1. (Simplified version of Heckscher-Ohlin model). Consider a country which can produce two goods: manufactures (M) and food (F) using two inputs: labor (L) and capital (K). Production of each good requires inputs to be used in fixed proportions as follows (these are called Leontieftechnologies):

To produce food (F): 2 units of labor and six units of capital are required for each unit of F. To produce manufactures (M): 6 units of labor and 2 unit of capital are required for each unit of M.

Let L, K represent the total amount of labor and capital available in the economy, let Pf , Pm denote the prices of output, and let W, R denote the prices of labor and capital, respectively.

a) Find production costs and hence output price (price=marginal cost) for each good in terms of factor prices (W, R). {Hint: To produce Qm units of M requires 6Qm workers and 2Qm units of capital; hence total costs are {WLm + RKm}={6W +2 R}Qm }.

i. Use your answers to solve for input prices in terms of output prices. How will an increase in the price of food affect factor prices?

b) Assume two countries (Trinidad and Jamaica) have identical tastes and technology, but Jamaica has more capital per labor unit than does Trinidad. Assuming the relative demand (ratio of demand for food to demand for manufactures) is independent of income, discuss how autarky goods prices and factor prices differ between the two countries, then discuss how trade affects factor prices in each country. Will factor prices be equalized between the two countries?

c) Modify the above model by assuming Jamaica's productivity in both sectors doubles. Thus, in Jamaica:

To produce food: (2/2) units of labor and (6/2) units of capital are required for each unit of F. To produce manufactures: (6/2) units of labor, and (2/2) units of capital are required for each unit of M.

Trinidad's technology remains unchanged. Viewed in a Ricardian context, Jamaica has an absolute advantage in both goods but a comparative advantage in neither good (due to technology).

i. Find how this Jamaica's productivity change affects its autarky output prices and factor prices.

ii. Assuming free trade between Trinidad and Jamaica, what will the pattern of trade be? Will free trade equalize factor prices? Will trade eliminate the pressure for factor migration?