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.

a.     Derive equations for P_C and P_F. Now solve the equations for w (wage rate) and r (capital rental rate). (No need to write the expressions on the answer space provided). Answer the following questions in the answer space provided.

1)     What happens to w and r when P_C rises?

2)     What happens to w and r when P_F rises?

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

Answer 1

Since 2 units of capital K and 2 units of labor L is required to produce one unit of cloth.

So for cloth, P_C = 2* r + 2 * w [ where w is wage rate of labor and r is capital rental rate ]

Similarly for food , P_F = 3 * r + 1 * w

But 2 r + 3 r = 3000 or r = 3000/5 = 600

and 2w + w = 2000 or w = 2000/3 = 666.66

1) When P_c rises, r increases and w goes down

2) When P_F rises, w increases and r goes down

3) Yes these conform to changes as per factor substitution where labor and capital are substituted for each other as production of cloth or food rises.