Question

4. A small country is producing potatoes and carrots. Every worker can produce either 3 kilos of potatoes or 9 kilos of carrots per week. Use the Ricardian model to answer the following questions. Assume throughout that consumers want to consume at least a small amount (i.e. not zero) of each good. a) Draw the Production Possibility Frontier (PPF) for the country. Moreover, in autarky when the country is not trading with any other country, what will the relative price be for the two goods? (6 points) b) Assume now that the relative world market price of potatoes in terms of carrots is 1, and that the small country we study can trade on the world market. Will the small country trade? If so, what good(s) will it export and what will it import? What will be the new price in the country? (7 points) c) Analyze the welfare effects of international trade by computing how the real wages in the Home country change. Explain your answers. (6 points) d) Assume now that technology in the Home country evolves so that a worker can now produce 9 kilos of potatoes per week instead of just 3 kilos as before. How will this technological progress affect the way in which Home trades with the rest of the world? (6 points)

Answer 1

a)

A Production possibility curve (PPF) gives the different combination of output that a country can produce using all of its resources efficiently. Any point on the production possibility curve represents the efficient allocation of resources. The slope of the PPF gives the opportunity cost of producing one good relative to other. The PPF has a negative slope because as the production of one good increase, we have to give up the production of another due to limited resources. A constant opportunity cost PPF will be a negatively sloped straight line.

Here we assume that the country has only one factor of production, labor and two goods, potatoes and carrots. The production data are summarized in the table below:

           

	Potato (in kilos)	Carrots (in kilos)
Quantity (In a week per labor)	3	9

The opportunity cost of one additional kilos of carrots is 3/9 kilo Potato. That is, we have to give up 1/3 Potato in order to produce 1 additional kilos of carrots. On the other hand, if we have to produce one additional Potato the country has to give up 3 kilos of carrots. Let the country has 90 labors. If the country employs all the labors in carrots, they will give up 90*1/3=30 kilos of potatoes.

The opportunity cost of production for both the good is constant. Hence, the PPF will be a negatively sloped straight line. We draw the PPF in the figure below. Here we measure the quantity of carrots on the horizontal axis and quantity of Potato on the vertical axis.

Here AB is the PPF of country. If the country employs all its labor to carrots, it will produce 810 kilos of carrots; this is given by point B (810, 0). On the other hand, if the country employs all its labor to potatoes, it will produce 270 kilos of potato; this is given by point A (0, 270). As the opportunity cost of production is constant, the slope of the PPF will be constant. It will be a straight line passing through A and B.

b)

The relative price of carrot on world market is 1. That is the country can have 1 kilos of carrot for 1 kilos of potato. Thus, carrot is expensive in world market. The country can produce 1 kilos of carrot for 1/3 kilos of potato and can exchange it for 1 kilos of potato. This way the country can have 1 kilos of potato instead 1/3 kilo under auterky. By the same logic the potato is cheaper in world market.

Then the country will produce carrots and will exchange it for potato in world market or, the country will export carrots and will import potatoes.

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c)

Real wage in industry is the productivity of a labor in that particular industry. Under auterky the nominal wage in the industry was same. That is accross industry the labor was paid same wage. Then under auterky, the real wage in Under free trade the demand for labor in carrot industry rises. As the country produces only carrots and the real wage is determined by the productivity of the factors. Then everyone in the country, all of the 90 labor earn real wage 9. While under auterky only those who engaged to carrot industry earn a wage 9 and those who engaged in potato earns a real wage 3. Then free trade increases real wage and made everyone better off in the country.

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d)

If the productivity increases to 9 kilos of potato in a week. the relative price of potato becomes 1. That is 1 kilos of potato cost 1 kilo of carrot. Then the price in home becomes equal to world market. Then trade implies no extra gain and the country will be indifferent to trade in the world market.