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 specic to the manufacturing sector and land is a factor of production specic to agriculture. The production functions in the two sectors are:
\(YM = \sqrt{K}\sqrt{LM}\)
\(YA = \sqrt{T} \sqrt{LA}\)
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) = log CA +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 V A).
b) Suppose the world price of agriculture is Pw = 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: remember that optimal choice for the consumer requires \(MUA/MUM = PA/PM = PA\)
, where MUA is the marginal utility of agriculture consumption and MUM is the marginal utility of manufacturing consumption. Use the condition that MUA/MUM = PA/PM, together with the fact that the total value of country's consumption must equal the total value of country's production). Calculate the utility from the consumption of the two goods in free trade (call it V FT ).
c) (30 pts) Now suppose the government is imposing a 100% import tari (i.e. the domestic price of the imported good is now P = 2 X PW). Redo part(b).
d) (20 pts VERY HARD) How much is a typical citizen in this economy willing to pay to avoid the import tari?