INTERNATIONAL TRADEEXERCISE 1Question Ricardian ModelConsider the Home country which is inhabited by a representative consumer who offers inelasticallyL units of labor and derives utility from two consumption goods z1 and 22.The preferences can berepresented by the utility function:U(x1,22)=In a1+In 22Consumption expenditures are financed by labor income where the wage rate is denoted by w.The pricesof commodities are pi and p2.The price of commodity x1 is normalized to be 1.Outputs of commoditiesQi and Q2 are produced by a Ricardian technology of the following form:Q1(L1)=L1,Q2(L2)=a2where Li and L2 are the amounts of labor used in production of commodities and z2,respectively,and a2 0 is a input coefficient for commodity 22.For the Foreign country,the production function for commodity xi and preferences are identical to theHome country.However,the Foreign country has labor endowment L*and the input coefficient in theproduction function of commodity x2 differs.We assume that 0 a a2,where denotes the Foreigncountry variables.(1)Derive the autarky equilibrium for the Home country,i.e.,determine the value for all endogenousvariables for the model.Determine also the autarky welfare level.(2)Determine the trading equilibrium for this two-country model under the assumption that each coun-try fully specializes in the production of the good in which it has a comparative advantage.(3)Derive conditions in terms of the exogenous parameters of the model which support the equilibriumthat you derived in (1).Provide economic explanations to your conditions.(4)Show that the utility of each country's representative consumer in the trading equilibrium is higherthan under autarky.