can = 36

a. Draw the PPF for each country in autarky. Clearly label the x and y intercepts and the slope.

b. What is the relative price of manufacturing to agriculture in each country in autarky?

c. Suppose the countries open up to trade, draw the relative supply curve.

d. Let the relative global demand curve be given by,

1/3 (Q^W_M/Q^W_A)= (P^W_A/P^W_M)

What is the equilibrium relative price of manufactured goods to agricultural goods?

e. Suppose there is an improvement in manufacturing technology in the Mexico, and the unit labor requirement falls from 2 to 1.1. Draw the new relative supply curve. How does this change affect the terms of trade? Who wins and who looses? Explain your answer.