Question

Oranges cost $1/kg and apples also cost $1/kg. Niki has $12 to spend on apples or oranges. He chooses to buy 5 kg of apples.

1. Draw (on a diagram measuring quantity of oranges on the horizontal axis) Niki’s budget line and show the optimal consumption point. Do not forget to draw the relevant indifference curve(s).

2. The government subsidizes consumption of apples so that apples now cost $0.5/kg). How does Niki’s budget line change? Show graphically (on the same diagram you used to answer question 3!) his optimal choice. Can you say whether he will buy more or less apples? Would Niki be better off, or worse off than in question 3?

In addition to the subsidy from question 4, the government has decided to introduce a head tax that would just allow him to continue purchasing the basket from question 3. How large should this tax rebate be? Show (on the same diagram you drew for question 3!) the new budget line and the new optimal basket. Can you say whether he will buy more or less apples? Would Niki be better off, or worse off than in question 3?

Answer 1

Answer: The solution to the above problem is described with the help of the following diagram:

Given the initial budget and the prices of Apple and Orange, the budget line draw in the diagram is AB. On that budget line Niki's preference is at point E on the Indifference curve IC and he purchases 5 kg of Apples.

Now, after the change in the price to 0.5/kg, his budget line shift rightward to AC from AB. As a result of fall in the price Niki can purchase more of Apples which is in the diagram 11. This price change has let her to move on a higher indifference curve which is IC' and on the curve his optimal point of consumption is point F.

Hence we see that Niki is better off from the price change.

Now, come to the second part where the Government introduces a head tax. Due to the imposition of the head tax, Niki has to adjust his expenditure which was increased due to fall in the price of Apple. As a result, Niki's budget line shifts downward to A'B' from AC. The difference between the previous budget line AC and the new budget line A'C' is AA' which is the amount of tax rebate. Though he can still lie on his previous indifference curve which yield her the same level of satisfaction with the optimal basket at point G on the indifference curve IC.

Note here that, on the previous indifference curve IC also she can now buy more of Apples than in the initial position but this amount of purchase is less than the amount which she could buy due to fall in the price of apple.

Hence, due to imposition of head tax also, Niki is better off than his initial condition.

Please note, the diagram above may not imply the actual amount of combinations in values.