# Calculating optimal amount of capital and labor

Suppose long run production for the firm is indicated by: Q=f(k,e) where: MPe=k-150 MPk=E-60

In addition, assume the firm's isocost equation is given by: C=wE+rK Where C=$240,000 r=$600 w=$800

1) Calculate the firm's optimal amount of capital and labor.

2) Suppose wages fall to w=$500. Calculate the firm's optimal amount of capital and labor in this case.

https://brainmass.com/economics/production-function/calculating-optimal-amount-capital-labor-278228

#### Solution Preview

1) Calculate the firm's optimal amount of capital and labor.

For optimal combination

MPe/w=MPk/r

(K-150)/800=(E-60)/600

600*(K-150)=(E-60)*800

600K-90000=800E-48000

600K=-48000+90000+800E

600K=42000+800E ...

#### Solution Summary

Solution describes the methodology to find out a firm's optimal amount of capital and labor.

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