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. Derive equations for
*P _{C}* and

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.

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