# Marginal Rate of Technical Substitution

The marginal rate of technical substitution (MRTS) tells us how much capital is needed to replace a bit of labor. $$MRTS = - \frac{MP_L\left( K, L\right)}{MP_K \left( K, L \right)}$$

## Example

The cookie factory's production function is q \left( K, L \right) = K L^2. The marginal rate of technical substitution is $$MRTS = - \frac{MP_L\left( K, L\right)}{MP_K \left( K, L \right)} = - \frac{2 K L}{L^2} = -\frac{2 K}{L}$$

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