Question

Consider two countries, Violet (Home) and Pink (Foreign), which can produce apples and lemonade. There is only one factor of production (labor). In order to produce a gallon of lemonade, Violet workers need 5 hours, while Pink workers need 10 hours. In an hour, Violet workers can produce 6 pounds of apples, while Pink workers can produce only 2 pounds of apples. Markets are perfectly competitive. Violet’s labor endowment is

L = 60,000 hours, while Pink’s labor endowment is L*= 90,000 hours.

a) What are the unit labor requirements for each product (apples and lemonade) in each country?

b) What is the opportunity cost of a gallon of lemonade in terms of pounds of apples in Violet? And in Pink?

c) What country has a comparative advantage in which good and why?

d) Draw the production possibility frontiers for Violet and Pink, with lemonade on the horizontal axis. What is the slope in Violet? And in Pink?

e) Draw the world relative supply, with the relative price of lemonade in terms of apples on the vertical axis, and the relative supply curve on the horizontal axis

f) Draw a world relative demand curve, crossing the relative supply curve at a point such that the relative price of lemonade in terms of apples is 20 pounds of apples for one gallon of lemonade. What good (or goods) will Violet produce at this price? What good (or goods) will Pink produce at this price?

g) Draw the consumption possibility frontiers for Violet and Pink (in two separate graphs) when there is international trade and the relative price of lemonade is 20 pounds of apples (as in the question above). Are there gains from trade for Violet? Why or why not? And for Pink? Why or why not?

Answer 1

a) Unit labour requirement

In violet: for apples and lemonade

In one hour, 6 pound of apple are produced, so it takes 1/6 hours to produce one pound of apple

a(va)=1/6 hours and a(vl)= 5 hours

In pink: for apples and lemonade

2 pounds per hour would mean That it would take 1/2 hours to produce one pound of apple

So unit labour requirement to produce one pound of apple would be 1/2 hours

And to produce one gallon of lemonade, it would be 10 hours

b) In violet, in each labour hour, either 1/5th gallon of lemonade can be produced or 6 apples can be produced

So the opportunity cost to produce one gallon of lemonade would be 30 apples

Similarly the opportunity cost to produce one pound of apple would be 1/30 th gallon of lemonade

In pink, either 1/10 gallon of lemonade be produced or 2 pounds of apple be produced in one hour.

So the opportunity cost to produce one gallon of lemonade would be 2*10=20 pounds of apple

Or the opportunity cost to produce one pound of apple would be 1/20 gallon of lemonade.

c) Comparative advantage is when there exists least opportunity cost in production of a good.

In this case, to produce one gallon of lemonade, violet has to forego 30 pounds of apple and pink has to forego 20 pounds of apple

Since the opportunity cost is lower for pink, pink wpuld have comparative advantage in production of lemonade and violet would have comparative advantage in production of apples.

d)

In PPF of violet, given 60,000 labour hours, 6 pounds of apple can be produced in one hour, so 360,000 be produced overall.

Similarly 5 hours are required for one gallon of lemonade, so 60000/5=12,000 gallons of lemonade

There are 90,000 labour hours. So if in one hour, 2 pounds of apple are produced, total production when only apple is produced would be 180,000 pounds of apple.

Similarly when only lemonade is produced 90,000/10=9000 gallons of lemonade be produced.

Pound of apple 360,000 PPF of violet Gallon of lemonade 12000

Pound of apple 180,000 PPf of pink Gallon of lemonade 9000

Slope in violet = rise/run= 360,000/12000= 30.

Slope in pink= rise/run= 180,000/9000=20