ECON 3110 : DAYS ONE & TWO:
HIS TEACHING PHILOSPHY:
1. Human Capital: term used to describe education.
a. “Getting a degree will allow me to earn more money”
b. He sees this as a class that will give you the ability to reason. 2. Intrinsic Value: another term used to describe education
a. Education is a means to an end of higher income
b. Improve your understanding of the work around you – more
3. Tools for citizenship:
a. Knowing of, understanding of, and caring about issues that are most prevalent.
b. Creating a public good – aka vote.
CHAPTER TWO : MONEY
There are three functions of money:
1. Medium of exchange
a. Say you produce one commodity, however you wish to consume another. You can either:
i. Barter / trade
ii. Use a medium of exchange / money
b. Without money, we have what is called a double coincidence, where the person who has the good that you want, may not want the good that you have. (Airplane example).
i. This means you would have to find someone who has the good that the other person wants, who also wants to good that you
ii. Transaction costs: the cost of trading one good for another. 1. if trading is expensive, there is less specialization; vice
c. Benefits of using a medium of exchange is that it reduces the cost of trading, which in turn encourages more people to specialize in
We also discuss several other topics like How do you know if a molecule is nonpolar?
producing what they’re good at.
i. Solves the double coincidence
ii. Increased productivity, efficiency, and output.
d. CLDC: Complete Lack of Double Coincidence:
i. Say person 1 can only make good 1, and will only consume good 2, which gives them 3 utils. It costs person 1 one util to make
good 1, and 2 utils to make good 2. Therefore it is cheaper for
them to specialize in their good and trade for the good that they want.
2. Unit of Account
a. Simplifies confusion over what something is worth – is the medium of exchange as one generally agreed upon standard unit.
b. Overlapping Generations Model of Money: this is completely made up
i. There is no money, only a perishable good (it goes bad).
ii. Solution: get something worthless and make the older people use it to trade for the things that they want (Fiat Money).
1. Social contrivance / benign Ponsy Scheme.
2. Why would the old people want it? They can use it to
trade with the younger people by telling them that the
next generation after them will also end up wanting it as
c. Rate of Return on Holding Money: for each unit that I save today it will be more or less units tomorrow. Don't forget about the age old question of Where did the idea of where the world first started come from?
i. One unit -> 1.1 units has a Gross return of 1.1 and a net return of 0.1.
ii. Gross Real Rate of Return: Goods not money.
iii. There will be positive net return if prices fall, and there will be negative net return if prices rise. We also discuss several other topics like What is telencephalon and diencephalon?
How to get a market to clear:
1. N(t) = the number of young people at time t
2. N(t+1) = the next time interval
3. N(t+1) = N(t)(1+n) constant rate of growth n = growth. : 1+n 4. M = our fixed supply of money.
a. Say each young person wants to save S* units of goods.
b. N(t) x S* = M ; Pt / Pt+1
c. This means you will earn +1.
d. This is our social security! The young people are taxed and then that money is redistributed to the old.
i. The catch is that there has to be a constant amount of growth to be able to have the supply constantly increasing.
5. There is no technology today that transforms goods today into viable goods tomorrow.
QUESTION: why hold fiat money ( something of no value?)
∙ We accept it because there is a convention that gives it value ; we think someone else will want it later on after us.
QUESTION: why do we have Canadian coins in circulation in the US? We will know they will be accepted somewhere else if we give them to them. Definitive Money vs Non-Definitive Money
1. Definitive Money – cannot be converted into anything more basic a. Gold standard
b. We don’t need a lot of money because we have credit.
2. Non-Definitive Money – promise to pay definitive money that itself is a medium of exchange. If you want to learn more check out What is instinct theory?
a. Exchangeable for goods and services
b. Checks -> clearing system
FUNCTIONS OF MONEY : STORE OF VALUE
A. Money has advantages and disadvantages: We also discuss several other topics like How price discrimination can restore efficiency?
a. Has no interest / nominal rate of return – disadvantage
b. Liquidity and able to be used today right now – advantage
B. How should we hold our wealth?
a. Opportunity cost of nominal return of other assets.
b. Interest rates are the cost of liquidity. We also discuss several other topics like How long ago did eukaryotic cells evolve?
i. An asset that may be more liquid, may not have the highest rate of return.
WHAT DO WE MEAN BY A FINANCIAL SYSTEM?
A. Where capital / money flows from savers to borrowers.
a. A good financial system does this very efficiently.
b. Makes us expand the capital, which in turn helps us expand the economy as well.
DIRECT VS INDIRECT FINANCE
B. Direct: we match the saver directly to the borrower.
C. Indirect: savers place their assets with a financial intermediary such as banker who then loans the money to borrowers.
DESIRABLE PROPERTIES OF THE FINANCIAL
1. Risk of the saver is being kept at a minimum.
2. Maximum liquidity
a. Can trade off risk and liquidity for return.
3. Maximum information about credit worthiness.
a. Avoid loans to those unlikely to pay you back
b. This is why we have credit check systems to be able to avoid these situations.
A. Risk Aversion : a person is said to be risk averse if he or she prefers certainty of X, over a gamble of an expected value, equal to X.
B. How to economists explain risk aversion?
a. Utility of consumption : happiness from consumption
b. Diminishing marginal utility: the greater the consumption level of some good, the smaller the utility or happiness added by each unit.
i. Doesn’t entail that it becomes negatively, it is just increasingly more slowly.
ii. We can say the same for income.
C. The greater the income, the smaller the amount of utility added per dollar added.
a. The importance / value / excitement of getting more money goes down.
ECON 3110 – NOTES CONTINUED – Continuation of Risk Aversion Marginal Utility = The change in utility divided by the change in income
A. Certainty equivalent of a gamble – the amount of money that makes someone indifferent between the gamble or the sure option.
a. The amount of money received with certainty that gives someone the same amount of utility as the gamble does.
i. Makes you just as happy.
B. Risk Premium - the difference between the expected monetary value of the gamble and the certainty of the other option.
C. If you have two options:
c. How do we write the expected utility of this gamble?
i. (1/2 * Square root of the number) so ½(sq rt of 50)
ii. And then ½ ( sq rt of 150)
iii. ADD THEM TOGETHER AND WE GET : 9.659
d. How do we find the certainty equivalent?
i. We square the gamble
ii. 9.659^2 = $93.29 (this will be written as units in dollars)
D. The gamble’s expected value is 100, however the certainty value is only $93.29
E. How do we calculate the risk premium?
a. 100 – 93.29 = $6.71
b. Our risk premium is $6.71
F. What we can determine from this is that the person will be indifferent at the $93.29 point, and then anything below that will not take the risk, and anything about that, they will take the risk.
a. Risk averse people want to be compensated with a higher rate of return in order to be rewarded for taking the risk.
G. Using the insurance example:
a. The insurance people is going to take in Premiums (p) from n amount of people.
b. NP – ½ n*50 50 is standing in for $50,000
c. What premium would give them zero profits? Just set the equation = 0 d. P = 25 this is known as the actuarily fair premium.
i. If we charge a premium equal to the expected loss, then at least the loss will be covered, but we do have a bunch of other costs that will need covered.
ii. This is why we have higher and lower premiums depending on the company.
iii. We have an expected income of $75
iv. So then we have $75 – P at least.
A. Say you have the opportunity for a chance of 50% of $300 or 50% $0. Would someone pay $100 to take this bet?
The expected utility is ½(300)+1/2(0) = 150
∙ We take half of each possibility and add them together
Expected Utility (EU) = ½(sqrt 300) = 8.66
∙ We take ½ of the square root of the highest
The certainty equivalent (CE) is 8.66^2 = 75
∙ We take the certainty equivalent and square it.
A risk averse person would not take this gamble because they would have to give up $100, while only getting 75 utils in return.
B. Let’s see if we could split the risks and the costs among two people? Two people going in halves.
When they go in they each give up $50, and they keep their other $50. SO, they’ll either have $200 (50+150), or they’ll be left with the $50 that they didn’t invest in the gamble.
So now we have 50% $200 and 50% $50
SO we have an expected utility is ½(sqrt 200) + ½(sqrt 40) = 10.60 (improvement)
Certainty equivalent = 10.60^2 = 112.36 (improvement as well) C. Let’s see the results of splitting the risk between 100 people They’re each only giving up $1 of their $100 so they keep $99.
Expected Utility = ½(sqrt102) + ½(sqrt 99) = 10.02469
Certainty equivalent = 10.02469^2 = 100.49
D. If we end up having enough investors, then they will be eventually heading towards begin risk averse, which is kind of against the point of investing because you then don’t really get any return on your investment. a. No reward for the risk.
When we thinking about financial intermediation, we want to think about risk pooling.
A. We have a bunch of savers who have $100 each in savings, as well as a bunch of firms who want to use money to invest.
B. The business says that they will give the savers $13 in interest for loaning them the $100 to start off. There is a 50% chance of failure, and in that case, the firms will pay back the savers $7 in interest.
C. So now we have a 50 percent chance of getting 113 and a 50 percent chance of 104:
a. Expected return: ½(13) +1/2(7) = 10
b. So we have a deviation of 3
c. Variance: ½(13-10)^2 + ½(7-10)^2 = 9
d. This gives us a riskiness of 9 for going in on this investment
D. The utility of the certain amount of income is quadratic:
b. This is going to look like an upside down parabola, however we are going to only be concerned with the increasing part because another dollar will never actually make you less happy.
E. The idea of risk pooling is: there are as many firms as there are savers, so each of us makes a loan to one of these companies, or we each loan different amounts to different amounts of companies to diversify their portfolio.
a. For our purposes we are going to all come together and pool our savings before we disperse our money/savings to the firms who need it.
F. So we are going to take two people and pool their money, and have them agree to split the returns from each company:
a. Loan 1 – will either pay 13 or 7 dollars
b. Loan 2 – will either pay 13 or 7 dollars
c. So when we put trees together: the first outcome is 26 if they both do well.
i. 20 in the middle two if one does well and another doesn’t.
ii. 14 if both of the companies don’t do well.
d. We can then compare this to the amount of return they would get if they simply invested on their own.
i. Together : 13 at 25% chance, 10 at 25% chance ,10 at 25%
chance ,7 at 25% chance.
1. Expected return: ¼(14)+1/4(10)+1/4(10)+ 1/4 (7) = 10
2. This isn’t different from if you would invest on your own,
however the variance is going to be smaller.
3. Variance: ¼(13-10)^2 + ¼(10-10)^2 + ¼(10-10)^2 +
¼(7-10)^2 = 4.5
a. We have cut the risk in half as opposed to investing
on your own.
ii. Individual: expected return of 10.
iii. We have a variance of 9 her instead of 4.5
e. Probability: we simply multiply their chances of happening (1/2 or 50%) by each other’s steps to get to the end.
G. The law of large numbers – consider n independent random variables, x1, x2….xn : all with identical mean E, and same Variance V.
a. X1=return on loan to company 1 and so on through the x
b. The composite composed random variable x_ = the sum of all the individual random variables / n .
c. This will have expected return E, and variance equal to V/n (calculating the loans per saver)
d. X_ will be calculating the loan per saver.
Econ September 19th:
Coupon bond with a 3yr life and a coupon rate of 5% and a face value of $1000
1. Coupon payment = 0.05*1000 = $50
a. I=coupon rate
b. P= f1/1+i + f2/(1+i)2 + f3/(1+i)3
c. F1= 50
d. F2= 50
e. F3 = 1050
2. If I is equal to the coupon rate, then the bond will sell at par. 3. The bigger the “I” the smaller the price.
a. If I is greater than the coupon rate, then that is going to lower the price, making it lower than face value.
i. The bond will sell at a discount.
b. If I is less than the coupon rate, then the price is going to go up, making it higher than the face value.
i. The bond will sell at a premium.
CP = coupon payment
Perpetuity: p= CP/1+I + CP/ (1+i)2 + CP/(1+i)3 ………. CP/(1+i)n
Fixed Payment Loan
Z= amount of the loan
P = z/(1+i) + z/(1+i)2 + z(1+i)2
Multiple both sides by (1+i)
P(1+i) = z + z/(1+i)+ z/(1+i)n-1
(1+i)(p) – P = iP = Z – z/(1+i)n
N to infinity goes to z/i
P = Z/i
P = 50/0.05 = 1000
I= 50/1000 = 0.05
New problem as $120 is the annual payment:
P = 120/ (1+i) + 120/ (1+i)2 + ….120/(1+i)n
P= 120/I [1- 1/(1+i)10]
P = 120/0.04 [ 1 – (1/1.04)10]
P = 973
The price of a stock at time T is : Pt
The dividends received is : Dt
Pt = Dt+1 / (1+i) + Dt+2/ (1+i)2 ……. Dt+n/ (1+i)n
Pt = Pt+1 + Dt+1 / (1+i) : a basic no arbitrage idea, earning the same as those in the same class of assets.
Pt+1 = Pt+2 + Dt+2 / 1+i
The two above combined = Pt =
Classical theory – the price of an asset is the present value as expected income for the asset (this is also known as the fundamental value of an asset)
No arbitrage: Pt = (Pt+1 + Dt+1) / (1+i)
Pt+1 = (Pt+2 + Dt+2) / (1+i)
Imagine the following stock where the expected dividend is constant: Dividend = $1 per year.
We are looking to get the fundamental value of the stock: the income is the dividends:
1/(1+i)) + 1/(1+i)2 + 1/(1+i)3……………………….= 1/i
Fundamental value will get down to 1/0.1 = $10 (satisfies the no arbitrage condition)
The price of a stock today is $12, then increases to 12.20, 12.42, 12.66, 12.42 12 = (12.20 +1) / 1.1
“Weak” Efficiency of asset markets – an asset market is weakly efficient if it is impossible, except by chance, to earn a rate of return other than “i” on any asset, or collection of assets.
A. You can’t beat the market – grounded in the no arbitrage idea.
“Strong” Efficiency of asset markets – an asset market is strongly efficient if , asset prices equal fundamental values.
If a market is strong, it implies weak efficiency
If a market is weak, it does not imply strong efficiency.
All grasshoppers are green, however not all green things are grasshoppers.
September 26th – Calculating the price of an asset.
Two assets: the rate of return for each is 10%
Asset A: is a one year discount bond with a face value of $110
∙ Price of asset A = 110/1.1 = 100
Asset B: is ten year discount bond with a face value of $259.37
∙ The price of asset B = 259.37/(1.1)10 = 100
SO what if we raise the rate of return to 11%
Asset A: 110/1.11 = 99
Asset B: 259.37 / 1.1110 = 91
Pi or the rate of inflation = Pt+1 – Pt / Pt
= 2.04-2.00 / 2.00 = 0.02 = 2% inflation
The Fisher effect – changes in expected inflation lead to point for point changes in the nominal rate in the same direction