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Remarks on Consumer Theory

Linh Bun

Winter season 2012 (UCSC)

1 . Consumer Theory –Utility Functions

1 . 1 . Types of Electricity Functions

Listed here are some of the type of the power functions which might be important: Best Complements

Excellent Substitutes

Cobb-Douglas

Quasilinear

1 ) 2 . Ideal Complements

The Utility function:

U (x; y) sama dengan M in fx; yg

The Budget Limitation:

px times + py y = m

exactly where m is usually income, and px and py is definitely the price of good x and y correspondingly. The chart of the indi¤erence curves intended for Perfect Completments is as follows:

Y

U

U

By

Perfect suits: L-shaped indi¤erence curves

This notes can be prepared with some help coming from Aadil Nakhoda

1

Case in point:

Right footwear and Still left shoe: If we purchase one proper shoe, we have to purchase one still left shoe likewise. The cosumer maximization problem for Perfect Complements:

M ax U (x; y)

subject to

px x + py con = m

The optimal allocation, the intake bundle that gives the highest electricity (x; con ); is definitely when by = sumado a Replacing sumado a with by into the budget constraint as x sama dengan y, we certainly have the following: px x + py x = m

x (px + py ) sama dengan m

Therefore,

x =y =

m

px + py

1 . 3. Perfect Substitutes

Y

Budget line

U2

U1

X

Consider the above chart:

The slope of the finances line is Steeper than the slope with the indi¤erence figure. The slope of the budge line in absolute benefit is px, where px and py is the value of good back button and con respectively. py

The slope of the indi¤erence curves in absolute worth is jM RSj, where M RS is the Marginal Rate of Substitutions

" @U (x; y) #

M Ux

Marginal Utility of Good times

@x

Meters RS =

=

sama dengan

@U (x; y)

Little Utility great y

Meters Uy

@y

The slope of the finances line is usually Steeper compared to the slope with the indi¤erence figure. This is equal to having the next:

px

> jM RSj

py

The perfect Allocation (x; y ) is

m

0; py. Equivalently, the number of good times and sumado a demanded can be

m

0; py:

Case in point:

Suppose we have two items, Pepsi (x) and Coke (y). Which usually good might you prefer to obtain? Spending most income m on Cola (y), my spouse and i. e. purchasing only Cola (y); is going to put you within the highest indi¤erence curve offered the budget limitation.

The budget range is tangent to a higher indi¤erence curve in the y Axis; than it is at the x Axis:

a couple of

Y

Spending budget line

U2

U1

Back button

Consider these graph:

The slope from the budget line is Accent than the slope of the indi¤erence curves. The slope of the budge range in absolute value is px, in which px and py is the price of good x and y correspondingly. py

The slope in the indi¤erence figure in total value can be jM RSj, where Meters RS may be the Marginal Level of Substitutions

Marginal Electricity of Good back button

M Ux

M RS =

=

=

Limited Utility great y

Meters Uy

@U (x; y)

@x

@U (x; y)

@y

The slope from the budget line is More shapely than the slope of the indi¤erence curves. This can be equivalent to getting the following:

px

< jM RSj

py

The Optimal Share (x; sumado a ) can be

m

px; 0

m

px; zero

. Equivalently, the amount of good times and con demanded is usually

:

Example:

Suppose we have two goods, Pepsi (x) and Coke (y). Which very good would you obtain? Spending most income meters on Soft drink (x), my spouse and i. e. getting only Soft drink (x); is going to put you around the highest indi¤erence curve given the budget constraint.

The budget line is tangent to a higher indi¤erence curve in the x

axis; than it is at the con

axis:

Best Substitutes:

Rules to follow:

If the slope from the budget limitation is Steeper than the incline of the indi¤erence curve, all of us consume the good on the sumado a axis:

Specifically,

px

> jM RSj

py

Wherever px and py is definitely the price great x and y correspondingly.

If the slope of the price range constraint can be Flatter than the slope in the indi¤erence competition, we take in the good around the x axis:

In particular,

px

< jM RSj

py

Where px and py is the cost of good back button and con respectively.

Whenever we were to consume the good within the x axis; we signify it since:

3

Case in point:...