Q.A consumer wants to consume two goods. The prices of the two goods are Rs 4 and Rs 5 respectively. The consumer's income is Rs 20.

A consumer's budget line shows all combinations of two goods she can afford given her income and the prices of the goods. If good 1 has price $p_1 = 4$ and good 2 has price $p_2 = 5$, and her income is $M = 20$, then the budget constraint is $p_1 x_1 + p_2 x_2 = M$.

(i) Substituting the values, the budget line equation is

(ii) If the consumer spends her entire income on good 1, then $x_2 = 0$. From the budget line: $4x_1 = 20$, so $x_1 = 5$ units.

(iii) If she spends her entire income on good 2, then $x_1 = 0$. From the budget line: $5x_2 = 20$, so $x_2 = 4$ units. …

Understanding the Budget Line

A consumer's budget line represents the boundary of what is affordable. It captures a simple constraint: total spending on all goods cannot exceed income. When there are two goods, the budget line is the set of all combinations $(x_1, x_2)$ such that the expenditure on good 1 plus the expenditure on good 2 exactly equals income.

The expenditure on each good is its price multiplied by the quantity consumed. If good 1 costs $p_1$ per unit and good 2 costs $p_2$ per unit, and the consumer buys $x_1$ units of good 1 and $x_2$ units of good 2, then total spending is $p_1 x_1 + p_2 x_2$. Setting this equal to income $M$ gives the budget line equation.

This is a linear equation in two variables, which graphs as a straight line in $(x_1, x_2)$ space.

(i) The Budget Line Equation

Given:

• Price of good 1: $p_1 = 4$
• Price of good 2: $p_2 = 5$
• Income: $M = 20$

Substituting into the budget line formula:

This is the equation of the budget line. Every point $(x_1, x_2)$ satisfying this equation represents a consumption bundle the consumer can exactly afford.

(ii) Maximum Consumption of Good 1

If the consumer spends her entire income on good 1 alone, she buys zero units of good 2. Set $x_2 = 0$ in the budget equation:

She can consume 5 units of good 1 if she devotes all Rs 20 to it. This is the horizontal intercept of the budget line.

(iii) Maximum Consumption of Good 2

Similarly, if she spends everything on good 2, she buys zero units of good 1. Set $x_1 = 0$:

She can consume 4 units of good 2 if she allocates her entire income to it. This is the vertical intercept.

(iv) The Slope of the Budget Line

The slope measures the rate at which the consumer must give up one good to obtain more of the other, while staying on the budget line. Rearrange the budget equation to express $x_2$ as a function of $x_1$:

$x_2 = 4 - \frac{4}{5}x_1$ …