Reference no: EM13183611
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(Ca,Cm) = 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) 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
• Find the allocation of labor in a free trade equilibrium. •
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 country's consumption must equal the total valueof country's production). Calculate the utility from the consumption of the two goods in free trade (call it V F T ).
c) 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 ).
d) How much is a typical citizen in this economy willing to pay to avoid the import tariff?
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