**Consider the HO Model of a Country**

1. (30 points) Consider the HO model of a country, which produces cars and fish, using capital and labor. Suppose

that at current prices a car is produced using 8 hours of labor and 12 units of capital, and fish is produced using 2

hours of labor and 1 unit of capital.(a) If the economy’s total resources are 80 hours of labor and 100 units of capital, what is employment and output

in each industry? (Hint. Use the box diagram)

(b) Now suppose that the labor supply falls to 76 hours. Answer question (a) in this case. Show that your answers

in (a) and this part confirm the Rybczynski theorem. Show the change in the box diagram.

2. (30 points) Consider the specific factor model of a country, which produces 2 goods, apples and TVs. Assume

that land (denoted by T) is specific to apples and T = 300, capital (denoted by K) is specific to TVs and K = 800,

and labor (denoted by L) is free to move between the two industries, with L = 1000. When this country is engaged

in free trade, the prices are $500 per TV and $600 per unit of apples (1 unit = 1 ton). The production functions in

two industries are:

**QTV = 10(L)0.5(K)0.5**

**QA = 20(L)0.7(T)0.3**

(a) Calculate the equilibrium factor prices and employment levels and outputs in each industry.

(b) Calculate the values from part (a) for the case when due to emigration the number of workers falls to L = 800.

Given your answer, what can you tell about the Rybczynski theorem in this setting?3. (40 points) “A 10% increase in productivity of workers at Home (that is, in any production relationship, any

given output can be produced with 10% less labor than was needed before) is equivalent to a 10% increase in labor

force at Home.” Discuss whether this statement is true or false in the context of:

(a) A Ricardian 2-good model of a small open economy that is completely specialized under free and frictionless trade.

(b) The specific factor model with labor mobile between sectors and other factors permanently dedicated to their current sectors.

In each case do not forget to describe the implications of this change for the country’s prod uction, trade, and real factor prices.