4.5 Mr. A derives utility from martinis (m) in proportion to the number he drinks: U (m) %3D т. 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, 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 p,. Hint: Because this problem involves a fixed-proportions utility function, you cannot solve for utility-maximizing decisions by using calculus.

4.5 Mr. A derives utility from martinis (m) in proportion to the number he drinks: U (m) %3D т. 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, 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 p,. Hint: Because this problem involves a fixed-proportions utility function, you cannot solve for utility-maximizing decisions by using calculus.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus.

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.

Question

4.5
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(, 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 p, and p,. Hint: Because this
problem involves a fixed-proportions utility function, you cannot solve for utility-maximizing decisions by using calculus.

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