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 $68 and the price of a strawberry (Y) is $136.

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

A chocolate is worth `\frac{68}{136} = 1 / 2` strawberries.