## Answered: - Supply of labor: There are 10 skilled workers and 100 unskilled

Supply of labor: There are 10 skilled workers and 100 unskilled workers in Denmark. There are 15 skilled workers and 300 unskilled workers in Hungary.

1. ?Given the supply of unskilled workers in Denmark and the supply of unskilled work- ers in Hungary, how many basic bricks can be produced and used for assembly in Denmark? (net of the melt during transportation!)
2. Similarly, how many complex bricks can be put in Lego boxes? (net of transportation melt) What is the ratio of complex to basic bricks that can be put in Lego boxes?

Problem set 3: ?Everything is Awesome?

Due date: Thursday March 17th

Lego boxes: A box of Legos consists of complex bricks and basic bricks. The production

function of Lego boxes is assumed to be:

2/3

1/3

Y = B1 B2

Where B1 denotes the number of basic bricks and B2 the number of complex bricks.

Boxes of Legos are assembled in Denmark, combining these complex and basic bricks.

1) What is the marginal product of a basic brick? Note: it depends on the ratio B1 of

B2

complex and basic bricks being used. This is very similar to what you would do to

compute the marginal product of capital, with bricks instead of capital.

2) What is the marginal product of a complex brick? Again, note that it depends on the

ratio B1 of complex and basic bricks being used.

B2

3) Assuming that the Lego company optimizes its production, explain why the relative

price of a complex brick relative to a basic brick should be equal to the ratio of

marginal product of a complex brick over the marginal product of a basic brick.

Production of bricks: While boxes of Legos are assembled in Denmark, the production

of some of the bricks can be o?shored to Hungary.

Producing one complex brick requires one skilled worker (Danish or Hungarian). Producing one basic brick requires two unskilled workers (Danish or Hungarian). However,

bricks melt on the way from Hungary to Denmark, and one needs to produce three bricks

in order to receive one brick in Denmark (2 out of 3 bricks melt during transportation).

This applies to any type of brick, they both melt in the same proportions.

4) In equilibrium, why is the skill premium the same in Hungary as in Denmark?

5) Depending on the skill premium (unknown variable to be determined later), what is

the price (=unit cost) of complex bricks relative to basic bricks?

1

Supply of labor: There are 10 skilled workers and 100 unskilled workers in Denmark.

There are 15 skilled workers and 300 unskilled workers in Hungary.

6) Given the supply of unskilled workers in Denmark and the supply of unskilled workers in Hungary, how many basic bricks can be produced and used for assembly in

Denmark? (net of the melt during transportation!)

7) Similarly, how many complex bricks can be put in Lego boxes? (net of transportation

melt) What is the ratio of complex to basic bricks that can be put in Lego boxes?

New equilibrium: Now, suppose that bricks no longer melt during transportation. Each

brick produced in Hungary safely arrives in Denmark and can be used for the production

of Lego boxes.

9) How many complex bricks can be produced, combining Danish and Hungarian production? How many complex bricks can be produced, combining Danish and Hungarian

production?

10) What is the skill premium in the new equilibrium?

Intuition: Summary and e?ect of trade on the skill preimum in an alternative setup:

11) Explain in words why the skill premium increases in both countries when transportation cost (melt) declines.

12) Suppose that Hungary was initially producing its own Lego boxes instead of shipping

bricks to Denmark.

a) Which country would have the highest skill premium? Why?

b) In the new equilibrium, Denmark and Hungary produce together. How would the

skill premium evolve in each country compared to the initial equilibrium where

each country would produce its own Lego boxes?

2

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