Question

Consider the following data on quantities of two factors, capital and labor, available, and their use to produce a unit of each of the two goods, cloth and food: K = 3000, L = 2000, a_KC = 2, a_LC= 2, a_KF = 3, a_LF = 1.

Now assume the economy’s supply of machine-hours (K) increases from 3,000 to 4,000. Derive the new production possibility frontier (no need to write the expression in the answer space provided). Just answer the following questions in the answer space provided.

1)     How much cloth and food will the economy produce after this increase in its capital supply?

2)     Describe how the allocation of machine-hours and work-hours between the cloth and food sectors changes.

3)     Do those changes conform with the changes described for the case with factor substitution?

Answer 1

1. original PPF:

a_KC.C + a_KF.F= 3000, which is 2C + 3F= 3000

a_LC.C + a_LF.F= 2000 which is 2C + F= 2000

Solve the two equations to see the amount of cloth and food the economy will produce

2F= 1000 so F=500

C= 2500/2= 1250

New PPF:

a_KC.C + a_KF.F=​​​​​​​ 4000 which will become 2C +3F= 4000

a_LC.C + a_LF.F= 2000 which will become 2C + F= 2000

Solving the two equations we get

2F= 2000 so F=1000

2C= 1000 so C= 500

Ans. Food rises from 500 to 1000 and Cloth falls from 1250 to 500.

2. a_LC/ a_{KC= 2/2= 1}

a_LF/a_KF = 1/3

So, a_LC/ a_KC>a_LF/a_KF which means cloth is more labour intensive than food.

So, a rise in endownment of capital will cause rise in production of food and fall in production of cloth. This means, in the short run, there will be a rise in machine hours and labour hours in production of food compared to cloth.