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 bar 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 above.

Question

Alice has $258 to buy chocolate (X) and strawberries (Y). The price of a chocolate is $74 and the price of a strawberry is $6.

Can she afford 4 chocolate bars and 3 strawberries at the same time?

In total, 4 chocolates and 3 strawberries cost Alice

$$74 \times 4 + 6 \times 3 = 314$$

No! Alice cannot afford 4 chocolate bars and 3 strawberries.