Unit 9 Flashcards
(21 cards)
What is wealth and income?
Wealth is the value of assets owned. Assets include a house, car, intellectual property, shares etc. Debt is negative wealth as it is something you owe.
Wealth can generate income but can also lose value over time (depreciate)
Income (disposable) is the amount of profit, interest, rent, wages (from FOP) and other earnings received, net of taxes.
It is the maximum amount you could consume per period leaving your wealth unchanged.
Income either adds to wealth (savings) or is used for consumption.
Income is a flow (measured over time), wealth is a stock.
How does consumption, depreciation and saving affect wealth?
When an individual earns income, they can either choose to save or consume that income.
If income>consumption, the household has saved. Saving increases wealth.
Households can save by depositing money in banks or buying assets like shares or bonds.
Depreciation is the reduction in value of a stock of wealth over time.
To take into account depreciation, it must be subtracted from gross income.
Hence income is net of depreciation
Outline the intertemporal choice model
This is a constrained choice model representing decision making concerning borrowing, lending and investing as ways of moving purchasing power forward or backward in time.
There are two goods: consumption now and future consumption.
Giving up some goods now will allow us to have more goods later. The opportunity cost of having more goods now is having fewer goods later.
There are two actors:
1. A: needs to borrow money. They can rely on their family now and in the future to provide bare necessities but they want to consume more now.
2. B: has wealth in the present but does not anticipate receiving future income.
Explain the feasible set of A in the intertemporal choice model
The feasible set applies to person A.
A has no money now but in the next period they will have $100 as they are paid in the end of the year.
We use a diagram with consumption later on the y axis and consumption now on the x axis.
- If they were to spend $0 now, they could spent $100 in the future. This represents the y intercept (their endowment). If they want to consume something now, they must take a loan.
- assuming a 10% interest rate, A could borrow a maximum of $91 to consume now and promise to pay the lender $100 in the future. This represents the x intercept.
Joining these two intercepts together via a straight line gives A’s feasible set. All points on and within this line represent feasible set of combinations of borrowing and repayment, and hence consumption now and later.
An increase in the interest rate makes the feasible set steeper (same y intercept but lower x intercept)
What does the interest rate represent in the intertemporal choice model?
Assuming a 10% interest rate, A could borrow 91$ now and promise to repay $100 that they will have later.
This total repayment of $100 includes the principal (how much they borrowed, $91) and the interest charge ($9) at the rate r .
Repayment = principal + interest = 91+91r = 91(1+r )
Assuming ‘later’ means 1 year from now we can say:
interest rate = repayment/principal -1 (100/91-1=0.1=10%)
The interest rate can be thought of as the price of bringing some spending power forward in time.
By borrowing, A can consume now rather than only later, but the more they consume now, the less they consume later.
At a 10% interest rate, the opportunity cost of spending $1 now is that A spends 1+r = $1.10 less in the future
1+r is therefore the marginal rate of transformation n of goods from the future to the present because to have one unit of good now you must give up 1+r goods in the future
What is consumption smoothing, why do people want to smooth consumption and how does it relate to the intertemporal choice model?
Actions taken by a household to sustain a constant level of consumption.
Consumption smoothing means preferring to consume some now and some later rather than everything now or everything later.
Diminishing marginal utility explains the incentive for consumption smoothing. The value of the additional unit of consumption declines as more of a good is consumed.
Indifference curves join together combinations of equal utility.
Consumption smoothing means bringing forward consumption from the future to the present falls as we move along an indifference curve.
The slope of the indifference curve is the MRS, so MRS declines from left to right because when future consumption is high, an additional unit of present consumption brings more utility than an additional unit of future consumption so the MRS is high and indifference curve is steep, but the curve gets flatter as present consumption increases.
The indifference curve is bowed/convex to the origin
What is situational impatience?
Impatience is the preference for consuming something sooner rather than later.
Situational impatience is when the person has little now and will have more later, so they prefer to smooth their consumption between now and later rather than consuming nothing now and all later.
The marginal utility of a dollar now is greater than the marginal utility of a dollar later so we are willing to give up more than a dollar in the future to get a dollar now.
Because A can consume nothing now and $100 in the future, the marginal return to consuming now is greater than in the future, so they will have a high MRS and steep indifference curve.
As you move rightwards, A is able to consume more now and less in the future, so the marginal return of consumption now is lower than in the future, so MRS is lower and the IC curve is shallower.
What is intrinsic impatience?
If A is able to consume the same amount in both periods and is given the choice to consume more now and less later, they are intrinsically impatient if they choose to consume more now.
Two reasons for intrinsic impatience are:
1. Myopia; people experience the present satisfaction of a desire more strongly than they imagine the same satisfaction at a future date.
2. Prudence; people know the opportunity to consume the good in the future may not be available so choosing present consumption is a good idea.
Using indifference curves we can compare people’s intrinsic impatience.
Two people have an initial endowment of $50 now and $50 later.
To stay on the same indifference curve (have the same utility), person A requires $12 later to compensate for losing $10 now, whilst person B requires $20 later to compensate losing $10 now.
Person B is intrinsically more impatient than person A.
What is the reservation indifference curve in the intertemporal choice model?
Person A’s reservation indifference curve is made up of all the combinations of present and future consumption at which they would be just as well off as in their reservation position - their endowment of consuming nothing now and $100 later. This is the closest indifference curve to the origin.
The next highest indifference curve assumes they already have $100 now.
At this point , their indifference curve is very flat, and so their desire to smooth consumption means they would like to have more consumption in the future and less now.
They would be willing to give up a dollar now even if they got less than a dollar in return later.
As such, smoothing can happen in either direction, moving consumption from the future to present or present to future.
How can someone’s patience be measured?
The discount rate, rho, (how much someone values an additional unit of consumption now relative to later) measures impatience.
It is the absolute slope of the indifference curve minus 1 (MRS-1)
What combination is chosen in the intertemporal choice model?
Like in other constrained choice models, in this model, A wishes to get to the highest possible indifference curve but is limited by the feasible frontier.
The highest feasible indifference curve will be the one that is tangent to the feasible frontier. At this point, MRS=MRT because the slope of the indifference curve equals the slope of the feasible frontier.
MRS=1+rho
MRT=1+r
So at MRS=MRT, 1+rho=1+r so rho=r
Discount rate = interest rate
When MRS>MRT, the discount rate>interest rate, so the benefits of bringing consumption forward in time outweigh the costs, so A would like to bring consumption forward in time and chooses to borrow more.
When MRT>MRS, the interest rate>discount rate so A would like to push consumption backward in time.
How does a higher interest rate affect the optimal choice in the intertemporal choice model?
When the interest rate rises the slope of the feasible frontier increases, with the x intercept decreasing and y intercept staying the same.
A still chooses the highest feasible indifference curve which is tangent to the feasible frontier.
At a higher interest rate, the price of bringing consumption forward has increased, so:
- A is less well off than with a lower interest rate as they are on a lower indifference curve
- A will borrow less and consume less now
A’s future consumption may increase, decrease or stay the same following a higher interest rate.
The income effect means that at the higher interest rate, A is less well off and has a smaller feasible set which would reduce her future consumption.
The substitution effect means that at the higher interest rate it is costlier to bring consumption forward, which would increase her future consumption.
How do we model person B’s situation in the intertemporal choice model?
Person B’s endowment is that they have $100 of consumption now and none in the future.
B has the same preferences between consumption now and later as A and the same degree of intrinsic impatient.
But they have different situational impatience, whilst A wanted to bring consumption forward to the presenter, B wants to push consumption backward to the future.
B can do this by saving his money in a drawer, we assume no inflation so the value remains constant.
B’s reservation indifference curve starts on the x axis at their endowment of $100 now and $0 later.
For every dollar B saves, they will have a dollar to spend later so there is a 1-to-1 trade off between consumption now and later, and MRT=1.
Their feasible set is from (0,100) to (100,0).
B chooses the highest feasible indifference curve which is tangent to the feasible frontier, MRS=MRT.
What is the effect of an interest rate on saving for person B in the intertemporal choice model?
If B could lend their wealth to someone trustworthy, they would be assured a repayment of (1+r) for every dollar lent. If they saved all $100, they could consume 100(1+r) later, so their feasible frontier becomes steeper with the y intercept increasing and x axis remaining the same, so the feasible set expands.
The MRT has increased as the frontier has become steeper. MRT=1+r
B again chooses the brightest feasible indifference curve which is tangent to the feasible frontier, so MRS=MRT.
At this higher interest rate, the feasible set has expanded so B has reached a higher indifference curve such that their utility has increased and they are better off.
B’s consumption later increases, but their consumption now may increase, decrease or stay the same depending on their indifference curves and the income and substitution effects.
How can we model investment in the intertemporal choice model?
Suppose B owns land and has $100 worth of grain rather than cash. They could either consume or invest the grain and consume later. If they invest, they expand their feasible set as they would earn a return on investment, allowing them to consume more later.
Suppose if they invested all $100 of grain, they could harvest $150 of grain later, so the profit rate is 50%.
This would take B to point (0,150) on the y axis, and joining this to their endowment of (100,0) on the x axis gives a feasible frontier with a slope of -1.5 (=MRT) MRT=1+rate of return on investment.
B chooses the highest feasible indifference curve which is tangent to the feasible frontier, so MRS=MRT.
What is the effect on person B if they could acquire a loan for their investment project in the intertemporal choice model?
If B could get a loan, they could reach a higher indifference curve. They would invest all $100 and harvest $150 next year, but also borrow now in order to consume more both now and in the future.
Assuming a 10% interest rate, B could consume up to 150/1+0.1=136 now.
This expands their feasible set by making their feasible frontier shallower such that the x intercept increases while y intercept stays the same.
Again, B chooses the highest feasible indifference curve which is tangent to the new feasible frontier, so MRS=MRT.
Here, B reaches a higher indifference curve with an even higher utility
How do B’s different options compare in the intertemporal choice model?
According to utility (determined by highest indifference curve and hence largest feasible set):
Best: investing and lending (50% rate of return, -10% interest on lending, $100 investment)
Then investing (50% rate of return, lower investment)
Then lending (10% interest rate, no investment)
Then storage (20% depreciation)
What if person A can borrow to invest?
Suppose A can choose to invest some money and earn income from the investment. Thus they can choose to borrow and then split how much they have borrowed between consuming now and investing.
If they borrow at an interest rate of 78%, they can invest some of this at a return on 200%.
This expands their feasible set by increasing the y intercept whilst the x intercept stays the same.
They choose the highest feasible indifference curve which is tangent to the higher feasible frontier, where MRS=MRT
How do A and B’s situations compare and differ?
Same:
- A and B have the same shaped indifference curves and have equal intrinsic impatience. B’s indifference curve is higher than A’s.
- In the credit market, the feasible frontiers of both have a slope (1+r). B receives the interest rate and A pays it. They face the same price of moving consumption in time.
Differ:
- A starts with wealth and B starts with nothing. B has the guarantee of a similar asset later, but this puts the two on opposite sides of the credit market.
- Both can benefit from participating in the credit market, A by borrowing and B by lending.
- A wishes to bring consumption forward in time, B wishes to push consumption back to the future.
- B gains from a higher interest rate while A loses, because the cost of moving consumption forward (interest rate) by borrowing for A is the same as the gain of postponing consumption for B (lending).
How can the relationship between borrowers and lenders be seen as a principal-agent problem?
The lender (principal) faces the risk of not being repaid and the extent of that risk is determined by the borrower (agent), not the lender.
When a loan is arranged, unanticipated events beyond the control of the borrower can occur.
The lender cannot be sure the borrower exerts enough effort to make the project succeed and the borrower has more information than the lender about the quality of the project ands its likelihood of success.
If the project fails, it is the lender, not the borrower who loses money as the loan will not be repaid.
The borrower does not always act in the best interest of the lender.
What are some solutions to the principal-agent lender-borrower problem?
- the lender cannot require the borrower to put some of their wealth into the project, called equity. The more the borrower’s own money that is invested in the project, the more closely aligned their interests are with those of the lender.
- the lender cannot require require the borrower to set aside property that will be transferred to the lender if the loan is not repaid, this is collateral. As long as the collateral can readily be sold for more than the amount of money owed, the lender is secure and doesn’t run substantial risk.
