ECON - Problem Set A
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ECON - Problem Set A
1. Comparative Advantage and Gains from Trade
Consider a Ricardian model where the world economy consists of two countries, Home (H) and Foreign (F). Labor is hired to produce wine and bread. Let Lw and Lb denote the respective labor input in the production of wine and bread, and L denotes the total labor endowment in the country. Labor is perfectly mobile across the two sectors within the country, and Lw + Lb = L describes the labor market equilibrium. Take bread as the unit of account, i.e., Pb = 1. Pw denotes the relative price of wine in terms of bread, and W denotes the wage rate.
For simplicity, assume that workers prefer to consume wine and bread in equal amounts. Thus, we can use the 45◦ line in the sectoral production/consumption diagram to show the optimal consumption path. Use the asterisk superscript for the variables in Foreign.
|
|
Labor endowment (L) |
MPL in Wine Production |
MPL in Bread Production |
|
Home |
60 |
8 |
4 |
|
Foreign |
240 |
1 |
2 |
(a) The two countries are initially under autarky. In each country, calculate the autarkic price of wine, use the labor market equilibrium condition to specify the production possibility frontier (PPF), and calculate the sectoral production and consumption. Use the PPF and the optimal consumption path (the 45◦ line) to present your results in the diagram. [Hint: by hiring Lw and Lb units of labor, Home produces Yw = 8Lw units of wine and Yb = 4Lb units of bread. Reformulate the labor market equilibrium condition as 
+ 
= L, which is the PPF. Under autarky, sectoral consumption is equal to sectoral output, Cw = Yw and Cb = Yb . If workers prefer to consume wine and bread in equal amounts Cw = Cb , sectoral output must equalize Yw = Cw = Cb = Yb . Combine it with the PPF to solve for Yw ,Yb ,Cw ,Cb .]
(b) The two countries plan to open up for free trade. According to Adam Smith’s theory of absolute advantage, which product(s) should Home export/import? According to David Ricardo’s theory of comparative advantage, which product(s) should Home export/import?
(c) Today, the two countries move from autarky to free trade, and the world equilibrium price of wine is Pw = Pw(*) = 1. Calculate numerically the sectoral production and consumption in the two countries. Use the trade triangle to show the imports/exports of each country in the diagram. How much does trade affect the consumption level in the two countries?
(d) Suppose each worker is endowed with one unit of labor. In other words, there are 60 workers in Home and 240 workers in Foreign. Calculate the wage rate (or equivalently, income per worker) in each country before and after free trade. In which country is the wage rate higher? Explain your findings intuitively.
(e) Rather than opening up for trade, Home may choose to remain under autarky but adopt a new technology raising its MPL for bread production. How much should Home improve the MPL for bread production so that it can reach the same consumption level as under free trade [see question (c)]?
2. Distributional Effects of Trade in the Specific-Factors Model
Consider a specific-factors model where the world economy consists of two countries, Home (H) and Foreign (F). Home is endowed with L units of labor, T units of land, and K units of capital. Lw units of labor and T units of land are hired to produce Yw = ^Lw T units of wheat, while Ls units of labor and K units of capital are hired to produce Ys = ^Ls K units of shirts. Land and capital are specific to the production of wheat and shirts, respectively. Labor is perfectly mobile across the two sectors within the same country Lw +Ls = L. Take shirt as the unit of account, i.e., Ps = 1. Pw denotes the relative price of wheat in terms of shirt, W denotes the wage rate, RT and RK denote the respective rental rate of land and capital.
For simplicity, assume that workers prefer to consume wine and shirts in equal amounts. Thus, we can use the 45◦ line in the sectoral production/consumption diagram to show the optimal consumption path. Use the asterisk superscript for the variables in the Foreign country.
|
|
Labor (L) |
Land (T) |
Capital (K) |
|
Home |
10 |
10 |
40 |
|
Foreign |
4000 |
4000 |
1000 |
(a) Suppose that Home is under autarky. Calculate numerically the sectoral production and consumption in Home. Use the PPF curve and the optimal consumption path (the 45◦ line) to show your results in the diagram. Compute numerically the relative price of wheat in Home. [Hint: given the production function of wheat Yw = ^Lw T = Lw(0.)5T0.5 , the marginal product of labor is MPLw = 
= 0.5Lw(0.)5−1T0.5 . The same approach applies to the derivation of MPLs in shirt production. As shirt serves as the unit of account Ps = 1, the relative price of wheat is Pw = 
]
(b) In which product(s) does Home have a comparative advantage? Explain your result intuitively and numerically. Suppose that Home and Foreign move from autarky to free trade.
How does the relative price of wheat change in each country? In which country is the price change larger? Explain your results intuitively and diagrammatically. [Hint: you may derive the Home export supply curve and Foreign import demand curve before showing the equilibrium world price of wheat under free trade.]
(c) Use the PPF, the world price line, the optimal consumption path (the 45◦ line) to show the consumption and production in Home. [Hint: you may show the results qualitatively, no need to calculate the numerical values for this sub-question.]
2023-06-24