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Bl. Consider a partial equilibrium framework representing the local market of shoes. With perfect competition, the supply of shoes in country H is given by S = 20 + 2p while the demand for shoes is D = 400 p, where p is the market price. (a) Determine the autarkic price and quantity of demand/supply. Also, determine the consumers' surplus, the producers' surplus, and welfare of the market. Derive the export supply function within the price range in which both demand and supply are positive. (b) Consider another country, F, which produces and consumes the same product, shoes. Its export supply function is given by E\" = 240 + 4p"', where an asterisk is used to denote a variable of country F. Determine the autarkic price in the country. (d) Suppose that free trade with no transport costs is allowed between the countries. Determine the free-trade equilibrium price and trade volume. Which country exports shoes? (e) Compare the autarkic prices in the two countries. How are these two prices be used to nd out: (a) which country exports the good; (b) the range of the free- trade price in the world? Can you use the result here to establish a theory that is analogOus to the Law of Comparative Advantage? (e) Focus now on country H. In a diagram that shows the local demand and supply, indicate the autarkic price and the free-trade price. Explain, using the diagram, how free trade affects local consumption and production. Determine the new consumers' surplus, producer surplus, and welfare of the market. Can you say whether free trade is good for the country? Can you give an economic intuition of your result in terms of whether free trade is good or bad