Advanced International Trade Problem Set Question 1: Consider an economy which is inhabited by a representative consumer who offers inelastically L units of labor and derives utility from two consumption goods c 1 and c2. The preferences can be represented by the utility function U (c 1 , c 2 )=ln (c1 )+ln (c 2)

Consumption expenditures are financed by labor income where the wage rate is denoted by w. The prices of commodities are p1 and p2. Let us normalize the price of good one to be 1. Outputs of commodities one and two, Q1 and Q2, are produced by a Ricardian technology of the following form

Q1 (L 1)=L 1 and Q 2 ( L2 )=

L2 a2

where L1 and L2 are the amounts of labor used in production of commodity one and two, respectively, and a2>0 is a parameter. a) Derive the autarky equilibrium for this economy, i.e., determine the value for all endogenous variables of the model. Determine also the autarky welfare level. Assume in the following that there is a second country. The production function for commodity 1 and preferences are identical to the first country. However, the second country has labor endowment L* and the input coefficient in the production function of commodity two differs. Let 00 and u ' '