Question

A consumer wants to consume two goods. The prices of the goods are Rs 4 and Rs 5 respectively. The consumer's income is Rs 20.
(i) Write down the equation of the budget line.
(ii) How much of Good-1 can the consumer consume if she spends her entire income on that good?
(iii) How much of Good-2 can she consume if she spends her entire income on that good?
(iv) What is the slope of the budget line?

Answer 1

Let $X_1$ denote Good-1 and $X_2$ denote Good-2.
$P_1=Rs4,P_2=Rs5,Y=Rs20$
(i) $P_1{X}_1+P_2{X}_2=Y$
$4X_1+5X_2=20$
Thus, the equation of the budget line is $4X_1+5X_2=20$.
(ii) We know equation of the budget line is:
$P_1{X}_1+P_2{X}_2=Y$
If the consumer spends her entire income on Good-1, then
$X_2=0$
$P_1{X}_1=Y\Rightarrow 4X_1=20$
$X_1=5$
Thus, the consumer can buy 5 units of Good-1 if she spends her entire income on that good.
(iii) If the consumer spends her entire income on Good-2, then
$X_1=0$
$P_2{X}_2=Y\Rightarrow 5X_2=20$
$X_2=4$
Thus, the consumer can buy 4 units of Good-2 if she spends her entire income on that good.
(iv) Slope of budget line = $\frac{P_1}{P_2}=\frac{4}{5}$.