2. In 2000 Ellis spends his snack dollars on chocolate chip cookies (x) and graham crackers (y). His preferences over chocolate chip cookies (x) and graham crackers (y) can be represented by the utility function U(x,y) = x+ 4lny.

a) If the price of a chocolate chip cookie is Px, the price of a graham cracker is Py and he has I=Income to spend each week on snacks then find his (Marshallian) demand functions for chocolate chip cookies and graham crackers.

b) Suppose that Px= $1.50, Py= $1 and I = $9. Using your answer to (a) find his demands for chocolate chip cookies and graham crackers. Illustrate your answer in an indifference curve diagram. Include in your diagram an indifference curve through his best bundle.

By 2010 the price of a chocolate chip cookie has risen to $4 and the price of a graham cracker has risen to $2.

c) Which good has become relatively cheaper?

d) If Ellis would like to continue to purchase the bundle of chocolate chip cookies and graham crackers that he purchased in 2000 then how much money will he need in 2010?

e) What is the rate of inflation for snack expenditures between 2000 and 2010?

Suppose that in 2010 Ellis's income is adjusted for the rate of inflation calculated in part (e).

f) Will Ellis purchase the same bundle of goods in 2010 that he purchased in 2000? Briefly explain your answer. You must refer to his MRS in order to receive full credit.

g) Is Ellis better or worse off in 2010 if his income is adjusted for the rate of inflation?

h) An ideal cost of living adjustment would adjust income so that an individual is no better nor worse off after prices change. What problem do you have to solve to find the ideal cost of living adjustment for Ellis? What are the first-order conditions for that problem?