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 $1345 to buy chocolate (X) and strawberries (Y). The price of a chocolate is $49 and the price of a strawberry is $95.

Write Alice's budget constraint. Can he afford 8 chocolates and 8 strawberries at the same time?

Alice's budget constraint is

$$ 49 X + 95 Y \leq 1345 $$

In total, 8 chocolates and 8 strawberris costs Alice

$$ 49 \times 8 + 95 \times 8 = 1152 $$

Yes! Alice can offord 8 chocolate bars and 8 strawberries.