### Solutions One

From Dec 7 2009 Final – Long Problem 2 – Trade with Identical Populations

First, write out what’s given to you,

 America (Country A) Belgium (Country B) Labor Force 10 10 Number of beers one worker can produce 4 6 Number of pizzas one worker can produce 4 2 Spending Preferences 50% 50%

(a) Suppose that there is no trade (Autarky). What is per-capita consumption of each good in each country?

Per capita consumption under Autarky

 America Belgium 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. I’ll calculate prices of each product in terms of the other. The pricing unit is called the numeraire.

Price in terms of beer

 America Belgium Price of beer in terms of beer Price of pizza in terms of beer

Intuition: the price of a pizza in America is 1 beer. Given that a worker can either produce 4 beers or 4 pizzas, if producers of one good were to exchange it for the other, they’d exchange it at the exchange rate of one-to-one.

In Belgium, the worker can produce 6 beers or 2 pizzas (hmmm, Trappist), with pizza more difficult to produce relative to beer, pizza costs more.

Price in terms of Pizza

 America Belgium Price of beer in terms of pizza Price of pizza in terms of pizza

Intuition: If Americans want to exchange pizza for beer, they’d need to give 1.5 pizzas for a single beer. Belgians would exchange 1/3 a pizza for a single beer.

Comparative advantage is determined by relative prices.

1. Because American can produce pizza relatively more cheaply than Belgium (1 < 3), they have the comparative advantage in producing pizza.
2. Because Belgium has the lower price of beer (1/3 < 1), they possess the comparative advantage in producing beer.

Intuition: Imagine you were an American with the ability to cheaply ship pizzas to Belgium. You see that in the States you could get (only) 1 beer for a single pizza. But if you ship those pizzas over to Belgium you’d get 3 beers! A wonderful arbitrage opportunity that doesn’t exist for pizzas going from Belgium to America.

(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?

America & Belgium Under Free Trade

 America Belgium Fraction of labor working on beerFraction of labor working on pizzacountries specialize in the good for which they have the competitive advantage. 0%100% 100%0% Total Production of BeerTotal Production of Pizza Price of Beer (in terms of Pizza) Price of Pizza (in terms of Beer) Wage, w (in terms of beer)Workers productivity, times the value of that productivity in terms of the numeraire. 6=6*1 Wage, w (in terms of pizza)Workers productivity, times the value of that productivity in terms of the numeraire (pizza in this case).

The price of pizza (in terms of beer) has been equalized to 1.5. That is, it takes 1.5 beers to buy a single pizza.

(d) With the patterns of production in each part, what are the wages in each country in terms of beer? What is per capita consumption of beer and pizza in each country? How does this differ from consumption under autarky.

Wages, Per-Capita Consumption under Autarky

 America Belgium Wage, w (in terms of beer)Workers productivity, times the value of that productivity in terms of the numeraire. 6 Per-capita Consumption – BeerPer-capita Consumption – PizzaRecall, 50% consumption on each good 2 31

Wages, Per-Capita Consumption with Free Trade

 America Belgium Wage, w (in terms of beer)Workers productivity, times the value of that productivity in terms of the numeraire. 6 Per-capita Consumption – BeerPer-capita Consumption – PizzaRecall, 50% consumption on each good 32 32

Wages

1. Each worker in American produces 4 pizzas. Valued at 1.5 beer per pizza, American wages are 6 beers. Before American workers wage was only worth 4 beers. Free trade has increased American wages by 2 beers!
2. Each Belgium worker produces 6 beers. Their wage is already priced in terms of beer. Belgium wages are unchanged.

Per-Capita Consumption

1. American workers have increased the number of beers they consume by one (and it’s probably Trappist beers; better than typical American brew). Pizza consumption is unchanged.
2. In Belgium, beer consumption is unchanged but free trade has provided for an extra pizza. Which is an improvement.