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 $344 to buy chocolate (X) and strawberries (Y). The price of a chocolate is $23 and the price of a strawberry is $55.

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

In total, 4 chocolates and 4 strawberries cost Alice

$$23 \times 4 + 55 \times 4 = 312$$

Yes! Alice can offord 4 chocolate bars and 4 strawberries.