Problem 2 Many elderly people in the US receive 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 (inflation). This process is called indexing"; this question will lead you through the process. Suppose that in the year 2018, a typical Social Security recipient consumed only Food (F) and Housing (H). The price of housing was $150/unit and the price of food was $50/unit. Denote the quantities of food and housing per month by F and H respectively. This consumer received $1500/month and consumed 5 units of housing and 15 units of food. (a) Write out the consumer's budget constraint and demonstrate that the bundle chosen falls on that budget constraint. (b) Draw the budget constraint on a graph (Housing on the horizontal axis) with the optimal bundle labeled. Draw the indifference curve through that optimal bundle. Assume preferences are well behaved. Suppose that in 2019, the price of food increased to $100 and the price of housing increased to $200. (c) What is the cost of the consumer's original 2018 bundle at the new 2019 prices? How much additional income would this consumer need in order to afford the original bundle? Using your answer to (c), calculate the rate of inflation using the con- sumer price index based on the 2018 bundle (more generally called a Laspeyres price index). (d)