4.5 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 (G) to one part vermouth (V). Hence, we can rewrite Mr. A's utility function as U(M) = U(G,V) = min I j,v\

a. Graph Mr. A's indifference curve in terms of G and V for various levels of utility. Show that regardless of the prices of the two ingredients, Mr. A will 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 utility function?

d. Calculate Mr. A's expenditure function; for each level of utility, show spending as a func tion of PG and Pv.

Hint: Because this problem involves a fixed proportions utility function you cannot solve for utility-maximizing decisions by using calculus.