1. Consider the maximization of the Heckscher-Ohlin model where we have the following specific functional forms for output production of good 1 and 2, y₁ and y₂:

y₁ = L₁^1/3 K₁^2/3 and y₂ = L₂^3/4 K₂^1/4

a) Show that there are constant returns to scale in each industry. Then show that the capital-labor ratio in industry 1 will always be 6 times the capital-labor ratio in industry 2.

b) Derive equations (16-50) from the assigned Silberberg text for these specific functional forms. In other words, verify that each a_ij^* is a function of the factor price ratio ONLY for this model.

c) Show that ∂a_Lj^* / ∂w < 0, ∂a_Kj^*/ ∂r < 0 directly from the equations for a_ij*_.

d) On the basis of the factor intensities in each industry, which factor price would you expect to increase and which to decrease when p₂ increases? Find the explicit functions w = w^*(p₁, p₂) and r = r^*(p₁, p₂) and verify these predictions.