Answer to Question #221816 in Microeconomics for D12

Question

3. Consider a consumer who wants to consume only two commodities and has an income of $100. Assume the price of good 1 is $10 per unit and the price of good 2 is $20 per unit. Now, inflation causes the price of good 1 to increase to $20 per unit, while the price of good 2 increases to $25 per unit. On the other hand, the consumer also gets a raise of $100 (so her new income is $200). Is she better off or worse off?

Answer 1

Solution:

First, derive the original consumer’s budget constraint before the changes:

Budget constraint: I = PxX + PyY

Where: I = Income = 100

           Px = Price of good 1 = 10

           Py = Price of good 2 = 20

           X = Good 1

           Y = Good 2

Budget constraint:

100 = 10X + 20Y

The horizontal intercept (Good 1) =$\frac{I}{Px} = \frac{100}{10} = 10$

The vertical intercept (Good 2) =$\frac{I}{Py} = \frac{100}{20} = 5$

 

After the changes, the consumer’s new budget constraint becomes:

200 = 20X + 25Y

The horizontal intercept (Good 1) =$\frac{I}{Px} = \frac{200}{20} = 10$ (Which is the same as before)

The vertical intercept (Good 2) = $\frac{I}{Py} = \frac{200}{25} = 8$ (Higher than before)

Therefore, as per the new budget constraint, the consumer’s budget set has increased and now the consumer can afford more bundles than before, while still affording the same bundle as before. As such, the consumer is better off.