Consider a firm using labor and capital as its only inputs. The price of capital

Question

Consider a firm using labor and capital as its only inputs. The price of capital is $40 where the price of labor (wage) is $60. Using 500 units of labor and 500 units of capital the firm is producing 1200 units of output. At this mix of input, the firm's MPL is 10 while its MPK is 5

a.) Write the firm's isocost equation. What is the slop of the isocost?

b.) Determine if the frim's mix of inputs is optimal. Explain.

c.) If your answer to b is no, what should the firm do to improve its performace? Explain.

d.) Now suppose as a result of a mandated increase in the minimum wage the wage increases to $80. What would be the implication of this change for this firm?

Explanation / Answer

PART-1) Iso-quant equation will be : C = wL + rK

Differentiating equation; we get

dC = w*dL + r*dK

As applying the first order condition wherein dC = 0, thus we have w*dL + r*dK = 0

It gives the slope of isoquant i.e. (dK/dL) = -(w/r)

We are given; w = $60 and r = $40

Thus Slope of isocost = -(60/40) = -1.5

Hence it will be downward sloping

PART-2) Slope of isoquant, the optimality condition of input is:

MPK/MPL = (w/r)

Here we have MPL = 10 and MPK = 5,

So, (MPK/MPL) = (5/10) = 0.5

However in Ppart-1 we have computed w/r = 1.5

Because (MPK/MPL) does not equal to (w/r), thus we can conclude that the firm's mix of inputs is not optimal.

PART-3) For enhancing the performance, the firm either can either n decrease its wage to rent ratio (w/r) (either by raising the rent of capital or by lowering the wage) or improve the ratio (MPK/MPL) by generating more capital intensive production such as introduction of new technologies. A rational producer will target to maximizing the total output (Q) or to minimizing the total cost (C).

PART-4)

Total previous cost = C1 = wL + rK = $ (60*500 + 40*500) = $50,000

Revised cost = C2 = wL + rK = $ (80*500 + 40*500) = $60,000

w/r = (80/40) = 2

It reflects that the firm goes away from its optimality from previous because of increase in wage.

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