1.6 Savings and Borrowings Flashcards
In our models so far we have assumed non-saitation i.e more is better so everyone spends there money, as there is no future to think about, but is this the case in real life?
No it isn’t the case in the real world, people save and consume now and in the future.
What does intertemporal decisions mean?
These are decisions that happen across periods, months, days etc.
Is £1000 today worth £1000 IN A YEARS TIME?
No it isn’t lets say you put the £1000 in the bank and interest rates are positive, you would save and get interest on top of this, so would be more.
What does discounting mean?
Discounting is the process of converting FV into PV
• Divide by (1 + r) to discount back by one time period
If you future value is y, a years time, how do i find the value of this today?
y/(1+r)
If i want one extra unit of consumption in the next period (£1) , how much do i have to save today also what does this imply about consumers)?
£1/1+r), so you have to sacrifice consumption in the present to get consumption in the future.
Consider an income stream over a series of dates t {0,1,2…T}
y0,y1,y2…..yt….yT, ( and what is this)
What are the income streams discounted look like?
And do the same thing for consumption
c0, c1,c2….ct…cT( what is this)
The present value of my lifetime wealth
The present value of my lifetime consumption
What are some model assumptions we are going to use here?
Let there be two time periods: 0 (present) and 1 (future)
• Income in these two periods: y0 and y1 ( don’t have to consume all your income in one period, you can save or borrow)
• Saving and borrowing is possible at interest rate r
Does consume derive utlitiy from consumption in two periods and are we trying to maxmise this?
The consumer derives utility from consumption in the two periods, with
preferences described u(c0,c1)
• The consumer chooses c0 and c1 to maximise utility subject to an
intertemporal budget constraint and non-negativity constraints
What does the maximisation problem depend on?
It depends on three things
1) Preference: you prefer consume more today or more tomorrow
2) Patience: if impatient, tends to consume more today
3) How 𝑦0 𝑎𝑛𝑑 𝑦1 relate to each other: if your income is low today but you project it will be high tomorrow, you’re more likely to borrow today (student); if you project y1 will be less than y0, then save more today (near the retirement)
Can you die with debts in this model?
No
What are we going to assume about the credit market ?
There are Perfect credit markets
No uncertainty
Saving and borrowing at the same rate
Consumer has enough income to repay debt
Perfect mechanism that ensure no one takes on loans that cannot repay
Now we are going to look at the intertemporal budget constraint, so show the decision a consumer can do in period 1 if they save and what does that mean in the future, do the same if they have to borrow in the future?
Now combine these equations and rearrange to find the equation of the intertemporal budget constraint? what is the gradient and y intercept and what does the y intercept tell us too?
Gradient = -1+r ( the interest rate determines how steep the budget line is)
Y intercept = [y1 + (1+r)y0] y intercept tells the wealth over 2 years( the future value of lifetime wealth)
Draw this intertemporal budget constraint on a graph?
What is the intution of the gradient being -(1+r) and what does the endowment point mean?
price of consumption today = forgone interest rate I could have earned
(opportunity cost of the money that I didn’t save: for every money you choose to spend today, you sacrifice the interest rate I could have earned on it)
Endowment point: (𝑦0, 𝑦1)
not borrowing and not saving, just consume exactly what the income I earned
Why is the x intercept this and what is y intercept?
The income he has today + the present value of his future income. Remember money doesn’t grow on trees, you can only consume what you earn.
It is your future income + the money you saved from the current period + interest( this is if you saved), if you have borrowed in the current period, then the y intercept will be reduced. meaning you consume less today.
Show your that the intertemporal budget constraint can be shown in future and present value terms?
1) INTERTEMPORAL BUDGET CONSTRAINT FOR FUTURE: First of all collect like terms so that income today and tomorrow = consumption today and tomo.
What is the right handside of both equations called?
The lifetime wealth which is the quanitiy of resources avaliable for the consumer to spend on consumption over 2 periods).
Remind me what the maximisation problem here is?
Now we are going to look at the saving and borrowing decisions of a consumers
Assume all conditions hold:
⚫ Preferences: completeness, transitivity and continuity
→ so, can be represented by a utility function 𝑢(𝑐0, 𝑐1)
⚫ Maximization problem
⚫ Non-satiation and Convexity assumptions are satisfied ( indifference curves convex to origin)
What is the optimal choice for a borrower, where is utlitliy maximised ?
MRS = 1+r similar to MRS = P1/P2
Now we are going to look at the saving and borrowing decisions of a consumers
Assume all conditions hold:
⚫ Preferences: completeness, transitivity and continuity
→ so, can be represented by a utility function 𝑢(𝑐0, 𝑐1)
⚫ Maximization problem
⚫ Non-satiation and Convexity assumptions are satisfied ( indifference curves convex to origin)
What is the optimal choice for a lender, where is utlitliy maximised ?
Now lets look at the effect of an increase in interest rate from Ra to Rb? what happens to the budget line, illustrate on diagram?
Steeper budget line ( makes it look more inelastic than elastic)
It pivots around the endowment point
Show the effect of an increase in interest rate for a borrower ?
Show the effect of an increase in interest rate for a lender and using the diagram explain why they cannot be worse off?
the original point (A) the chose to consume at is still available, they can still continue to choose A if they want even though B is better, so they cannot be worse off.
Decompose the income and subsitution effect for a borrower ( lets first assume that they will maintain being a borrower) ( so you borrow quite a lot) What is the price of borrowing? What is the effect on Utility too(look at overall effect) ?
Decompose the income and subsitution effect for a lender ? What is the effect on Utility too? ( look at overall effect)? ( will the answer be different if the goods are not normal goods? )
Yes the answer will be different if both are not normal goods.
How can a borrower switch to a saver? decompose the substation and income effect?
only happen when you just borrow a little bit, the SE push you to go the other side!
→ Same effect as in saver case
Show on the diagram the optimal choice of a borrower and lender when Rb>Rs?
We except for a saver, there part of budget line will be shallower compared to borrower.
Show households optimising at kink, when there is a different interest rate for borrowers and lenders?
Suppose there now is a credit limit, who will this affect and illustrate on diagram ( you can only borrow a certain amount) , give an example on why this might happen too?
The dotted line represents what would happen if there is no borrowing constraint( no credit constraint so credit limit < your income)
It dozen t affect saver
Explain the concepts of decision and experience utility. How might they give rise to Erik undersaving in his youth? Illustrate this in your diagram.
Summarise what happens with an increase in current dispoable income?
Current and future consumption will go up ( shift outwards)
Savings will increase ( the consumer acts to smooth consumption)
Summarise what happens if there is an increase in future dispoable income?
So diagramtically
Current and future consumption increases shift outwards
Savings decrease ( in the future i will have a lot of money, so you currently you consume a lot)
The consumer acts to smooth consumption
Do the derivations
Also answer this in general if it was lenders and borrowers and if the preferences were perfect substitutes?
Lenders better off ( impossible to be worse off, as they can still afford same bundle)
Borrowers worse off ( could become a lender, if they borrower a little)
If it was perfect substitutes there is no substation effect so no change.
Mock exam question 2a)
Part B
a
Remember endowment point is where you just consume all or income you don’t borrow or save.
(b) Find Sonia’s optimal consumption bundle (𝑐0, 𝑐1) and the credit card debt she repays next month. What is Sonia’s utility level at the optimal bundle? Illustrate these in your diagram, including her indifference curve at the initial endowment and the indifference curve at the optimal bundle.
[10 marks]
Perfect complements suggests she will consume min of ( co, c1) = co=c1, we have the budget constraint equation where C1(co) as they are the same, we set c1 = 0, then solve for c0, which gives us c1.
As she has no income in the current, it must of meant she borrows £1000 in the current period, and in the future she pays back 1000 x 1.2 = 1200
Utility is min [1000,1000] = 1000.
(c) Now suppose Sonia’s decision utility when shopping is given by 𝑢(𝑐0, 𝑐1) = min(0.8𝑐0, 𝑐1), whereas 𝑢(𝑐0, 𝑐1) = min(𝑐0, 𝑐1) describes her experience utility. How much will Sonia spend using the credit card? Illustrate the outcome in your diagram and explain why it is suboptimal.
With this question
We know that she is going to spend more on her credit card than when she was at her decision utlitiy and hence utility will be lower.
1) we know that now 0.8c0 = c1 is her decision utlitiy which she wants to maxmise. The original budget constraint was c1 = 2200 - 1.2C0. We can sub c1 = 0.8co into the budget constraint and find that co = 1100>1000. Thats how much we spends on credit card. Thus sonia has overspent leading to lower consumption next month
Most credit cards have a credit limit, which denotes the maximum that can be spent in any given month. Normally the credit limit is set at a default level but can be adjusted upwards if the credit card company is confident the consumer can repay. (i) What credit limit enables Sonia to attain the utility level found in (b)? Add this credit limit
(ii) Will your chosen credit limit in (i) be effective if Sonia can choose to increase it? What are the incentives of the credit card company when setting the credit limit? [5marks]
Yes, it may still be effective if raising the credit limit requires some steps (calling or making a request online) so Sonia is in the ‘cold state’ when making that decision…she would thus opt not to change the limit. The default credit limit serves as a nudge!The credit card company presumably profits from Sonia’s spending and would be willing to allow her to borrow up to 2200/1.2, the maximum she is able to repay.
