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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