j. Given what we know about the utility functions of Home and Foreign, what is the world price of cloth relative to wheat with trade. - How much wheat and cloth are produced by Home and Foreign under trade (Remember in the Ricardo model both countries would specialize)? Why? - Using the utility functions work out the world price where total demand equals total supply for each commodity. - What would be the quantities of cloth and wheat consumed by home and foreign? - Do both countries gain from trade at this price? Explain. Question 1 Quantitative/Graphing Problem on the Ricardo Model (50 points) Apply the Ricardian model to the following scenario: Two countries, Home (H) and Foreign (F) produce two goods, clothing (C) and wheat (W) using labor as the only factor of production. Marginal productivity of labor is constant in each country and is defined by the following schedule: 1 worker can produce 1 yard of cloth or 1/4 a bushel of wheat at home, while 1 worker produce 1 yard of clothing or 1/2 bushels of wheat. Finally, each country has 1000 workers. a. a.\" what are the production functions for cloth and wheat in each country and the marginal product of labor in each? Which country has absolute advantage in the production of clothing? How about wheat? Explain. Which country has comparative advantage in clothing? How about wheat? Why? What is the price of cloth in terms of wheat in the home country? According to the principle of comparative advantage, which country should specialize and export what good? In order for Home to gain from trade the world price of Clothing in terms of Wheat should be lower than . At what price of clothing, in terms of wheat, will the benets to Foreign from trade be largest? What will the benefit for home be at this price? Draw the Production possibilities frontier (PPF) for home in Autarky by putting clothing on the X- axis and wheat on the y-axis. Make sure that you label each axis and that you mark down the appropriate numbers for the maximum amounts ofwheat and clothing that can be produced. What is the slope of the PPF? What is the equation for the PPF curve? Include the utility function in your drawing and show where the economy would operate in autarky (mark A). Can you explain why this is the autarkic equilibrium? i. Now assume that home and foreign start trading (at zero cost) at a relative price of wheat in terms of clothing that is feasible. Use graphical analysis, to show that Home can gain from trade. Denote the new trade equilibrium T. Now let's put some numbers and equations to the autarkic and with-trade equilibriums h' Assume that preferences in home and foreign are identical and described by a Cobb Douglas utility function: U = C1/2.W1/2 In autarky, how much (2 and W will be produced and consumed in the home country
