Question

Consider our usual setting with two goods (food and clothing) and two inputs (capital and labor). Units of
labor and capital respectively needed to produce one unit of food are given by LF = 4, KF = 1, meaning that
you need 4 units of labor and 1 unit of capital to produce 1 unit of food. The input requirements to produce
one unit of clothing are given by LC = 1, KC = 2. Denote LC and KC as labor and capital used in the clothing
sector and LF and KF as labor and capital used in the food sector.
a) Which good is relatively labor intensive, which one relatively capital intensive?
b) Suppose the total capital stock in the country is given by K = 500 and the total labor force by L =
1200. This implies that KF + KC ≤ 500 and LF + LC ≤ 1200. Draw the production possibility frontier
(PPF) of the country (draw clothing on the X-axis and food on the Y-axis). At which point are both
factors fully employed? (You do not need to calculate how many units of each good are produced,
just show the production point graphically)

Answer 1

(a) Here, LF= 4 and KF=1

LC=1 and KC=2

LF/KF > LC/KC

i.e, 4/1 > 1/2

So, food is relatively labour intensive and clothing is relatively capital intensive.

(b) Total capital stock in the country, K=500

Total labour force in the country, L=1200

Q_C = Quantity of clothing produced

Q_F = Quantity of food produced

Then, Capital constraint will be,

KC Q_C + KF Q_F​​​​​​ = 500

Then labor constraint will be,

LF Q_F + LC Q_C = 1200

The production possibility frontier of the country is shown graphically below:-