Pxx I The book derives the equality xnx + 0yny = 1 where 0x = x is the share of income spent on the x good and nx is the income elasticity of the x good, donuts (similarly ey and ny are the share of income and the income elasticity of the y good, croissants. The income elasticity of Edith's demand for donuts is 1, and the own price elasticity of Edith's demand for donuts is - Px Px+2Py) a) Use income elasticities above to verify that this expression holds for Edith's demands. дох )? b) In general (not just for Edith's demands) how does 6x vary when I changes (i.e. find ai c) If x <1 then what is the sign of the derivative in part (f)? If nx=1 then what is the sign of the derivative in part (f)? If a good is a necessity then as income rises does the share of income spent on that good rise or fall? d) Given the income elasticity for donuts, what will be the derivative of 0x with respect to I for Edith's demands? e) Write 0x as a function of only prices and income for Edith's demand for donuts. Verify your answer to part d (ie calculate the derivative directly to show that it equals your answer). f) The income-consumption curve (icc) shows how Edith's consumption of donuts and croissants increases as her income increases. Illustrate the icc in your diagram above.
Pxx I The book derives the equality xnx + 0yny = 1 where 0x = x is the share of income spent on the x good and nx is the income elasticity of the x good, donuts (similarly ey and ny are the share of income and the income elasticity of the y good, croissants. The income elasticity of Edith's demand for donuts is 1, and the own price elasticity of Edith's demand for donuts is - Px Px+2Py) a) Use income elasticities above to verify that this expression holds for Edith's demands. дох )? b) In general (not just for Edith's demands) how does 6x vary when I changes (i.e. find ai c) If x <1 then what is the sign of the derivative in part (f)? If nx=1 then what is the sign of the derivative in part (f)? If a good is a necessity then as income rises does the share of income spent on that good rise or fall? d) Given the income elasticity for donuts, what will be the derivative of 0x with respect to I for Edith's demands? e) Write 0x as a function of only prices and income for Edith's demand for donuts. Verify your answer to part d (ie calculate the derivative directly to show that it equals your answer). f) The income-consumption curve (icc) shows how Edith's consumption of donuts and croissants increases as her income increases. Illustrate the icc in your diagram above.
Principles of Microeconomics
7th Edition
ISBN:9781305156050
Author:N. Gregory Mankiw
Publisher:N. Gregory Mankiw
Chapter5: Elastic And Its Application
Section: Chapter Questions
Problem 7PA: Maria has decided always to spend one third of her income on clothing. a. What is her income...
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Question
Transcribed Image Text:Px
0,ny = 1 where 0x
* is the share of income spent on
%3D
The book derives the equality 0xnx +
are the share
and
My
the x good and x is the income elasticity of the x good, donuts (similarly 0,
of income and the income elasticity of the y good, croissants.
The income elasticity of Edith's demand for donuts is 1, and the own price elasticity of Edith's
Px
demand for donuts is
Px+2Py/
a) Use income elasticities above to verify that this expression holds for Edith's demands.
)?
b) In general (not just for Edith's demands) how does 0, vary when I changes (i.e. find
10
c) If
the derivative in part (f)? If a good is a necessity then as income rises does the share of income
spent on that good rise or fall?
<1 then what is the sign of the derivative in part (f)? If nx = 1 then what is the sign of
d) Given the income elasticity for donuts, what will be the derivative of 0, with respect to I for
Edith's demands?
e) Write 0, as a function of only prices and income for Edith's demand for donuts. Verify your
answer to part d (ie calculate the derivative directly to show that it equals your answer).
f) The income-consumption curve (icc) shows how Edith's consumption of donuts and croissants
increases as her income increases. Illustrate the icc in your diagram above.
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Step 1: Define income elasticity of demand
VIEWStep 2: Verify the expression for Edith's demands.
VIEWStep 3: Calculate the derivate of θ with respect to I
VIEWStep 4: Interpret the derivative
VIEWStep 5: Derive the derivative of θx
VIEWStep 6: Write θx as a Function of Prices and Income
VIEWStep 7: Graph the ICC
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