Question

Assume throughout that those two countries (Italy and Sweden) are the only two countries in the world, at least for purposes of trade. There are two goods: shoes and calculators. Consumers in both countries always spend half of their income on shoes and half of their income on calculators. The only factor of production is labour. Each Italian worker can produce 1 shoe or 2 calculators per unit of time. Each Swedish worker can produce 4 shoes or 2 calculators per unit of time. There are 80 workers in Italy and 60 workers in Sweden. You need to provide conditions in each country by stating:

a) Derive the relative demand curve relating the relative demand for calculators to the relative price of calculators. and then show what the curve looks like in a diagram (put the relative price of calculators on the vertical axis and the relative quantity of calculators demanded on the horizontal axis).

b) Derive the world relative supply curve of calculators (put the relative price of calculators on the vertical axis and the relative quantity of calculators supplied on the horizontal axis).

c) Put in the same figure the relative demand curve for calculators that you found in part (a) and the world relative supply curve of calculators that you found in part (b). Determine the equilibrium relative price of calculators and the equilibrium relative quantity of calculators under free trade.

d) Under free trade, which country produces which good(s)? How many units?

e) Who gains from trade? Who loses from trade? State labours' stance towards free trade in each country.

Answer 1

Let the number of shoes be s and the number of calculators be c.

Total income of consumer be m.

As half income is spent on s and half on c. So, sm/2 + cm/2 = m

So, s+c = 2

Given the total labor in Italy is 80 and in Sweden be 60.

	Italy	Sweden
Shoes(s)	1	4
Calculators(c)	2	2

The slope of PPC for Italy will be = - 2/1 = P_{​​​​​​c} /P_{​​​​​​s}

The slope of PPC for Sweden will be = -2/4 = -1/2 = P*c/P*s

The opportunity cost of producing shoes is less in Sweden and the opportunity cost of producing calculators is less in Italy. So, Sweden has a comparative advantage in shoes and Italy has a comparative advantage in calculators.

Relative demand (RD) for c = 1/relative price of c

So, RD for c in Italy = 1/2

RD for c in Sweden = 2

a) b) c)

The equilibrium relative price of calculators is 1/2 and the equilibrium relative quantity of calculators is 8/3

d) Under free trade, Italy produces calculators and Sweden produces Shoes. Italy produces 40 units calculators and Sweden produces 15 units of shoes

e) Sweden gains from trade while Italy loses from trade. Thus, this will make the labor want to produce more calculators than shoes.