Budget Constraint

The budget constraint represents what a consumer can buy. $$X p_X + Y p_Y \leq I$$

Example

Alice has $8 to buy chocolate (X) and strawberries (Y). So she can buy chocolate and strawberries, as long as she spends less than $8.

The price of a chocolate is $4. She finds strawberries for $2 each.

Her budget constraint is

$$4X + 2Y \leq 8$$

A tiny bit of algebra gives

$$Y \leq - 2X + 4$$

The budget constraint is the shaded area in the plot below

Question

Alice has $187 to buy chocolate (X) and strawberries (Y). The price of a chocolate is $83 and the price of a strawberry is $7.

Write Alice's budget constraint. Can he afford 2 chocolates and 5 strawberries at the same time?

Alice's budget constraint is

$$ 83 X + 7 Y \leq 187 $$

In total, 2 chocolates and 5 strawberris costs Alice

$$ 83 \times 2 + 7 \times 5 = 201 $$

No! Alice cannot afford 2 chocolate bars and 5 strawberries.