# Marginal Rate of Technical Transformation

The Marginal Rate of Technical Transformation is the quantity of capital (K) to give up to get an extra unit of labor (L). $$MRT = -\frac{w}{r}$$

## Example

Ziggy pays a grandma (L) $100,000 to bake cookies for a year, and the cost of a oven (K) for the year is$10,000.

A grandma is worth \frac{100000}{10000} = 10 ovens.

The marginal rate of technical transformation is $$MRTT = - 10$$ The minus sign indicates that, to hire (+) one grandma, Ziggy can forego (-) 10 ovens.

The marginal rate of technical transformation is the slope of the cost curves: \begin{align*} C &= rK + wL \\ C &= 10000K + 100000L \\ -10000K &= 100000L - C \\ K &= - \frac{100000}{10000}L + \frac{C}{100000} \\ K &= - 10L + \frac{C}{100000} \end{align*}

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