Question

Can you please explain how you get to this answer? Thank you!

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Suppose Home has unit Labor requirements: 3 units of labor (hours) to produce one pound of apples, 2 units of labor (hours) to produce one pound of banana. Suppose Foreign has unit Labor requirements: 5 units oflabor (hours) to produce a pound of apples, 1 unit of labor (hours) to produce one pound of banana.

1) Draw the Relative Supply of Apples for the world (Home and Foreign).
2) Suppose the Relative Demand for Apples is as follows: Relative Demand: (Qa/Qb)^D = (PB/PA)
If Both countries trade, what will be the traded relative price of Apples, (PA/PB) ?
3) Show that Home Benefits from trade.

Answer 1

	Apple	Banana
Home	3 = a(LA)	2 = a(LB)
Foreign	5 = a*(LA)	1 = a*(LB)

The above table shows the per unit labor requirement of producing apple and banana in both the countries. Home per unit requirements are called a_(LA) and a_(LB). Similarly, foreign per unit labor requirements are called a*_(LA) and a*_(LB).

1) Producers supply in the market as per their opportunity costs (the amount of other commodity foregone to produce a given commodity). So, in order to find orelative supply for the world, we find the opportunity cost of producing apple in both countries.

Opportunity cost of producing apple in home is given by:  a_(LA)/ a_(LB)

Putting the numbers from the table,   a_(LA)/ a_(LB) = 3/2 = 1.5

Opportunity cost of producing apple in home is given by:  a*_(LA)/ a*_(LB)

Putting the numbers from the table,   a*_(LA)/ a*_(LB) = 5/1 = 5

So we have,   a_(LA)/ a_(LB) <   a*_(LA)/ a*_(LB). It means that home is more efficient in producing apple than foreign, simply because its per unit labor requirements are lower (1.5 < 5).

The diagram in the following image shows the relative supply of apples for the world:

The relative price of apple in home is represented by P_A/P_B. For a market price below  a_(LA)/ a_(LB), there will be no world production of apples. At market price =  a_(LA)/ a_(LB) i.e. P_A/P_B = a_(LA)/ a_(LB), the home can produce any amount of apple because prices are equal to opportunity costs, so workers are paid equal to what they give up in other market.

At market price > a_(LA)/ a_(LB) i.e. P_A/P_B > a_(LA)/ a_(LB), the home definitely produces all apples because it pays more to produce apples. So for P_A/P_B > a_(LA)/ a_(LB), total quantity of apple in the home will be L/a_(LA), where L = total labor in home country.

As the market price = a*_(LA)/ a*_(LB) i.e. PA/PB = a*_(LA)/ a*_(LB), foreign will also join home in producing apples because price is now equal to cost of producing apples in foreign i.e. market price = 5. At this price, the foreign can produce any amount of apple because prices are equal to opportunity costs.

For market price > a*_(LA)/ a*_(LB) i.e. P_A/P_B > a*_(LA)/ a*_(LB), both countries definitely produce apples.

2) If Both countries trade, traded relative price of Apples, (PA/PB) is determined where Relative demand = Relative supply. Relative demand is a normal downward sloping curve. the point where it intersects relative supply will be market equilibrium.

The following image shows the two possible points of intersection of relative supply and relative demand.

If the RD cuts RS at point like 1, then the relative price will be between 1.5 and 5.

If the RD cuts RS at point like 2, then the relative price will be 1.5

So, the relative price of apple in world market depends on position of Relative Demand (RD) curve.

3) Gains from trade are shown with the hepl of a numerical example.

To show the benefits from trade let's assume that RD and RS intersect at apoint like 1 in the above diagram such that home produces only apples. Let's say corresponding relative price of apple is 2 so that each apple can be purchase two bananas. Let's also assume both home and foreign has 100 units of labor. So now we see the production and consumption possibilities of home from trade will be greater than from those without trade.

Without trade:

Home will need to produce both apple and banana for itself. So let's say it divides the workers equally to produce apple & banana.

3 labor hrs produce = 1 pound apple

50  labor hrs produce = 50/3 = 16.7 pound apples

Similarly,

2 labor hrs produce = 1 pound banana

50  labor hrs produce = 50/2 = 25 pound banana.

So without trade home produces, 25 pound banana and 16.7 pound apples.

With trade:

Home specialises in apple production. So,

3 labor hrs produce = 1 pound apple

100 labor hrs produce = 100/3 = 33 pound apples

Each apple can buy 2 banans. Assuming home keeps 16 pound of apple to itself and trade rest of 17 apple with 34 bananas in the world, it will have 16 pound of apple and 34 bananas. This is significantly more than what home had in without trade situation. So we see home can consumer more, that's why it gains from the trade.