Question

Consider a Ricardian model. There are two countries called Australia and New Zealand and two goods called beer and cheese. In Australia the unit labour requirement for a beer is 6 hours and for a cheese is 12 hours. In New Zealand the unit labour requirement for a beer is 4 hours and for a cheese is 1 hour. Australia has an endowment of 3600 hours of labour. New Zealand has an endowment of 400 hours of labour.

1. Draw a production possibility frontier (PPF) diagram for Australia and a PPF diagram for New Zealand (separate diagrams please). Cheese must be on the vertical axis and beer must be on the horizontal axis.

2. For both countries state the opportunity cost of producing a beer.

3. Suppose now that we have trade between the countries and the world price is 1 cheese for 1 beer. For each country draw in the budget constraint. For each country label the production point on the diagram.

4. Denote the world prices in dollars as PB and PC respectively. Denote the respective quantities of beer and cheese consumed in New Zealand (following,trade, of course) as DB and DC . Using this notation, write out the budget constraint for New Zealand. Rearrange this budget constraint so that it is clear that the ratio of these world prices is reflected by the slope of the budget constraint. [ DC should be on the left hand side and the rest of the stuff should be on the right hand side.]

5. While the ratio of prices is apparent from Question 3, we will assume from here on that the price of beer is $1 and the price of cheese is $1. If 300 beers are consumed in New Zealand, how many cheeses will be consumed in New Zealand? Now if only 200 beers are consumed, how many more cheeses will be consumed?

6. For both countries calculate the hourly wage rate (with international trade).

Answer 1

With 3,600 units of labor hours, Australia can produce either 3600/6 = 600 units of beer or 3600/12 = 300 units of cheese.

Similarly, with 400 units of labor hours, New Zealand can produce either 400/4 = 100 units of beer or 400/1 = 400 units of cheese.

Now, plotting cheese on vertical axis and beer on horizontal axis, PPF for Australia has a vertical intrercept of 300 and a horizontal intercept of 600 whereas, PPF for New Zealand has a vertical intrercept of 400 and a horizontal intercept of 100 as shown in the diagram below:

Here, opportunity cost of producing beer in Australia = Units of cheese sacrificed/Units of beer produced = 300/600 = 0.5

Again, opportunity cost of producing beer in New Zealand = Units of cheese sacrificed/Units of beer produced = 400/100 = 4

As opportunity cost of producing beer is lower for Australia, Australia has comparative advantage in the production of beer.

Similarly, New Zealand has comparative advantage in the production of cheese.

Let us assume, before trade, Australia was consuming at point A (300 beer and 150 cheese) whereas, New Zealand was consuming at point C (50 beers and 200 cheese)

Now, with trade, Australia must specialize in beer (produce 600 beer only) whereas, New Zealand must speacialize in cheese (produce 400 cheese only) according to concept of comparative advantage.

If exchange takes place at 1 beer = 1 cheese, then, Australia can consume 300 beers and export 300 beers (out of 600 beers of production) to New Zealand for which it can gain 300 cheese (point B).

Similarly, New Zealand can consume 200 cheese and export 200 cheese (out of 400 cheese of production) to Australia for which it can gain 200 beer (point D).

The slope of each CPF will be equal to -1 (as consumption of cheese will be equal to consumption of beer).

If 300 beer is consumed in New Zealand, 100 cheese will consumed by it.

If 200 beer is consumed in New Zealand, 200 cheese will consumed by it. Thus, consumption of cheese will rise by 100.

As prices of beer and cheese are equal to $1, wage rates will be equal to their slope.

Then, WC/WB = (PB*MPLC)/(PC*MPLB)

or, WC/WB = 1

or, WC = WB