Many elderly people have Social Security payments as their sole source of income. Because of this, there have been attempts to adjust these payments so as to keep up with changing prices. This process is called "indexing"; this question will lead you through the process.
Suppose that in the year 2000, a typical Social Security recipient consumed only Food and Housing. The price of housing was $15/unit and the price of food was $5/unit. Denote the quantities of food and housing per month by F and H respectively. This consumer received $150/month and consumed five units of housing and 15 units of food.
a. Write down the algebraic representation of this consumer's budget constraint.
b. Show that the bundle (5,15) is just affordable. Identify another bundle on the budget constraint where both goods are consumed in positive amounts. Suppose that in 2004 the price of food rose to $10/unit and housing rose to $20/unit.
c. How much additional income is required such that the original bundle is just affordable at the new prices.
d. On the graph with Housing on the horizontal axis and food on the vertical axis, depict the original budget constraint and the new budget constraint after income is compensated according to c. Include the indifference curve going through the point (5,15).
f. Is the consumer better, worse, or equally well off in 2004 relative to 2000 following the compensation? Explain. What will happen to the consumer's choice of food and housing consumption? How can you tell?
g. The Laspeyres Price Index, as we have been describing above, measures inflation by looking at how the cost of a particular bundle of goods a consumer purchases in a previous year changes. Critics claim that this measure of inflation overstates changes in the cost of living. Do you agree or disagree? Explain.
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