Posted by Anjali Kaur on May 26, 2020

Microeconomics: Numerical problem on Budget Set

Today, I am going to solve a question asked from me on the ‘Quora platform’. Some of you, who have not studied the concept of income and substitution effect might find it difficult to understand. It is a higher-level problem. Let’s solve one Numerical problem on Budget Set.

The question is: A consumer consumes two goods, X and Y, where good X is an inferior good and good Y is a normal good. Income is equal to \$100 and Py=\$1 per unit. Initially Px= \$1.25 per unit, but then this price decreases to \$1 per unit. The consumer optimal bundle contains 60 units of good X and 25 units of good Y. As the price of good X falls, the consumer optimal bundle changes to 65 units of good X and 35 units of good Y. Use the diagram to show the income and substitution effect on good X.

Solution. Numerical problem on Budget Set. Let’s start with the meaning of some basic terms:

Inferior goods are poor quality goods which have a negative income effect whereas Normal goods are the best quality goods which have a positive income effect.

As per the question our budget equation is :

XPx+ YPy= M

After placing the first values from the question we get:

1.25X+1Y=100 (By placing Px=1.25 and Py=1 in Budget equation)

So, when good X price was \$1.25 then consumer was purchasing 60 units of X and 25 units of Y.

Look at the budget line AB and indifference curve 1. (Indifference curve shows the combination of 2 goods which a consumer consumes and it provides the same level of satisfaction to the consumer)

After the price of good X falls, the consumer starts purchasing more of X and more of Y. Consumer purchases 65 units of good X and 35 units of good.

1X+1Y=100 (Now, Px=\$1 and Py remained the same at \$1)

This is shown with the budget line AC and indifference curve as 2. The vertical intercept is the same at 100. Because when we divide income by price of Y, it is \$100 only as the price of Y did not change. (Vertical intercept = Income/Py)

Whereas the Horizontal intercept changed from \$80 (Income/price of X) to \$100 (100/1).

Indifference curve bundle changes from (60,25) to (65,35).

As, shown with the fall in the price of good X budget line rotated outward on X axis.

The substitution effect is the change in the quantity demanded of a commodity due to change in the relative prices of the commodities, the real income of the consumer remaining constant. Income effect refers to the change in the quantity demanded of a commodity arising from change in real income (purchasing power of money income) relative prices remaining constant. An inferior good is one which consumer consumes due to the inability of the consumer to afford close substitutes; consumption of inferior goods decreases with an increase in income.

So, to explain the substitution effect, we drew a budget line ‘DE’ parallel to ‘AC'( after the price fall budget line)

C0 indicates the original consumption bundle before any change (60,25) then C1 is the bundle to show a substitution effect in case income falls (75,15). So, the Substitution effect is ‘C0 to C1‘ that is indicated in the diagram.

Income effect is from ‘C1 to C2’.

I hope it was helpful. You can try going through the basics of the budget line and indifference curve approach for better clarity.

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