Mr. A derives utility from martinis (m) in proportion to the number he drinks: U(m) = m Mr. A is 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 (g/2, 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 function of pg and pv. Hint: Because this problem involves a fixed-proportions utility function, you cannot solve for utility-maximizing decisions by using calculus.
Mr. A derives utility from martinis (m) in proportion to the number he drinks:
U(m) = m
Mr. A is 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 (g/2, 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 function of pg and pv. Hint: Because this problem involves a fixed-proportions utility function, you cannot solve for utility-maximizing decisions by using calculus.
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