Cost minimizing input choice, Microeconomics

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The Cost Minimizing Input Choice

- Assumptions

Two Inputs: Labor (L) & capital (K)
Price of labor: wage rate (w)
The capital price

- R = depreciation rate + interest rate

- Question

If capital was rented, would it change the value of r?

* The Isocost Line

- C = wL + rK

- Isocost: A line which shows all the combinations of L & K which can be purchased for same cost

- Rewriting C as linear:

K = C/r - (w/r)L
Slope of the Isocost:

is the ratio of wage rate to rental cost of capital.

* This shows the rate at which capital can be substituted for labor with no change in cost.

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