Reference no: EM133133568
A country can produce two goods, machines (M) and food (F). Machines are produced using only capital, and food is produced using only labor: Machines : qM = KM Food : qF = LF A representative consumer has preferences represented by the utility function U (cM, cF) = ln (cM) + ln (cF). The endowments of labor and capital are L¯ = 200, K¯ = 400.
(a) Solve for the autarky equilibrium. You should give values for capital and labor used in each industry, consumption and output of goods in each industry, and the wage, rental rate, and price of food relative to manufactures (you may normalize the price of manufactures to 1). (Hint: pay careful attention to the production functions).
(b) Suppose that this country is open to trade at fixed world prices, p¯M = p¯F = 1 (this is called the small open economy assumption). Now, it is no longer the case that cM = qM and cF = qF. Calculate the equilibrium wage and rental rate, the quantities of capital and labor used in each sector, and consumption and production of each good.
(c) Now interpret the world of part (b) as being one in which there is a worker and a capital owner in the country. The worker has income wL¯, and the capital owner has income rK¯. Each one has identical preferences, which are the same as the representative consumer of part (a) and (b). Who wins and who loses relative to autarky? Does the gain to the winner outweigh the loss to the loser (that is, does the economy gain overall)?
(d) Briefly state (in 2-3 sentences) how the result in part (c) relates to the Stolper-Samuelson theorem prediction.