Question

Question 2. At one time, Social Security payments to the elderly were adjusted every year in the following way: The government determined a bundle of goods consumed by an "average" elderly person. Each year, the government then, in response to any change in prices of goods in this bundle, raises social security payments by the amount required to allow the "average" elderly person to continue consuming that same bundle. Suppose the average elderly person only consumes good 1 and good 2, and has utility function U(X1, X2)= X1 X2. Assume the price of good 1 increases by 10% each year while the price of good 2 is unchanged. Is the government making seniors better off, worse off, or leaving them indifferent over time? To answer this, consider two years and suppose the government makes the adjustment in the second year, assuming the price of good 1 will increase 10% over year 1.

Answer 1

Let's assume that the prices of the two goods are the same in Y1, say, 100 per unit, and that the average elderly person has an income of 200. Their budget line is as follows (X1 on vertical axis and X2 on horizontal axis).

051 1. 52 2 2.5

We can also add an indifference curve as follows:

| 0 0.5 11. 52

Now in Y2, with the increase in X1's price to 110 (by 10%), which results in an overall price rise of 5% for this bundle (average of 10% and 0% price rise in X1 and X2), the Government increases the payment to $210. The new budget line will become flatter (as more quantity of X2 can be purchased, if all income is spent on X2, with the possibility of same quantity of X1).

Pls see graph below with a line added to show the change. (the difference is very slight, but with the possiblity of acquiring 2.1 units of X2, the average elderly person can actually attain a slightly higher indifference curve.)