Chapter 8 Flashcards
What are the assumptions about the model?
- Two period model
- Income is exogenous (no work/ leisure, therefore we can just focus on their consumption decisions)
- Focus on consumption/saving decisions
- Lump sum taxes
- Consumers can be different
- Same interest rate in which consumers can borrow and lend
What is the current period equation to show the amount of disposable income?
- c: current consumption
- s: Bond
- y: income
- t: taxes to the government
What does it mean when s<0?
Consumer is a borrower
What does it mean when s>0?
Consumer is a lender
What is a bond?
A promise to pay something in the future in exchange for some consumption goods
- No risk associated and consuemrs never default
- Bought and sold by consumer so no financial intermediaries
- If a consumer lends, then they buy a bond
- If the consumer borrows, there is a sale of bonds
What is the private disposable income?
Income left after tax is taken away
What does a prime (‘) mean?
The future period
What is the relative price of future consumption?
1/1+r
What is an equation for future consumption?
- c’: future consumption
- y’: future income
- t’: future taxes
- (1+r)s : Interest recieved on bonds/savings
- Only two periods so this is the final period and the consumer needs to spend all the disposable income and the earnigns from interest
- If s<0, the consumer pays interets on the bond taken in the first period
What is lifetime wealth?
Quantity of resourcs available to consumer (in current consumption goods) to spend on consumption goods over their lifetime (2 periods)
- Present value of lifetime consumption is equal to the present value of lifetime income minus the present value of lifetime taxes
- Red square is lifetime wealth and is denoted by a
- Includes r,y and t
What is the proof for lifetime wealth?
Diagram
- Slope is equal to negative interest rate
- Lifetime goods is multiplied by (`1+r ) for vertical intercept to show the current consumption of goods represented in future terms, and c=0
What is the endowment point?
What is the proof for the linear equation of the intertemporal budget constraint?
Lenders and borrowers
- X is a lender: c
- Y is a borrower: c > y-t: They consume more than their private disposable income, therefore they are taking out a bond and in the future period, they have to pay back the amount borrowed with interest.
Smooth consumption
Smooth transition between periods, therefore no stark differences in the bundles.
As both current and future goods are normal, then when there is a shift in the budget constraint, there is an increase in current and future income
What causes the budget constraint to shift?
Changes in lifetime wealth
What represents preferences?
Indifference curves
- Utility increases, as the curve shifts to the right
- Slope is the negative marginal rate of subsitution between the current and future consumption
Optimal choice for a lender
- Situated on the left of the endowment point
- Able to consume more in the second period
Optimal choice for a borrower
- Borrower is further down as they consume more in the first period and consume less in the second period, as they have to pay back what they lent
Where is the optimal choice?
Where the utility function and budget line meet at one point
Marginal rate of subsitution = 1+r
rate at which he or she is willing to trade off current consumption for future consumption is the same as the rate at which he or she can trade current consumption for future consumption in the market (by saving).
Impact of an increase in current disposable income on the budget lines
- Endowment point moves right
- Curve shifts by the amount y2-y1
- Slope remains unchanged but moves to the right
- Greater disposable income
- Change in taxes
*
Increase in current disposable income on the optimal choice:
- Assuming it is a normal good, therefore when income increases, there is more demand for the good
- Higher lifetime wealth means an increasing current and future consumption with regards to normal goods
- Savings increase
- Change in savings = (Change in savings)- (change in taxes)-(Change in consumption)
*
Increase in future consumption on the budget line:
- New endowment allows for an increase in future consumption, therefore it just moves up
- Current disposable income remains the same
- Lifetime wealth increases so there are higher intercepts
- Slope is the same as the interest is the same
Increase in future disposable income on optimal choice
- Because the consumer wants to smooth consumption overtime, they would save less in the current period, and the increase in future income would compensate the increase in current spending, so there isn’t a stark contrast when the future income arrives
- Change in savings = (Change in savings)- (change in taxes)-(Change in consumption)
- Change in current taxes and current income is 0, the change in savings would be the neagtive change in consumption so the change in savings is negative
*
- Change in current taxes and current income is 0, the change in savings would be the neagtive change in consumption so the change in savings is negative
Friedman: Permenant income hypothesis
- Permenant changes in income (lifetime wealth) leads to large changes on consumption
- Small changes that lead to changes in the permanent income have small effects (Temporary, only in one period)
- FG is permemant (changes in income are the same for both periods) whilst DE is temporary
- When there is a temporary increase, there needs to be consideration for savings but with permenant, consumption can increase the same as income
Intertemporal preferences
- Blue: If they care more about current consumption, then the indifference curve will be blue, as a change in present will need to have massive change in future consumption in order to comepnsate for the change in present consumption
- Black: If they care more about the future, there would need to be a massive change in present whenever there is a change in future consumption, as
Increase in real interest rate
- Increase in a, as a result of the increase in r
- Change in slope as there is the potential to gain more from lending a bond, due to higher interest and less chances to borrow due to the increase cost of bonds
Increase in real interest rate, when the consumer is a lender
- Changing lifetime wealth
- Subsitution effect: Yellow line, which is parallel to the new budget constaint, with the new interest rate. Touches the inital indifference curve. Movement from x0 to D is the subsitution effect. Incneitve to save more, so reduction in current consumption, as the price of future consumption is lower. (Blue arrow)
- Income effect: Reaches a consumption bundle which we could not have accesed before with the previous budget, as they are richer so there is a movement from D to x1. Increases current and future consumption
- The impact depends on which impact is stronger
- Subsitution > Income: Decrease in current consumption
- Subsitution < Income: Increase in current consumption
*Assuming it is a normal good
Increase in real interest rate, when the consumer is a borrower
- Subsitution effect: Yellow line. Parallel to the new budget line but tangent to the previous indiffernce curve. Increases future consumption, as there is more to gain through saving
- Income effect: Borrowing costs more therefore reduces current and future consumption, therefore curve shifts inwards from the yellow line
- Current consumption decreases, as it is costly to borrow and the income and subsitution effect move in the same direction
- Future effect depends on which effect is stronger
- Income < Subsitution: Increase in future consumption
- Income > Subsitution: Decrease in future consumption
Perfect complements
No subsitution effect therefore increase in r depends on whether the consumer is a lender or borrower
What is the governmetn budget constraint?
- Plugging the future budget constraint into the current budget constraint
- Left hand side: What the govenment spends/ requires
- Right hand side: How much the governmetn gets/ resources available
- Debt must be repaid, which is done through future taxes
- Total taxes must match liabilities
Credit market equilibrium
- Sp(r): private savings which should equal bonds: Sp(r)=B
- The credit market clears when the net quantity that consumers want to lend in the current period is equal to the quantity that the government wishes to borrow.
- Sb(r)=-B:
- Derived for the equaition where Sp(r) +Sb(r)= CA+I (No investment or current account =0 )
- Implies Y=C+G (Sp(r)=Y-C-T)
*Assuming the subsitution effect dominates so increase in interst rates = greater savings
Relationship between government budget constraint and cosnumers
Government liabilities determines taxes
What happens when there is a reduction in taxes?
- Change in taxes = -x
- In the first period, we reduce taxes but in the second period we increase taxes by x with interest
- When taxes are paid does not matter but government liabilities matters
When there is a tax cut in the first period:
- Private disposable income in the first period is higher due to a tax cut therefore there is more money to spend.
- In the second period, they have to pay more tax therefore there is less disposable income
- Endowment point shifts
- Consumers save the entire tax, as it will recieve interest and they can use this to pay the increasing taxes.
Credit market equilibrium and Ricardian equivalance
- Interest rates don’t change
- Government has to financve tax cut through increasing debt so increase in B by N, which shows the amount that needs to be issued
- People knowing that they have to pay higher taxes in the future save the gain in income, therefore SP also shifts
For the neoclassical consumption model, what is the two budget constraint?
- f is the financial wealth (The net financial assets, such as stocks, bonds, saving accounts, and checking accounts that an individual possesses.)
- Current consumption = Income - amount added to financial wealth
*
What is the neoclassical intertemporal budget constraint?
- Present discounted value of consumption must equal total wealth
Diminishing marginal utility
As a consumer, consumes more then they derive more utility but for each extra unit of consumption, there is less utility derived and this applies to all kinds of consumption
What is the neoclassical utility function?
Greater consumption increases utility but with diminishing marginal utility
How to maximise the utility of a neoclassical intertemporal budget constraint?
- Want to maximise u’(ct)
- Want to maximise utility of future consumption: βu’(ct+1)
- Agents can either consume today or save and consume (1+r) units in the future
- Saving for the future means each future unti acquires (1+r)
Utility is maximised when agents are indiffernet between consumimng more today or more tomorrow
What is the Euler equation?
If Irving consumes today, he gets the marginal utility of consumption today—the left-hand side of the equation, u′(ctoday). If Irving saves that unit instead, he gets to consume 1 + R units in the future, each giving him u′(cfuture) extra units of utility. Becuase the utility comes in the future it must be discounted by β
- these two sides must be equal is what guarantees that Irving is indifferent to consuming today versus consuming in the future.
Solving the Euler Equation
What is the growth rate of consumption?
A higher interest rate raises the return to saving, and consumption growth is faster.
If the consumer wants to consume immediately and doesn’t care for the future β will be lower
Explains why interest rates and growth rates are often similar numbers, as it is only the value of β that determines the difference.
Solving the for current and future consumption using log utility
