Marginal Rate of Transformation

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