Question

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 fifive 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 affffordable. 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 affffordable

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

(e) Include the indifffference curve going through the point (5,15).

(f) Is the consumer better, worse, or equally well offff 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?

Answer 1