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 $665 to buy chocolate (X) and strawberries (Y). The price of a chocolate is $44 and the price of a strawberry is $75.

Write Alice's budget constraint. Can he afford 4 chocolates and 9 strawberries at the same time?

Alice's budget constraint is

$$ 44 X + 75 Y \leq 665 $$

In total, 4 chocolates and 9 strawberris costs Alice

$$ 44 \times 4 + 75 \times 9 = 851 $$

No! Alice cannot afford 4 chocolate bars and 9 strawberries.