2. Inequality and trade. This problem studies how opening to trade affects inequality differently in developed and developing countries. Consider an economy with two goods, food F and engineered goods G. A consumer has preferences U(F,G) = log F + log G and initial endowments Fe and Ge. The price of food F is normalized to 1 throughout the problem. The price of engineered goods G is denoted by p. Define I = Fe +pGe. a) Compute the consumer's individual demand for food FC and engineered goods G as a function of price p and his initial endowments Fe and Ge. b) Consider an economy with two consumers, both have preferences U(F, G) = log F+ log G. One consumer is a farmer, and the other is an engineer. Their respective endowments are Fe farmer = 1, Gfarmer = 0 Fe engineer 1. :0, Gengineer - What is the total supply of food? Write out the equation characterizing equilibrium on the market for food F. Denote by Fot the total endowment of food F and by Geot the total endowment of engineered goods G. Solve for the equilibrium price p of engineered goods as a function Fiot and Geot. c) Do we have equilibrium on the market for engineered goods G? Country A is a developed country consisting of 100 consumers with identical preferences U(F, G) = log F+ log G. 60% of citizens in the country are farmers and 40% are engineers. The endowments of each farmer and each engineer are still F - farmer = 1. Ge farmer 0 Fe engineer 0, Gengineer = 1. d) Using a), what is the individual demand for food of each farmer, what is the demand for food of each engineer? What is the total demand for food? What is the total supply of food? Compute the equilibrium price of engineered goods in country A. Denote this equilibrium price by pa. Given price p^, compute the equilibrium consumption and the utility of a farmer in country A. Compute the equilibrium consumption and the utility of an engineer in country A. Country B also has 100 consumers with identical preferences U(F,G) log F + log G. However, country B is still a developing country consisting of 90% farmers and 10% engineers. The endowments of each farmer, and each engineer are still F farmer =1, Gfarmer = 0 Fe engineer = 0, Gengineer = 1. f) Write out the equation expressing equilibrium on the market for food F in country B. Solve for the price of engineered goods p in country B. Solve for the price of engineered goods pB in country B. g) Given price pB, compute the equilibrium consumption and the utility of a farmer in country B. Compute the equilibrium consumption and the utility of an engineer in country B. Imagine that trade between country A and B becomes feasible, so that we can treat the two countries as one big exchange economy with 200 consumers. We denote by A + B this trading community. h) How many farmers are there in trading community A+ B? How many engineers are there in this trading community? What are the total endowments of food F and engineered goods G in community A+ B? i) Denote by pA+B the price of engineered goods in trading community A+ B. What is the total demand for food F in the trading community? Write out the equation expressing equilibrium in the market for food F. j) Compute the equilibrium price pA+B of engineered goods in trading community A+B. k) Compute the equilibrium consumption of a farmer in community A + B. Compute the equilibrium consumption of an engineer in community A+ B. 1) How does lifting trade barriers affect inequality between farmers and engineers in developed country A? How does lifting trade barriers affect inequality between farmers and engineers in developing country B? 2. Inequality and trade. This problem studies how opening to trade affects inequality differently in developed and developing countries. Consider an economy with two goods, food F and engineered goods G. A consumer has preferences U(F,G) = log F + log G and initial endowments Fe and Ge. The price of food F is normalized to 1 throughout the problem. The price of engineered goods G is denoted by p. Define I = Fe +pGe. a) Compute the consumer's individual demand for food FC and engineered goods G as a function of price p and his initial endowments Fe and Ge. b) Consider an economy with two consumers, both have preferences U(F, G) = log F+ log G. One consumer is a farmer, and the other is an engineer. Their respective endowments are Fe farmer = 1, Gfarmer = 0 Fe engineer 1. :0, Gengineer - What is the total supply of food? Write out the equation characterizing equilibrium on the market for food F. Denote by Fot the total endowment of food F and by Geot the total endowment of engineered goods G. Solve for the equilibrium price p of engineered goods as a function Fiot and Geot. c) Do we have equilibrium on the market for engineered goods G? Country A is a developed country consisting of 100 consumers with identical preferences U(F, G) = log F+ log G. 60% of citizens in the country are farmers and 40% are engineers. The endowments of each farmer and each engineer are still F - farmer = 1. Ge farmer 0 Fe engineer 0, Gengineer = 1. d) Using a), what is the individual demand for food of each farmer, what is the demand for food of each engineer? What is the total demand for food? What is the total supply of food? Compute the equilibrium price of engineered goods in country A. Denote this equilibrium price by pa. Given price p^, compute the equilibrium consumption and the utility of a farmer in country A. Compute the equilibrium consumption and the utility of an engineer in country A. Country B also has 100 consumers with identical preferences U(F,G) log F + log G. However, country B is still a developing country consisting of 90% farmers and 10% engineers. The endowments of each farmer, and each engineer are still F farmer =1, Gfarmer = 0 Fe engineer = 0, Gengineer = 1. f) Write out the equation expressing equilibrium on the market for food F in country B. Solve for the price of engineered goods p in country B. Solve for the price of engineered goods pB in country B. g) Given price pB, compute the equilibrium consumption and the utility of a farmer in country B. Compute the equilibrium consumption and the utility of an engineer in country B. Imagine that trade between country A and B becomes feasible, so that we can treat the two countries as one big exchange economy with 200 consumers. We denote by A + B this trading community. h) How many farmers are there in trading community A+ B? How many engineers are there in this trading community? What are the total endowments of food F and engineered goods G in community A+ B? i) Denote by pA+B the price of engineered goods in trading community A+ B. What is the total demand for food F in the trading community? Write out the equation expressing equilibrium in the market for food F. j) Compute the equilibrium price pA+B of engineered goods in trading community A+B. k) Compute the equilibrium consumption of a farmer in community A + B. Compute the equilibrium consumption of an engineer in community A+ B. 1) How does lifting trade barriers affect inequality between farmers and engineers in developed country A? How does lifting trade barriers affect inequality between farmers and engineers in developing country B