The document discusses the budget constraint and optimal consumer choice. It begins by explaining the budget constraint conceptually and mathematically, showing how a consumer's income and the prices of goods determine which bundles of goods are affordable. It then shows how consumers can determine their optimal bundle by finding the point where an indifference curve is tangent to the budget constraint. This ensures the marginal rate of substitution between goods equals the relative price ratio. Finally, it explains how changes in prices or income can be decomposed into substitution and income effects, with substitution effects occurring when relative prices change and income effects when real income changes.
Budget line is a graphical representation of all possible combinations of two goods which can be purchased with given income and prices, such that the cost of each of these combinations is equal to the money income of the consumer.
Presentation for Indifference curve analysis: Ordinal utility approach.
This presentation is made for the purpose of education & knowledge.
in this presentation we got to know about definition of indifference curve, assumption, indifference schedule, indifference curve, marginal rate of substitution, properties of indifference curve
Budget line is a graphical representation of all possible combinations of two goods which can be purchased with given income and prices, such that the cost of each of these combinations is equal to the money income of the consumer.
Presentation for Indifference curve analysis: Ordinal utility approach.
This presentation is made for the purpose of education & knowledge.
in this presentation we got to know about definition of indifference curve, assumption, indifference schedule, indifference curve, marginal rate of substitution, properties of indifference curve
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.
This is part of an introduction to indifference curve analysis. A budget line shows the combinations of two products that a consumer can afford to buy with a given income – using all of their available budget
The gradient of the budget line reflects the relative prices of the two products
Falcon stands out as a top-tier P2P Invoice Discounting platform in India, bridging esteemed blue-chip companies and eager investors. Our goal is to transform the investment landscape in India by establishing a comprehensive destination for borrowers and investors with diverse profiles and needs, all while minimizing risk. What sets Falcon apart is the elimination of intermediaries such as commercial banks and depository institutions, allowing investors to enjoy higher yields.
how to sell pi coins on Bitmart crypto exchangeDOT TECH
Yes. Pi network coins can be exchanged but not on bitmart exchange. Because pi network is still in the enclosed mainnet. The only way pioneers are able to trade pi coins is by reselling the pi coins to pi verified merchants.
A verified merchant is someone who buys pi network coins and resell it to exchanges looking forward to hold till mainnet launch.
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what is the future of Pi Network currency.DOT TECH
The future of the Pi cryptocurrency is uncertain, and its success will depend on several factors. Pi is a relatively new cryptocurrency that aims to be user-friendly and accessible to a wide audience. Here are a few key considerations for its future:
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1. Mainnet Launch: As of my last knowledge update in January 2022, Pi was still in the testnet phase. Its success will depend on a successful transition to a mainnet, where actual transactions can take place.
2. User Adoption: Pi's success will be closely tied to user adoption. The more users who join the network and actively participate, the stronger the ecosystem can become.
3. Utility and Use Cases: For a cryptocurrency to thrive, it must offer utility and practical use cases. The Pi team has talked about various applications, including peer-to-peer transactions, smart contracts, and more. The development and implementation of these features will be essential.
4. Regulatory Environment: The regulatory environment for cryptocurrencies is evolving globally. How Pi navigates and complies with regulations in various jurisdictions will significantly impact its future.
5. Technology Development: The Pi network must continue to develop and improve its technology, security, and scalability to compete with established cryptocurrencies.
6. Community Engagement: The Pi community plays a critical role in its future. Engaged users can help build trust and grow the network.
7. Monetization and Sustainability: The Pi team's monetization strategy, such as fees, partnerships, or other revenue sources, will affect its long-term sustainability.
It's essential to approach Pi or any new cryptocurrency with caution and conduct due diligence. Cryptocurrency investments involve risks, and potential rewards can be uncertain. The success and future of Pi will depend on the collective efforts of its team, community, and the broader cryptocurrency market dynamics. It's advisable to stay updated on Pi's development and follow any updates from the official Pi Network website or announcements from the team.
The European Unemployment Puzzle: implications from population agingGRAPE
We study the link between the evolving age structure of the working population and unemployment. We build a large new Keynesian OLG model with a realistic age structure, labor market frictions, sticky prices, and aggregate shocks. Once calibrated to the European economy, we quantify the extent to which demographic changes over the last three decades have contributed to the decline of the unemployment rate. Our findings yield important implications for the future evolution of unemployment given the anticipated further aging of the working population in Europe. We also quantify the implications for optimal monetary policy: lowering inflation volatility becomes less costly in terms of GDP and unemployment volatility, which hints that optimal monetary policy may be more hawkish in an aging society. Finally, our results also propose a partial reversal of the European-US unemployment puzzle due to the fact that the share of young workers is expected to remain robust in the US.
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Where can I sell my pi coins at a high rate.
Pi is not launched yet on any exchange. But one can easily sell his or her pi coins to investors who want to hold pi till mainnet launch.
This means crypto whales want to hold pi. And you can get a good rate for selling pi to them. I will leave the telegram contact of my personal pi vendor below.
A vendor is someone who buys from a miner and resell it to a holder or crypto whale.
Here is the telegram contact of my vendor:
@Pi_vendor_247
Turin Startup Ecosystem 2024 - Ricerca sulle Startup e il Sistema dell'Innov...Quotidiano Piemontese
Turin Startup Ecosystem 2024
Una ricerca de il Club degli Investitori, in collaborazione con ToTeM Torino Tech Map e con il supporto della ESCP Business School e di Growth Capital
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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.
What is a pi merchant ?
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 to sell pi coins effectively (from 50 - 100k pi)DOT TECH
Anywhere in the world, including Africa, America, and Europe, you can sell Pi Network Coins online and receive cash through online payment options.
Pi has not yet been launched on any exchange because we are currently using the confined Mainnet. The planned launch date for Pi is June 28, 2026.
Reselling to investors who want to hold until the mainnet launch in 2026 is currently the sole way to sell.
Consequently, right now. All you need to do is select the right pi network provider.
Who is a pi merchant?
An individual who buys coins from miners on the pi network and resells them to investors hoping to hang onto them until the mainnet is launched is known as a pi merchant.
debuts.
I'll provide you the Telegram username
@Pi_vendor_247
Exploring Abhay Bhutada’s Views After Poonawalla Fincorp’s Collaboration With...beulahfernandes8
The financial landscape in India has witnessed a significant development with the recent collaboration between Poonawalla Fincorp and IndusInd Bank.
The launch of the co-branded credit card, the IndusInd Bank Poonawalla Fincorp eLITE RuPay Platinum Credit Card, marks a major milestone for both entities.
This strategic move aims to redefine and elevate the banking experience for customers.
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.
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.
Because the core team has announced that pi network will not be doing any pre-sale. The only way exchanges like huobi, bitmart and hotbit can get pi is by buying from miners.
Now a merchant stands in between these exchanges and the miners. As a link to make transactions smooth. Because right now in the enclosed mainnet you can't sell pi coins your self. You need the help of a merchant,
i will leave the telegram contact of my personal pi merchant below. 👇 I and my friends has traded more than 3000pi coins with him successfully.
@Pi_vendor_247
The Evolution of Non-Banking Financial Companies (NBFCs) in India: Challenges...beulahfernandes8
Role in Financial System
NBFCs are critical in bridging the financial inclusion gap.
They provide specialized financial services that cater to segments often neglected by traditional banks.
Economic Impact
NBFCs contribute significantly to India's GDP.
They support sectors like micro, small, and medium enterprises (MSMEs), housing finance, and personal loans.
What website can I sell pi coins securely.DOT TECH
Currently there are no website or exchange that allow buying or selling of pi coins..
But you can still easily sell pi coins, by reselling it to exchanges/crypto whales interested in holding thousands of pi coins before the mainnet launch.
Who is a pi merchant?
A pi merchant is someone who buys pi coins from miners and resell to these crypto whales and holders of pi..
This is because pi network is not doing any pre-sale. The only way exchanges can get pi is by buying from miners and pi merchants stands in between the miners and the exchanges.
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Selling pi coins is really easy, but first you need to migrate to mainnet wallet before you can do that. I will leave the telegram contact of my personal pi merchant to trade with.
Tele-gram.
@Pi_vendor_247
2. The budget constraint
• The basic concept is really straightforward:
– The consumer has a limited income (I) to purchase
different goods
– Each type of good has a defined price (p) per unit
– We assume that the consumer does not save and
spends all his income
• This possibility will be examined later
3. The budget constraint
• The general budget constraint for n goods is:
• If we only look at 2 goods (Same simplification
as last week), it can be expressed as:
n
i i
i 1
I p x
1 1 2 2I p x p x
4. The budget constraint
• Imagine the following “student entertainment
budget”
– You have 50 €
– The price of a meal is 10 €
– The price of a cinema ticket is 5 €
• Your budget constraint is:
50 5 tickets 10 meals
1 1 2 2I p x p x
8. The budget constraint
max
cin.x Cinema
Meals
max
mealx
1 1 2 2I p x p x
2
1 2
1 1
pI
x x
p p
The budget constraint is
Dividing by p1 and rearranging:
cin.
meal cin.
meal meal
pI
x x
p p
slope
intercept
9. The budget constraint
Any bundle within the budget
constraint is affordable , but
not all the budget is spent
(C,D).
Any bundle beyond the
budget constraint cannot be
afforded (H,G).
C
H
D
G
Any bundle on the budget
constraint is affordable and
ensures all the budget is
spent (E,F).
max
cin.x Cinema
Meals
max
mealx
F
E
11. The budget constraint
• The position of the budget constraint depends
on
• The income of the agent (I)
• The price of the two goods (p1 and p2)
2
1 2
1 1
pI
x x
p p
16. Lets think about these things
• Budget constraint equation
• Slope of budget line – Px / Py
• budget line is of 45 ° if???
• Shifts in line can be caused by???
• Shows purchasing power of indivisuals
• Budget line and what it represents
17. Questions
A budget constraint
a.shows the prices that a consumer chooses to pay
for products he consumes.
b.shows the purchases made by consumers.
c.shows the consumption bundles that a consumer
can afford.
d.represents the consumption bundles that give a
consumer equal satisfaction.
18. A consumer that doesn't spend all of her
income
a.would be at a point outside of her budget
constraint.
b.would be at a point inside her budget constraint.
c.must not be consuming positive quantities of all
goods.
d.must be consuming at a point where her budget
constraint touches one of the axes.
19. The following diagram shows a budget
constraint for a particular consumer.
If the price of x is $10, what is the price of y?
a.$15
b.$25
c.$35
d.$70
20. Which of the
graphs in
the figure
reflects a
decrease in
the price of
good X only?
a.graph (a)
b.graph (b)
c. graph (c)
d.graph (d)
21. Which of the
graphs in
the figure
reflects an
increase in
the price
of good Y
only?
a. graph (a)
b.graph (b)
c. graph (c)
d.graph (d)
22. Which of the
graphs in
the figure
could
reflect a
decrease in
the prices
of both
goods?
a. graph (a)
b.graph (b)
c. graph (c)
d.graph (d)
23. • A halving of the prices good A and good B has
the same effect on the budget line as doubling
the income. Is this sentence true or false?
Show it by using the equation of the budget
line.
• What about the opposite? Doubling the prices
good A and good B has the same effect on the
budget line as halving of the income.
24. Suppose the price of pizza is $10, the price of cola is $1, and the
consumer’s income is $50. In addition, suppose the consumer’s
budget constraint measures pizza on the horizontal axis and cola
on the vertical axis.
1) If the price of cola doubles to $2, then the
a. budget constraint intersects the vertical axis at 25 colas.
b. slope of the budget constraint rises to -2.
c. budget constraint intersects the vertical axis at 100 colas.
d. budget constraint shifts inward in a parallel fashion.
2) If the consumer's income rises to $60, then the budget line for
pizza and cola would
a. now intersect the horizontal axis at 6 pizzas and the vertical axis at
60 colas.
b. not change.
c. now intersect the horizontal axis at 4 pizzas and the vertical axis at
16 colas.
d. rotate outward along the cola axis.
25. Answer the following questions based on the table. A consumer is
able to consume the following bundles of rice and beans when the
price of rice is $2 and the price of beans is $3.
RICE BEANS
12 0
6 4
0 8
a. How much is this consumer's income?
b. Draw a budget constraint given this information. Label it B.
c. Construct a new budget constraint showing the change if the price
of rice falls $1. Label this C.
d. Given the original prices for rice ($2) and beans ($3), construct a
new budget constraint if this consumer's income increased to $48.
Label this D.
26. Draw a budget constraint that is consistent with the
following prices and income.
Income = 200
PY = 50
PX = 25
a. Demonstrate how your original budget constraint
would change if income increases to 500.
b. Demonstrate how your original budget constraint
would change if PY decreases to 20.
c. Demonstrate how your original budget constraint
would change if PX increases to 40.
27. Evaluate the following statement, "Warren
Buffet is the second richest person in the
world. He doesn't face any constraint on his
ability to purchase commodities he wants."
28. The budget constraint and choice
The budget constraint
The optimal consumer choice
Income and substitution effects
29. The optimal consumer choice
• This requires bringing in the two elements of the
theory
– The indifference curves, which show how agents rank the
different bundles
– The budget constraint, which shows which bundles are
affordable, and which are not
• Both of these are defined over the “consumption
space”, so they can be superposed easily
30. The optimal consumer choice
max
cin.x Cinema
Meals
max
mealx
Which is the best bundle ?
F
Optimal bundle
C
D
E
B
A
31. The optimal consumer choice
max
cin.x Cinema
Meals
max
mealx
The budget constraint is
tangent to the
indifference curve at F
F
Definition of the
MRS at F !!!
32. The optimal consumer choice
• The optimal bundle is on the tangency between the
budget constraint and the indifference curve.
• This means that for the optimal bundle the slope of
the IC is equal to the slope of the budget constraint
MRS = ratio of prices
33. The optimal consumer choice
• This condition gives a central result of consumer
theory:
• The optimal bundle is the one which equalises the
marginal utility per € spent
– If you were to receive an extra € of income, your
marginal utility will be the same regardless of where
you spend it
2 2
1
2
1 21
1mU p
MRS
mU p
mU mU
p p
34. The optimal consumer choice
max
cin.x Cinema
Meals
max
mealx
Example of optimal choice with concave preferences
F
G
The optimal solution is a
“corner solution”
35. The budget constraint and choice
The budget constraint
The optimal consumer choice
Income and substitution effects
36. Income and substitution effects
• Consumer theory is used to understand how choice
is affected by changes in the environment
• These can be complex, and the theory helps to
isolate these different effects
• The separation of income and substitution effects is a
good illustration of the concept of “ceteris paribus”
– Each variable is isolated and analysed separately from the
others
37. Income and substitution effects
• 1: A change in real income
– A previously affordable bundle (A) is no
longer affordable
• 2: A relative price change
– The slope of the budget constraint
changes, and meals become relatively
cheaper
max
cin.x Cinema
Meals
max
mealx
An increase in the price of cinema tickets has 2 effects :
A
38. Income and substitution effects
• Fall in the consumption of cinema
• Increase in the consumption of meals
• Question: How can we separate the
effect of the change in real income from
the effect of the change in relative
prices ?
max
cin.x Cinema
Meals
max
mealx
A
B
Effect of an increase in the price of cinema tickets on
consumer choice
39. Income and substitution effects
• Parallel to the new budget constraint
• Tangent to the original IC
• There is only a single curve that satisfies
these two requirements
• This gives an imaginary optimal bundle
(Im)
max
cin.x Cinema
Meals
max
mealx
A
B
In order to separate the 2 effects, we add an imaginary
budget constraint
Im
40. Income and substitution effects
• From A to Im, real income is held
constant
– We are still on the same indifference
curve, so utility is the same
• The change of bundle is due entirely to
the change in relative price
• This is the substitution effect
max
cin.x Cinema
Meals
max
mealx
A
B
The substitution effect
Im
41. Income and substitution effects
• From Im, to B, relative prices are held
constant
– The two budget constraints are parallel,
so the slope is the same
• The change of bundle is due entirely to
the fall in income.
• This is the income effect
max
cin.x Cinema
Meals
max
mealx
A
B
The income effect
Im
42. Income and substitution effects
• By combining the two, one gets the
overall effect
• One can see that the interaction is
different for the two goods
– The 2 effects can work against each
other, or add up
– Depending on the relative strength of
the effects, this can lead to increases or
falls in consumption
max
cin.x Cinema
Meals
max
mealx
A
B
The overall effect
Im
43. Income and substitution effects
• This type of approach is fundamental to micro-economic
analysis
– Any price change is always accompanied by income and
substitution effects.
• So this helps understand the effects of taxation, shocks to
prices, taste changes, etc.
– Look at the complex effects of oil price increases on
consumption
• Price change ⇒ Complex change in bundle
– Clearly, this will also help understand how demand curves
are built (next week)
Editor's Notes
C
B
Initial budget line: M = PxX + PyY
New budget line:
· Halving of the prices: M = PxX + PyY
2 (Multiplying by 2)
2M = PxX + PyY
· Doubling the income: 2M = PxX + PyY
Result: Halving of the prices and doubling the income result in the same budget
line. Sentence is true.
Initial budget line: M = PxX + PyY
New budget line:
· Doubling the prices: M = 2(PxX + PyY) (Dividing by 2)
M
2 = PxX + PyY
· Halving of the income:
M
2 = PxX + PyY
Result: Doubling the prices and halving of the income result in the same budget
line. Sentence is true, too.