Fun with price indices. Suppose that your utility function over health care in} and other goods (c) is given by Ulh. cl and that you have a fixed income of $100. [Assume that the indifference curves of your utility function bear the usual convex shape.) Each year, you choose h and c to maximize your utility subjectto a budget constraint: phh + pcc = V where ph is the price of health care, pc is the price of other goods, and Y is your income. In year 1. the price of health care is $1, while the price of other goods is $2. At these prices, you demand 30 units of health care and 35 units of other goods. In year 2, your utility function and your income do not change. but prices do. Health care beoomes more expensive at $1.50. while other goods become cheaper at $1.50. At these prices, you demand 20 units of health care. a] Assuming you spend all your income in year 2. how many units of other goods do you buy? b) Draw a graph with your demand for health care on the horizontal axis and your demand for other goods on the vertical axis. On this graph, draw your budget constraints in year 1 and in year 2. On these budget lines. indicate your demand points for h and c in year 1 and year 2. Also draw concave indifference curves tangent the points in year 1 and year 2 that represent your demand. Label the indifference curves U1 and U2. cl Do the price changes leave you better off, worse off. or the same as before? Is this resultjust for the indifference curves you drew, or will it hold for any set of convex indifference curves