# Marginal Rate of Transformation

The Marginal Rate of Transformation is the quantity of an object to give up to get one unit of another object. $$MRT = -\frac{p_X}{p_Y}$$

## Example

Alice has $8 to buy chocolate (X) and strawberries (Y). The price of a chocolate bar is p_X =$4 and the price of a strawberry is p_Y = $2. The Marginal Rate of Transformation of a strawberry into a chocolate ibar s $$MRT = - \frac{p_X}{p_Y} = - \frac{4}{2} -2$$ So 1 chocolate bar is worth 2 strawberries. Graphically, it corresponds to the slope of the budget line: $$4 X + 2 Y = 8$$ Therefore, $$Y = - \mathbf{2} X + 4$$ To get 1 chocolate bar, Alice needs to give 2 strawberries. ### Question The price of a chocolate bar (X) is$12 and the price of a strawberry (Y) is \$24.

How many strawberries can Alice get if she forgoes a chocolate bar?

A chocolate is worth \frac{12}{24} = 1 / 2 strawberries.