Question

	Beer	Red Bull	Endowment
Capital	3	5	3000
Labor	6	1	3000

7) We are studying two products with the labor and capital input requirements summarized in the table above for Germany.
a) Find the labor and capital constraints in these countries.
b) Graph a linear PPF for these factor requirements.
c) Graph a PPF representing a more realistic Cobb-Douglas type production function.
d) Which product is capital intensive and which is labor-intensive.
e) Graph the factor/good price relationship next to the factor price/input relationship.

f) Use this graph to identify the impact of an increase in the price of beer on wage/rental rate and labor capital inputs of both products.
g) Now consider opening this economy to international trade with Switzerland whose capital endowment is 3000 and whose labor endowment is 1200. Which country is labor abundant and which is capital abundant? Why?
h) Which product will be exported from Germany? Which product will be exported from Switzerland?
i) Predict the direction of change for all four prices.
j) Draw a new version of the graph from part e. Predict changes in Germany of the wage/rental rate and labor capital inputs of both products.
k) Repeat part j for Switzerland

Answer 1

a).

Here there are two goods “B=beer” and “R=red bull” both needed two inputs “K=capital” and “L=labor”. Now the labor requirements of both goods are “6” and “1” respectively with endowment of “3000”. So, the labor constraint is given by, => 6*B + R = 3,000. Similarly, the capital requirements of both goods are “3” and “5” respectively with endowment of “3000”. So, the capital constraint is given by, => 3*B + 5*R = 3,000.

b).

The following fig shows the PPF of the country.

B=Beer 3000/3 = 1,000 3000/6 = 500 L2 > R=Red Bull 3000/5 = 600 3000/1 = 3,000

Here K1K2 is the capital constraint and L1L2 is the labor constraint, => the PPF of the economy is given by L1EK2, => here the PPF is kinky type, having two linear segments.

c).

Actually a more realist PPF should be concave in origin represent the increasing opportunity cost of one good in terms of other, => if we increase the production of one we have to sacrifices one and one of other goods.

B=Beer R=Red Bull

Here T1T2 is the PPF.

d).

Here beer needs “3 units” of capital and “6 units” of labor, => the capital labor usage ratio is “3/6 = 0.5”. Similarly, red bull needs “5 units” of capital and “1 units” of labor, => the capital labor usage ratio is “5/1 = 5”. So, red bull having higher capital labor ratio compare to beer, => beer is labor intensive and red bull is capital intensive goods.