Exercise 2 A country ("Home") is populated with workers who produce either food (F) or clothing (C). There are 200 workers producing food and 100...

Exercise 2

A country (“Home”) is populated with workers who produce either food (F) or clothing (C).

There are 200 workers producing food and 100 producing clothing - these numbers are fixed.

Each food worker produces 6t unites of food and each clothing worker produces 3 units of

clothing. Workers own the output they produce and can trade with one another. All workers

share the same preferences over food and clothing represented by the utility function:

U(Dc;Dc ) = (Dc)^1/3 (Df )^2/3

1. What is the autarky trade price (the relative price of food and clothing) in this economy?

Hint: recall the property of Cobb-Douglas utility functions relating expenditure shares

on both goods.

2. In autarky, how many units of food and clothing will be consumed by a clothing worker/

By a food worker?

There also exists another country (“Foreign”) that looks surprisingly like the Home

country except that there are 600 food workers and 300 clothing workers in this country.

These workers have different (lower) productivity levels: a food worker can produce only

1 unit of food while a clothing worker can produce 2 units of clothing. The workers in

Foreign share the same preferences as those in Home.

3. Answer questions 1 and 2 for the Foreign economy in autarky.

4. Compare the consumption levels of workers in both countries. What explains the

differences between the two consumption levels?

5. Now assume that these two countries open to trade with one another.

(a) What will be the free trade relative price of food and clothing?

(b) Describe the pattern of trade (who exports what, and how much). Verify that the

export supply matches the import demand for both goods.

(c) Calculate the new consumption levels of both types of workers in both countries.

(d) For each type of worker in both countries, assess whether they are better-off in

the new trade equilibrium. How might you have predicted this pattern before

calculating the new consumption levels and the free trade price equilibrium?

For the following questions, assume that all workers belong to a representative ’family’

– each containing 2 food workers and 1 clothing worker.

6. Describe how the consumption patterns (the number of units of food and clothing

consumed) of the ’families’ change between autarky and the trade equilibrium. Are the

’families’ in both countries unambiguously better-off? What is the intuition for this

result?

7. Without redoing the calculations in part 5, describe how your answers would change if

the productivity of both types of Foreign workers were multiplied by 10. In particular,

what would happen to:

2

(a) The pattern of trade (which good is exported by each country)

(b) The distribution of the gains from trade.

i. Which workers will gain from trade?

ii. What will happen to the ’families’ of workers in each country?

(c) What will be the most noticeable impact of this higher Foreign productivity? If

the productivity increase was such that the free trade price remains unaffected,

what would be the effect of the productivity increase on workers in Home?

8. Now return to the trade equilibrium described in 5. If workers can switch occupations

in the long run, what will happen to the number of workers in each industry (only

describe the direction – not the magnitude – of the change.

Extra Credit. The purpose of this exercise is to convince you that

this is indeed true.

1. A weighted average of two positive numbers X and Y is given by aX + (1-a)Y for

some a between 0 and 1. Show that this weighted average must always lie between X

and Y .

2. Show that (X1 + X2)/(Y1 + Y2)

can be written as a weighted average of X1/Y1

and X2/Y2

.