# Which good will the country export and which good will the country import?

A small open economy produ Show more EXTRA PROBLEM SET DUE: WEDNESDAY DECEMBER 4TH IN CLASS JACEK ROTHERT A small open economy produces two goods: Manufacturing (m) and Agriculture (a). Production of manufacturing uses capital (K) and labor (L) while production of agriculture uses land (T) and labor (L) i.e. capital is a factor of production specific to the manufacturing sector and land is a factor of production specific to agriculture. The production functions in the two sectors are: Ym = ? K ?Lm Ya =?T ? La The capital stock in the economy is K = 100. The total amount of land is T = 100 and the total labor is divided into the two sector and equals Lm + La =L ? = 100. The utility function of a typical citizen in the economy is U(CaCm) = logCa + log Cm . In the remainder of the exercise we normalize the price of manufacturing to 1 i.e. Pm = 1 and all the nominal prices wages rental rates are then expressed in units of manufacturing goods. a) (20 pts) With the above utility function the autarky price of agriculture is Pa = 1. Find the allocation of labor across the two sectors. Calculate the utility from the consumption of the two goods in autarky (call it Va). b) Suppose the world price of agriculture is P wa = 1/3 (5 pts) Find the allocation of labor in a free trade equilibrium. (5 pts) Which good will the country export and which good will the country import? With the above utility function how many units of each good will the country produce consume export and import? (HINT: re-member that optimal choice for the consumer requires MUa= Pa= Pa where MUa is the marginal utility of agriculture MUm Pm consumption and MUm is the marginal utility of manufacturing con- sumption. Use the condition that MUa = Pa MUM PM together with the fact that the total value of countrys consumption must equal the total valueof countrys production). Calculate the utility from the consumption of the two goods in free trade (call it V F T ). c) (30 pts) Now suppose the government is imposing a 100% import tariff (i.e. the domestic price of the imported good is now P = 2 P W ). Redo part(b). d) (20 pts VERY HARD) How much is a typical citizen in this economy willing to pay to avoid the import tariff? Show less

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