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 $690 to buy chocolate (X) and strawberries (Y). The price of a chocolate is $6 and the price of a strawberry is $90.

Can she afford 3 chocolate bars and 2 strawberries at the same time?

In total, 3 chocolates and 2 strawberries cost Alice

$$6 \times 3 + 90 \times 2 = 198$$

Yes! Alice can offord 3 chocolate bars and 2 strawberries.