Download presentation

Presentation is loading. Please wait.

Published byCarmen Pritchett Modified over 2 years ago

1
Properties of Demand Functions Comparative statics analysis of ordinary demand functions -- the study of how ordinary demands x 1 *(p 1,p 2,m) and x 2 *(p 1,p 2,m) change as prices p 1, p 2 and income m change. Own-Price changes: How does x 1 *(p 1,p 2,m) change as p 1 changes, holding p 2 and m constant?

2
x 1 *(p 1 ’’’) x 1 *(p 1 ’) x 1 *(p 1 ’’) p1p1 x 1 *(p 1 ’) x 1 *(p 1 ’’’) x 1 *(p 1 ’’) p1’p1’ p 1 ’’ p 1 ’’’ x1*x1* Own-Price Changes Ordinary demand curve for commodity 1 Fixed p 2 and m.

3
Own-Price Changes The curve containing all the utility- maximizing bundles traced out as p 1 changes, with p 2 and m constant, is the p 1 - price offer curve. The plot of the x 1 -coordinate of the p 1 - price offer curve against p 1 is the ordinary demand curve for commodity 1.

4
Own-Price Changes: Cobb-Douglas Take Then the ordinary demand functions for commodities 1 and 2 are What does the demand curve look like? What does a p 1 price-offer curve look like?

5
x 1 *(p 1 ’’’) x 1 *(p 1 ’) x 1 *(p 1 ’’) p1p1 x1*x1* Own-Price Changes Ordinary demand curve for commodity 1 is Fixed p 2 and m.

6
Own-Price Changes: Perfect complements Take Then the ordinary demand functions for commodities 1 and 2 are What does the demand curve look like? What is the p 1 price-offer curve?

7
p1p1 x1*x1* Ordinary demand curve for commodity 1 is Fixed p 2 and m. Own-Price Changes x1x1 x2x2 p1’p1’ p 1 ’’ p 1 ’’’ m/p 2

8
Own-Price Changes: Perfect Substitutes Take Then the ordinary demand functions for commodities 1 and 2 are What does the demand curve look like? What is the p 1 price-offer curve?

9
Own-Price Changes x2x2 x1x1 p1p1 x1*x1* Fixed p 2 and m. p1’p1’ p 2 = p 1 ’’ p 1 ’’’ p 1 price offer curve Ordinary demand curve for commodity 1

10
Income Changes How does the value of x 1 *(p 1,p 2,m) change as m changes, holding both p 1 and p 2 constant? A plot of quantity demanded against income is called an Engel curve. A plot of bundles chosen as we vary income is called the income-offer curve. Draw these two curves for Perfect complements, Cobb-Douglas, and Perfect Substitutes.

11
Income Changes In every example so far the income offer curves have all been straight lines for the origin? Q: Is this true in general? A: No. Income offer curves are straight lines only if the consumer’s preferences are homothetic.

12
Homotheticity A consumer’s preferences are homothetic if and only if for every k > 0. That is, the consumer’s MRS is the same anywhere on a straight line drawn from the origin. (x 1,x 2 ) (y 1,y 2 ) (kx 1,kx 2 ) (ky 1,ky 2 )

13
Why the connection? Take a budget and choice (x1*,x2*). Double the budget so new budget is 2m. Notice if (x1,x2) were in the old budget, (2 x1, 2 x2) is in the new budget. Homotheticity implies that if (x1*,x2*)> (x1,x2) then (2x1*,2x2*)>(2x1,2x2), thus new choice is (2x1*,2x2*). Notice if you draw a line from origin to (x1*,x2*) it goes through (2x1*,2x2*). Since these are the choices, the MRS must be the same at both points to be tangent to the ICs.

14
Homogeneous Utility Functions U(k x1,k x2)= g(k) u(x1,x2) and g(k)>0. This implies homotheticity! U(x1,x2)>U(y1,y2) => g(k) U(x1,x2)> g(k) U(y1,y2) => U(k x1,k x2)>U(k y1,k y2) Does Cobb-Douglas, Perfect Substitutes, Perfect Complements satisfy this?

15
Income Effects -- A Nonhomothetic Example Quasilinear preferences are not homothetic. For example, U(1,0)>U(0,3/4) but when k=4, we have U(4,0)__
{
"@context": "http://schema.org",
"@type": "ImageObject",
"contentUrl": "http://images.slideplayer.com/11/3269696/slides/slide_15.jpg",
"name": "Income Effects -- A Nonhomothetic Example Quasilinear preferences are not homothetic.",
"description": "For example, U(1,0)>U(0,3/4) but when k=4, we have U(4,0)
__

16
Income Effects A good for which quantity demanded rises with income is called normal. Therefore a normal good’s Engel curve is positively sloped. A good for which quantity demanded falls as income increases is called income inferior. Therefore an income inferior good’s Engel curve is negatively sloped. A luxury good is where the proportion of income spent on it goes up with income. The opposite of a luxury good is a necessary good. Is a necessary good always inferior? Is a inferior good always necessary? Can we have a necessary good w/o a luxury good? Vice-versa? Can we have an inferior good w/o a luxury good? Vice-versa?

17
Ordinary and Giffen goods. A good is called ordinary if the quantity demanded of it always increases as its own price decreases. If, for some values of its own price, the quantity demanded of a good rises as its own-price increases then the good is called Giffen. Example of a Giffen good – U(x 1,x 2 )=-e -x1 -e -x2

18
Cross-Price Effects If an increase in p 2 –increases demand for commodity 1 then commodity 1 is a gross substitute for commodity 2. – reduces demand for commodity 1 then commodity 1 is a gross complement for commodity 2. What happens with Cobb-Douglas preferences?

Similar presentations

Presentation is loading. Please wait....

OK

Consumer Preferences chapter 4

Consumer Preferences chapter 4

© 2018 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on notepad editor in java Ppt on self awareness theory Ppt on self awareness activities Ppt on job evaluation sample Ppt on mars one scam Ppt on business environment nature concept and significance of the study Ppt on use of maths in our daily life Ppt on old age homes Ppt on beer lambert law lab Ppt on building information modeling bim