Question

# Consider the following data on quantities of two factors, capital and labor, available, and their use...

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, aKC = 2, aLC= 2, aKF = 3, aLF = 1.

a.     Derive equations for PC and PF. 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 PC rises?

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

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

#### Homework Answers

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, PC = 2* r + 2 * w [ where w is wage rate of labor and r is capital rental rate ]

Similarly for food , PF = 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 Pc rises, r increases and w goes down

2) When PF 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.

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