Microeconomics: Concept of Indifference Curve and Budget Line. Definition of ...Rohan Byanjankar
Concept of Indifference Curve and Budget Line.
Derivation of Budget line. Calculation of slope of budget line and its intercepts. Calculus Proof of budget Line and Indifference Curve. Relationship of Budget Line and Indifference Curve. Contains some of the alternative questions.
Slope of Budget Line, intercepts of budget line along with figure.
Concept of Marginal Rate of Substitution. Causes of Shift and Swing of Budget Line.
The presentation aims to explain the meaning of ECONOMETRICS and why this subject is studied as a separate discipline.
The reference is based on the book "BASIC ECONOMETRICS" by Damodar N. Gujarati.
For further explanation, check out the youtube link:
https://youtu.be/S3SUDiVpUGU
Consumer preferences and the concept of utility by Dr.Nakul A. DeshmukhDr.Nakul Deshmukh
Consumer preferences are defined as the subjective (individual) tastes, as measured by utility, of various bundles of goods. They permit the consumer to rank these bundles of goods according to the levels of utility they give the consumer. Note that preferences are independent of income and prices.
Microeconomics: Concept of Indifference Curve and Budget Line. Definition of ...Rohan Byanjankar
Concept of Indifference Curve and Budget Line.
Derivation of Budget line. Calculation of slope of budget line and its intercepts. Calculus Proof of budget Line and Indifference Curve. Relationship of Budget Line and Indifference Curve. Contains some of the alternative questions.
Slope of Budget Line, intercepts of budget line along with figure.
Concept of Marginal Rate of Substitution. Causes of Shift and Swing of Budget Line.
The presentation aims to explain the meaning of ECONOMETRICS and why this subject is studied as a separate discipline.
The reference is based on the book "BASIC ECONOMETRICS" by Damodar N. Gujarati.
For further explanation, check out the youtube link:
https://youtu.be/S3SUDiVpUGU
Consumer preferences and the concept of utility by Dr.Nakul A. DeshmukhDr.Nakul Deshmukh
Consumer preferences are defined as the subjective (individual) tastes, as measured by utility, of various bundles of goods. They permit the consumer to rank these bundles of goods according to the levels of utility they give the consumer. Note that preferences are independent of income and prices.
Lecture slides on Decision Theory. The contents in large part come from the following excellent textbook.
Rubinstein, A. (2012). Lecture notes in microeconomic theory: the
economic agent, 2nd.
http://www.amazon.co.jp/dp/B0073X0J7Q/
In this paper, the L1 norm of continuous functions and corresponding continuous estimation of regression parameters are defined. The continuous L1 norm estimation problem of one and two parameters linear models in the continuous case is solved. We proceed to use the functional form and parameters of the probability distribution function of income to exactly determine the L1 norm approximation of the corresponding Lorenz curve of the statistical population under consideration.
These slides review basic math tools used in our economics course: the concept of multi-variate relations and their mathematical representation as functions, bivariate functions, linear functions, etc.
Even tho Pi network is not listed on any exchange yet.
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USDA Loans in California: A Comprehensive Overview.pptxmarketing367770
USDA Loans in California: A Comprehensive Overview
If you're dreaming of owning a home in California's rural or suburban areas, a USDA loan might be the perfect solution. The U.S. Department of Agriculture (USDA) offers these loans to help low-to-moderate-income individuals and families achieve homeownership.
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Guaranteed Loan Program: The USDA guarantees a portion of the loan, reducing risk for lenders and expanding borrowing options.
Eligibility Criteria:
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Income Limits: Applicants must meet income guidelines, which vary by region and household size.
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Application Process:
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USDA loans are an excellent option for those looking to buy a home in California's rural and suburban areas. With no down payment and flexible requirements, these loans make homeownership more attainable for many families. Explore your eligibility today and take the first step toward owning your dream home.
The secret way to sell pi coins effortlessly.DOT TECH
Well as we all know pi isn't launched yet. But you can still sell your pi coins effortlessly because some whales in China are interested in holding massive pi coins. And they are willing to pay good money for it. If you are interested in selling I will leave a contact for you. Just telegram this number below. I sold about 3000 pi coins to him and he paid me immediately.
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where can I find a legit pi merchant onlineDOT TECH
Yes. This is very easy what you need is a recommendation from someone who has successfully traded pi coins before with a merchant.
Who is a pi merchant?
A pi merchant is someone who buys pi network coins and resell them to Investors looking forward to hold thousands of pi coins before the open mainnet.
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@Pi_vendor_247
what is the best method to sell pi coins in 2024DOT TECH
The best way to sell your pi coins safely is trading with an exchange..but since pi is not launched in any exchange, and second option is through a VERIFIED pi merchant.
Who is a pi merchant?
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I will leave the telegram contact of my personal pi merchant to trade pi coins with.
@Pi_vendor_247
What price will pi network be listed on exchangesDOT TECH
The rate at which pi will be listed is practically unknown. But due to speculations surrounding it the predicted rate is tends to be from 30$ — 50$.
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I will leave the telegram contact of my personal pi vendor to trade with.
@Pi_vendor_247
Empowering the Unbanked: The Vital Role of NBFCs in Promoting Financial Inclu...Vighnesh Shashtri
In India, financial inclusion remains a critical challenge, with a significant portion of the population still unbanked. Non-Banking Financial Companies (NBFCs) have emerged as key players in bridging this gap by providing financial services to those often overlooked by traditional banking institutions. This article delves into how NBFCs are fostering financial inclusion and empowering the unbanked.
Financial Assets: Debit vs Equity Securities.pptxWrito-Finance
financial assets represent claim for future benefit or cash. Financial assets are formed by establishing contracts between participants. These financial assets are used for collection of huge amounts of money for business purposes.
Two major Types: Debt Securities and Equity Securities.
Debt Securities are Also known as fixed-income securities or instruments. The type of assets is formed by establishing contracts between investor and issuer of the asset.
• The first type of Debit securities is BONDS. Bonds are issued by corporations and government (both local and national government).
• The second important type of Debit security is NOTES. Apart from similarities associated with notes and bonds, notes have shorter term maturity.
• The 3rd important type of Debit security is TRESURY BILLS. These securities have short-term ranging from three months, six months, and one year. Issuer of such securities are governments.
• Above discussed debit securities are mostly issued by governments and corporations. CERTIFICATE OF DEPOSITS CDs are issued by Banks and Financial Institutions. Risk factor associated with CDs gets reduced when issued by reputable institutions or Banks.
Following are the risk attached with debt securities: Credit risk, interest rate risk and currency risk
There are no fixed maturity dates in such securities, and asset’s value is determined by company’s performance. There are two major types of equity securities: common stock and preferred stock.
Common Stock: These are simple equity securities and bear no complexities which the preferred stock bears. Holders of such securities or instrument have the voting rights when it comes to select the company’s board of director or the business decisions to be made.
Preferred Stock: Preferred stocks are sometime referred to as hybrid securities, because it contains elements of both debit security and equity security. Preferred stock confers ownership rights to security holder that is why it is equity instrument
<a href="https://www.writofinance.com/equity-securities-features-types-risk/" >Equity securities </a> as a whole is used for capital funding for companies. Companies have multiple expenses to cover. Potential growth of company is required in competitive market. So, these securities are used for capital generation, and then uses it for company’s growth.
Concluding remarks
Both are employed in business. Businesses are often established through debit securities, then what is the need for equity securities. Companies have to cover multiple expenses and expansion of business. They can also use equity instruments for repayment of debits. So, there are multiple uses for securities. As an investor, you need tools for analysis. Investment decisions are made by carefully analyzing the market. For better analysis of the stock market, investors often employ financial analysis of companies.
how to sell pi coins in South Korea profitably.DOT TECH
Yes. You can sell your pi network coins in South Korea or any other country, by finding a verified pi merchant
What is a verified pi merchant?
Since pi network is not launched yet on any exchange, the only way you can sell pi coins is by selling to a verified pi merchant, and this is because pi network is not launched yet on any exchange and no pre-sale or ico offerings Is done on pi.
Since there is no pre-sale, the only way exchanges can get pi is by buying from miners. So a pi merchant facilitates these transactions by acting as a bridge for both transactions.
How can i find a pi vendor/merchant?
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how to sell pi coins in all Africa Countries.DOT TECH
Yes. You can sell your pi network for other cryptocurrencies like Bitcoin, usdt , Ethereum and other currencies And this is done easily with the help from a pi merchant.
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Since pi is not launched yet in any exchange. The only way you can sell right now is through merchants.
A verified Pi merchant is someone who buys pi network coins from miners and resell them to investors looking forward to hold massive quantities of pi coins before mainnet launch in 2026.
I will leave the telegram contact of my personal pi merchant to trade with.
@Pi_vendor_247
how can i use my minded pi coins I need some funds.DOT TECH
If you are interested in selling your pi coins, i have a verified pi merchant, who buys pi coins and resell them to exchanges looking forward to hold till mainnet launch.
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2. 2
Objectives of the chapter
Study a way to represent consumer’s
preferences about bundles of goods
What are bundles of goods? =combinations of
goods. For instance:
X=slices of pizza
Y=glasses of juice
Bundles:
P: X=1, Y=1
Q: X=3, Y=0
R: Y=3, X=0
S: X=2, Y=1
3. 3
Objectives of the chapter
John’s preferences are such that:
P is preferred to both Q and R
S is preferred to P
This way of representing preferences would be
very messy if we have many bundles
In this chapter we study a simple way of
representing preferences over bundles of
goods
This is useful because in reality there are
many bundles of goods
4. 4
Axioms of rational choice
Before describing this simple method to
represent preferences over bundles, we will
study what requirements must the preferences
satisfy in order for the method to work
These requirements are the axioms of rational
choice
Without these requirements, it would be very
difficult to come up with a simple method to
represent preferences over many bundles of
goods
It is easy to read a tube map, but not so much to
read a tube-bus-and rail map !!!!
5. 5
Axioms of Rational Choice
Completeness
if A and B are any two bundles, an
individual can always specify exactly one of
these possibilities:
A is preferred to B
B is preferred to A
A and B are equally attractive
In other words, preferences must exist in
order to be able to describe them through a
simple method
6. 6
Axioms of Rational Choice
Transitivity
if A is preferred to B, and B is preferred to
C, then A is preferred to C
assumes that the individual’s choices are
internally consistent
If transitivity does not hold, we would need
a very complicated method to describe
preferences over many bundles of goods
7. 7
Axioms of Rational Choice
Continuity
if A is preferred to B, then bundles suitably
“close to” A must also be preferred to B
If this does not hold, we would need a very
complicated method to describe individual’s
preferences
8. 8
Utility
Given these assumptions, it is possible to
show that people are able to rank all
possible bundles from least desirable to
most
Economists call this ranking utility
if A is preferred to B, then the utility assigned
to A exceeds the utility assigned to B
U(A) > U(B)
9. 9
Utility
Game…
Someone state the preferences using
numbers from 1 to 10
Can someone use different numbers from 1
to 10 but state the same ordering?
Can someone use numbers 1 to 100 and
state the same preferences?
11. 11
Utility
Utility could be represented by a Table
Bundles Example Utility
P 1
Q 0
R 0
S 2
U(P)=1>U(Q)=0 because we said that P was preferred to Q
U(B)=U(C) because Q and R are equally preferred
12. 12
Utility
Notice that several tables of utility can represent the
same ranking Bundles Another
example
Example
Utility
P 1 1
Q 0 0
R 0 0
S 4 2
•We can think that the rankings are real. They are in anyone’s
mind. However, utility numbers are an economist’s invention
•The difference (2-1, 4-1…) in the utility numbers is
meaningless. The only important thing about the numbers is
that they can be used to represent rankings (orderings)
13. 13
Utility
Utility rankings are ordinal in nature
they record the relative desirability of commodity
bundles
Because utility measures are not unique, it
makes no sense to consider how much more
utility is gained from A than from B. This gain in
utility will depend on the scale which is
arbitrary
It is also impossible to compare utilities
between people. They might be using different
scales….
14. 14
Utility
If we have many bundles of goods, a Table is
not a convenient way to represent an ordering.
The table would have to be too long.
Economist prefer to use a mathematical
function to assign numbers to consumption
bundles
This is called a utility function
utility = U(X,Y)
Check that the previous example of the three columns
table is obtained with the following utility functions:
U=X*Y,
and U=(X*Y)2
15. 15
Utility
Clearly, for an economist it is the same to use
U=X*Y than to use U=(X*Y)2 because both represent
the same ranking (see the table), so both functions will
give us the same answer in terms of which bundles of
good are preferred to others
Any transformation that preserves the ordering
(multiply by a positive number, take it at a power of a
positive number, take “ln”) will give us the same
ordering and hence the same answer
We can use this property to simplify some mathematical
computations that we will see in the future
16. 16
Economic Goods
In the utility function, the x and y are
assumed to be “goods”
more is preferred to less
Quantity of x
Quantity of y
x*
y*
Preferred to x*, y*
?
?
Worse
than
x*, y*
17. 17
Indifference Curves
An indifference curve shows a set of
consumption bundles among which the
individual is indifferent
Quantity of x
Quantity of y
x1
y1
y2
x2
U1
Combinations (x1, y1) and (x2, y2)
provide the same level of utility
18. 18
Indifference Curve Map
Each point must have an indifference curve
through it
Quantity of x
Quantity of y
U1 < U2 < U3
U1
U2
U3
Increasing utility
19. 19
Transitivity
Can any two of an individual’s indifference
curves intersect?
Quantity of x
Quantity of y
U1
U2
A
B
C
The individual is indifferent between A and C.
The individual is indifferent between B and C.
Transitivity suggests that the individual
should be indifferent between A and B
But B is preferred to A
because B contains more
x and y than A
20. 20
Convexity
Economist “believe” that:
“Balanced bundles of goods are preferred to
extreme bundles”
This assumption is formally known as the
assumption of convexity of preferences
Using a graph, shows that if this assumption
holds, then the indifference curves cannot
be strictly concave, they must be strictly
convex
21. 21
Convexity
Formally, If the indifference curve is convex, then the combination
(x1 + x2)/2, (y1 + y2)/2 will be preferred to either (x1,y1) or (x2,y2)
Quantity of x
Quantity of y
U1
x2
y1
y2
x1
This means that “well-balanced” bundles are preferred
to bundles that are heavily weighted toward one
Commodity (“extreme bundles”).
The middle points are better than the
Extremes, so the middle is at a higher indifference
Curve.
(x1 + x2)/2
(y1 + y2)/2
22. 22
Marginal Rate of Substitution
Important concept !!
MRSYX is the number of units of good Y
that a consumer is willing to give up in
return for getting one more unit of X in
order to keep her utility unchanged
Let’s do a graph in the whiteboard !!!
MRSYX is the negative of the slope of the
indiference curve (where Y is in the
ordinates axis)
23. 23
Marginal Rate of Substitution
The negative of the slope of the
indifference curve at any point is called
the marginal rate of substitution (MRS)
Quantity of x
Quantity of y
x1
y1
y2
x2
U1
1
yx
U U
dy
MRS
dx
24. 24
Marginal Rate of Substitution
Notice that if indifference curves are strictly
convex, then the MRS is decreasing (as x
increases, the MRSyx decreases)
See it in a graph: As “x” increases, the amount
of “y” that the consumer is gives up to stay in
the same indifference curve (that is MRSyx)
decreases
If the assumption that “balanced bundles” are
preferred to “extreme bundles” (convexity of
preferences assumption” holds then the MRSyx
is decreasing!!
25. 25
Marginal Rate of Substitution
MRS changes as x and y change
and it is decreasing
Quantity of x
Quantity of y
x1
y1
y2
x2
U1
At (x1, y1), the indifference curve is steeper.
At this point, the person has a lot of y,
So, he would be willing to give up more y
to gain additional units of x
At (x2, y2), the indifference curve
is flatter. At this point, the person
does not have so much y,
so he would be willing to give up
less y to gain
additional units of x
26. 26
Utility and the MRS
Suppose an individual’s preferences for
hamburgers (y) and soft drinks (x) can
be represented by
y
x
10
utility
Solving for y, we get the indifference curve for level 10:
y = 100/x
• Taking derivatives, we get the MRS = -
dy/dx:
MRS = -dy/dx = 100/x2
27. 27
Utility and the MRS
MRSyx = -dy/dx = 100/x2
Note that as x rises, MRS falls
when x = 5, MRSyx = 4
when x = 20, MRSyx = 0.25
When x=20, then the individual does not
value much an additional unit of x. He is only
willing to give 0.25 units of y to get an
additional unit of x.
28. 28
Another way of computing the MRS
Suppose that an individual has a utility
function of the form
utility = U(x,y)
The total differential of U is
dy
y
U
dx
x
U
dU
Along any indifference curve, utility is constant (dU = 0)
dU/dy and dU/dx are the marginal utility of y and x
respectively
29. 29
Another way of computing the MRS
Therefore, we get:
U constant
yx
U
dy x
MRS
U
dx
y
MRS is the ratio of the marginal utility of x to the marginal
utility of y
Marginal utilities are generally positive (goods)
30. 30
Example of MRS
Suppose that the utility function is
y
x
utility
We can simplify the algebra by taking the logarithm of this
function (we have explained before that taking the logarithm
does not change the result because it preserves the ordering,
though it can make algebra easier)
U*(x,y) = ln[U(x,y)] = 0.5 ln x + 0.5 ln y
31. 31
Deriving the MRS
* 0.5
* 0.5
yx
U
y
x x
MRS
U x
y y
Thus,
Notice that the MRS is decreasing in x: The MRS
falls when x increases
32. 32
Examples of Utility Functions
Cobb-Douglas Utility
utility = U(x,y) = xy
where and are positive constants
The relative sizes of and indicate the relative
importance of the goods
The algebra can usually be simplified by taking
ln(). Let’s do it in the blackboard….
33. 33
Examples of Utility Functions
Perfect Substitutes
U(x,y) =U= x + y
Y= -(/ )x + (1/ )U , indifference curve for level U
Quantity of x
Quantity of y
U1
U2
U3
The indifference curves will be linear.
The MRS =(/ ) is constant along the
indifference curve.
34. 34
Examples of Utility Functions
Perfect Substitutes
U(x,y) =U= x + y
dU= dx + dy
Notice that the change in utility will be the
same if (dx= and dy= 0) or if (dx= 0 and
dy= ). So x and y are exchanged at a fixed
rate independently of how much x and y the
consumer is consumed
It is as if x and y were substitutes. That is
why we call them like that
35. 35
Examples of Utility Functions
Perfect Complements
utility = U(x,y) = min (x, y)
Quantity of x
Quantity of y
The indifference curves will be
L-shaped. It is called complements
because if we
Are in the kink then utility does not
increase by we increase the quantity
of only one good. The quantity of both
Goods must increase in order to increase
utility
U1
U2
U3
36. 36
Examples of Utility Functions
CES Utility (Constant elasticity of
substitution)
utility = U(x,y) = x/ + y/
when 0 and
utility = U(x,y) = ln x + ln y
when = 0
Perfect substitutes = 1
Cobb-Douglas = 0
Perfect complements = -
37. 37
Examples of Utility Functions
CES Utility (Constant elasticity of
substitution)
The elasticity of substitution () is equal to
1/(1 - )
Perfect substitutes =
Fixed proportions = 0