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 2014, 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 of five units of housing and 15 units of food is just affordable.
c. Suppose that in 2015 the price of food rose to $10/unit and housing rose to $20/unit. How much additional income is required so 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 that passes through the bundle of five units of housing and 15 units of food.
e. Is the consumer better, worse, or equally well off in 2015 relative to 2014 following the compensation? Explain. What will happen to the consumer's choice of food and housing consumption in 2015? How can you tell?