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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 proportionof two parts gin (g) to one part vermouth (v). Hence, we can rewrite Mr. As utility function asU(m)=U(g,v)=min(g/2,v)a. Graph Mr. As 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. As indirect utility function?
(question a.) Let’s draw a line described as v = g/2 ? Suppose that his utility is 1, Mr. A will get this amount of utility, 1, at the point (g, v) = (2, 1) because he gets a glass of martini from 2 parts of gin and 1 part of vermouth. And, even if the amount of gin increases from 2, his utility will stay at 1 from given conditions. Likewise, even if the amount of vermouth increases from 1, his utility will stay at 1. Therefore, his indifference curve for U(1)=1 should be described by a L-shaped line that consists of a vertical and horizontal line that meet at (2, 1) . In the same way, you can draw as many as L-shaped lines that have the corner on the line? for various levels of his utility. Regarding price changes, Price changes are reflected on the slope of the budget constraint equation. If a budget constraint equation cross at two point with an indifference curve, it is not a reasonable choice because he can realize the same amount of utility by a constraint equation with less budget. Thus, he will continue cutting his budget as long as lines cross at two points, and will finally reach the corner of the…

rence curve where martinis are mixed in the same proportion, 2 gin and 1 vermouth. And, this process is all the same regardless of the angle of the slope. (question b.) From (a.) we can conclude that the condition? should be always satisfied, therefore, g = 2v ? The general form of the budget constraint equation is, let p1, p2, and M represent the prices of gin, vermouth, and the total budget respectively, as follows. p1*g + p2*v = M, where * represents multiplication. Plugging in ? for this 2p1*v + p2*v = M v = M/(2p1 + p2) Then g = 2M/(2p1 + p2) (question c.) I’m not sure what “indirect utility function” means, but as the amount of “m” always equals that of g/2 or v from the above discussion, I could say that U(m) = m = g/2 = v = M/(2p1 + p2)

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