Suppose there are three different goods: cans of Coke (x1), cups of coffee (x2) and cans of Pepsi (x3).
A. Suppose each of these goods costs the same price p and you have an exogenous income I
(a) Illustrate your budget constraint in three dimensions and carefully label all intercepts and slopes.
(b) Suppose each of the three drinks has the same caffeine content, and suppose caffeine is the only characteristic of a drink you care about. What do “indifference curves” look like?
(c) What bundles on your budget constraint would be optimal?
(d) Suppose that Coke and Pepsi become more expensive. How does your answer change? Are you now better or worse off than you were before the price change?
B. Assume again that the three goods cost the same price p.
(a) Write down the equation of the budget constraint you drew in part A(a).
(b)Write down a utility function that represents the tastes described in A(b).
(c) Can you extend our notion of homothetic city to tastes over three goods? Are the tastes represented by the utility function you derived in (b) homothetic?