Question

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.

(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

(i) Assume:
Good 1 be X
Good 2 be Y
Given:
Price of X = Rs. 4 (P = Rs. 4)
Price of Y = Rs. 5 (P = Rs. 5)
Income of the consumer = Rs. 20
$\because$ Budget line $\Rightarrow P_x+P_y=$ Income
$\therefore$ Budget line will be 4X + 5Y = 20

(ii) If she spends her entire income on good 1 (X) then the consumption of good 2(Y) will be zero.
Budget line $=P_x+P_y$ Income (from (i))
$\therefore$ 4X + 5(0) = 20
$X=\frac{20}{4}=5$ units

(iii) If she spends her entire income on good 2(Y), then the consumption of good 1(X) will be zero.
Budget line $=P_x+P_y=Income\left(from\right(i\left)\right)$
4(0) + 5Y = 20
$\therefore Y=\frac{20}{5}=4$ units

(iv) Slope of budget line
$=\frac{\text{Units of good 1 willing to sacrifice}}{\text{Units of good 2 willing to gain}}$
$=\frac{-\Delta P_x}{\Delta P_y}=\frac{-4}{5}=-0.8$

[Note: Sacrificed units always have negative value]