3 8. Let be the utility function U(x, y) =(xi+ 2yä), , where x and y are the quantities consumed of two goods. (a) Show that the functional equation U(x, y) = U(2, 2) defines y as a function of x in a neighborhood of point (2, 2). (b) If the quantity consumed of good x increases by 1 unit, by how much does the quantity have to increase or decrease? Consumed of the good and to keep utility constant? (c) If the quantity consumed of good x increases by 1%, by how much does the quantity have to increase or decrease? Consumed of the good and to keep utility constant?

Microeconomics A Contemporary Intro
10th Edition
ISBN:9781285635101
Author:MCEACHERN
Publisher:MCEACHERN
Chapter6: Consumer Choice And Demand
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8. Let be the utility function U(x, y) =(xi + 2ya), , where x and y are the quantities
consumed of two goods.
(a) Show that the functional equation U(x,y)
U(2, 2) defines y as a function of x in a
neighborhood of point (2, 2).
(b) If the quantity consumed of good x increases by 1 unit, by how much does the
quantity have to increase or decrease? Consumed of the good and to keep utility
constant?
(c) If the quantity consumed of good x increases by 1%, by how much does the quantity
have to increase or decrease? Consumed of the good and to keep utility constant?
Transcribed Image Text:3 8. Let be the utility function U(x, y) =(xi + 2ya), , where x and y are the quantities consumed of two goods. (a) Show that the functional equation U(x,y) U(2, 2) defines y as a function of x in a neighborhood of point (2, 2). (b) If the quantity consumed of good x increases by 1 unit, by how much does the quantity have to increase or decrease? Consumed of the good and to keep utility constant? (c) If the quantity consumed of good x increases by 1%, by how much does the quantity have to increase or decrease? Consumed of the good and to keep utility constant?
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