The selected basket – another aspect

### Background 1. The derivative (derivative = slope) of an indifference curve at any point is the number of units of y that are equal in utility to 1 unit of x (each point on the indifference curve represents some composition of the basket). If, for example, the derivative is 4, this means that in the existing composition of the basket, 4 units of y are equal in utility to 1 unit of x. In a convex indifference curve, the result of the derivative varies from point to point, along its length. 2. The reason that any basket A becomes a **chosen basket** is that the monetary value required to add a unit of utility through x is equal to that required through y. In other words, the monetary value required for an additional unit of utility is the same for both products. If equality did not exist, we would increase utility by using the product that yields a unit of utility at a cheaper price, and as a result, the composition of the original **chosen basket** A would change and it would no longer be the **chosen basket**. The equality in monetary value of the 2 products could be presented in the following form: `f'(x) * (P_y) = 1*p_x` Interpretation:
`1*P_x` – the monetary value of the benefit (u), obtained from an addition of 1 unit of x.
`f'(x) * P_y` – the monetary value of the utility value (u), obtained through y.
If we isolate `f'(x)`, we get: `f'(x) =(P_x)/(P_y)` **And the conclusion:** The chosen basket is located where the slope of the indifference curve equals the slope of the budget line.