Mr. A derives utility from martinis (m) in proportion to the number he drinks: U(m) = m. Mr. A is very particular about his martinis, however: He only enjoys them made in the exact proportion of two parts gin () to one part vermouth (). Hence, we can rewrite Mr. A's utility function as ,v) for various levels of utility. Show that, U(m) = U( g, v) = min

a. Graph Mr. A's indifference curve in terms ofg and regardless of the prices of the two ingredients, Mr. A wll never alter the way he mixes martinis

b. Calculate the demand functions for g and v

c. Using the results from part (b), what is Mr. A's indirect uility function?

d. Calculate Mr. A's expenditure function; for each level of utility, show spending as a function of and p,. Hint: Because this problem involves a fixed-proportions utility function, you cannot solve for utility-maximizing decisions by using calculus.