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 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 is

$$MRT = - \frac{p_X}{p_Y} = - \frac{4}{2} -2$$

So 1 chocolate is worth 2 strawberries.

Graphically, it corresponds to the slope of the budget line:

$$ 4 X + 2 Y = 8 $$

Therefore,

$$ Y = - \mathbb{2} X + 4 $$

To get 1 chocolate, Alice needs to give 2 strawberries.

Question

The price of a chocolate (X) is $64 and the price of a strawberry (Y) is $5760.

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

A chocolate is worth `\frac{64}{5760} = 1 / 90` strawberrie(s).