Louis’s utility function for champagne (c) and soda (s) can be written as (c,) = 10c4. A bottle of champagne is $32 and a bottle of soda is $1. His monthly budget for champagne and soda is $80.
1. Find Louis’s optimal consumption bundle, (c∗,∗), and his utility level at this bundle.
2. Suppose a new study shows that champagne has tremendous health benefits, and a bill subsidizing the consumption of champagne is passed. The net price of champagne with the subsidy is $16. Find Louis’s new consumption bundle, (c∗∗,∗∗), and his utility level at this bundle.
3. Using the Hicks notion of income and substitution effects, calculate the dollar value of the income effect.