Solutions Two

From Nov 22 2010 Mid-Term 4 – Long Problem 1 – Trade & Differing Populations



First, write out what’s given to you,

Italy

Germany

Labor Force

10

20

Number of beers one worker can produce

2

4

Number of pizzas one worker can produce

8

2

Spending Preferences

50%

50%





(a) Suppose there is no trade, what is per-capita consumption of each good in each country? 


Production, Per capita Consumption under Autarky

Italy

Germany

Production of Beer

Production of Pizza

Consumption of beer (per person):

Consumption of pizzas (per person):





(b) What are the prices of pizza in each country? Who has a comparative advantage in producing beer? In pizza?


Prices are found by the following equation,


The choice of numeraire (pricing good) is arbitrary, so I’ll find prices in terms of both beer and pizza.



Prices in Terms of Beer - Autarky

Italy

Germany

Price of beer in terms of beer

Price of pizza in terms of beer


Beer is of course one beer in both countries.


Pizza in Italy is worth ¼ a beer, and worth 2 beers in Germany. Pizza is cheaper in Italy.


Prices in Terms of Pizza - Autarky

Italy

Germany

Price of beer in terms of beer

Price of pizza in terms of beer


Pizza in both countries is, of course, worth one pizza.


Beer in Italy is worth 4 pizzas. Where in Germany, a beer is worth ½ a pizza. Beer is cheaper in Germany.


Comparative Advantage – “whoever has the lowest opportunity costs

Comparative advantage is determined by relative prices.

  1. Because Germany can produce beer more cheaply than Italy (1/2 < 4) it comparative advantage in the production of beer.
  2. Because Italy can produce pizza more cheaply than Germany (1/4 < 2) it has comparative advantage in the production of pizza.


Intuition: Imagine you were an Italian with the ability to cheaply ship pizzas to Germany. You see that in the Italy you could get (only) 1/4 beer for a single pizza. But if you ship those pizzas over to Germany you’d get 2 beers (eight times as many!). A wonderful arbitrage opportunity that doesn’t exist for pizzas going from Germany to Italy.




(c) Now suppose that the world opens to free trade. If countries fully specialize according to their comparative advantage, what is the world production of beer and pizza? With this level of world production, what should the price of a pizza be in terms of beer? What is per capita consumption of beer and pizza in each country? How does this differ from consumption under autarky?


World Production of Beer and Pizza

Italy

Germany

Portion of labor force working on Beer

Portion of labor force working on Pizza

0%

100%

100%

0%

Production of Beer

Production of Pizza


World production of beer will be 80 beers (compared with 50 before trade)

World production of pizza will be 80 pizzas (compared with 60 before free trade)


World Prices of Beer & Pizza

Italy

Germany

Price of Pizza in terms of Beer

Price of Beer in terms of Pizza


Wages

Italy

Germany

Wages, w (in terms of beers)

Per Capita Consumption of Beer and Pizza

Italy

Germany

Per Capita Consumption of Beer

Per Capita Consumption of Pizza

Per Capita Consumption=


Per capita consumption: pre verses post free trade.


Italians get the same 4 pizzas they had with Autarky, but now get 4 beers too (an increase of 3 beers).


Germans get the same 2 beers they had before Free Trade, but now consume an additional pizza (2 pizzas instead of the single pizza under Autarky)


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