Consumption Flashcards
Keynes 3 Conjectures
- 0
Keynes Consumption Func GRAPH
- Slope & Intercept
- Show APC falls for ^Y
Look up pg1
Problems with Keysian C Func.
APC did not fall, C and Y grew at same rate.
Keynes predicted that Savings rate would increase, but just stayed stable
Keynes model is static [accounts for single period]
Intertemporal Chocie:
- Assumes consumer choose ____ & ___ ____to ____ ____ ___
- Consumers are subject to ____ ____ ____
Current, future consumption, max Lifetime utility/satisfac
Intertemporal budget constraint
Def Intertemporal Budget Constraint
total resources available for current and future C
What does ITC take as Exogenous?
Income - assumed to be Y1 and Y0
Do you save in future period? Why?
no only in current as only considered to be 2 periods. no consumption in t1 - assumed to be dead
(ITC) Real Budget Constraint at Time 0 & 1
Sub together and Rearrange for S0
What does S0 represent?
C0 + S0 = Y0
C1 = Y1 + (1 + r) S0
Real Savings
If s>0?
If s<0?
Lender
Borrower [need to repay in future so interest neg]
Lifetime Budget Constraint Y = W = Written as a line equation (slope & intercept) Written meanings for each term [W=]
Y= C0 + (C1 - Y1) / (1 + r) from [ C0 + S0 = Y ] W = [ (c0+c1)/(1+r) ] = [ (y+y1)/(1+r) ] c1= -(1+r)c0 + (1+r)W Wealth = PV lifetime C = PV lifetime Y
What does endowment mean?
The level of y0 to consume c0, y1 and c1.
exogenous income at time 0 & 1
3 assumptions of consumer preferences?
- more is better
- preference for diversity [eg 10 now and 10 in future]
- consumption today and tomorrow are normal goods [^y = ^d]
Slope of I.D curve = …
what does ID curve show?
MRSc0,c1 [marginal rate of intertemporal substiution]
Shows rate at which c1 is subbed for c0
Lifetime Utility formula
What does Beta equal and what is its value?
Slide 16
Consumers level of impatience, Beta < 1
Change in Lifetime utility formula
What does Beta equal?
slide 16 - requires derivation of c0 & c1
Consumers level of impatience, Beta < 1
What does change in U equal on same indifference curve?
= 0, because there is no change in utility on the same ID, only a change in preferences between c0 & c1
Write the change in lifetime utility formula in terms of MRSc0,c1
Think what MRSc0,c1 means
slide 16
At the optimal point, what about the gradient? Values?
(1+r) = MRSc0,c1
Budget constraint grad = ID grad
At t0, on the x axis of borrower …
What is repayment equal to?
c0 > y0
y1 - c1 +r
What is lagragian func used for?
What is the structure of Lag func?
Combines the function being optimized with functions describing the constraint or constraints into a single equation. Solving the Lagrangian function allows you to optimize the variable you choose, subject to the constraints you can’t change.
What are we maximising in Euler Eq? In terms of letters?
What is constraint in Euler? Letters? (think of max _____ ____ st. _____ ______)
What is Langrian of set up for Euler?
Slide 20
What are the steps for calc Euler Eq? [6
What is Euler in terms of (1+r) [=MRS]?
- set up lang func.
- FOC for Ct and Ct+1
- Make =0 (at max.)
- Rearrange for Lambda
- Make them equal each other & rearrange for Ct+1
- Sub this back into budget constraint
What happens to budget line when r increases?
Why? (x2 view points)
Always pivots around? Why?
Line becomes steeper [Remem: ^rate is pretty steep]
Savers: c1 becomes relatively cheaper, more interest earnt on savings so Wealth increases to W2
Borrowers: pay more for current period c0, so fall in W1
Endowment Point -lender/borrower must always be able to consume y0 &y1
Draw Intertemporal Choice for Lender?
Slide 25, sheet 4
explain steps of increase in interest rate for Lender? [stronger Negative substitution effect]
Point A to C same ID curve and imaginary BC that is tangental to C and parallel to final BC=Neg sub, Posi Wealth Effect
Point C to B, BC and ID Curve shift out due to higher Ct+1 = [new BC intersects Endowment point]
KEY POINT: decrease in c0 from wealth effect is greater than increase in c0 from sub effect [net fall in c0]
Draw the effect of increase in interest rate for Lender? [stronger negative substitution effect]
slide26
explain steps of increase in interest rate for Lender? [stronger positive substitution effect]
Point A to C same ID curve and imaginary BC that is tangental to C and parallel to final BC=Neg sub, Posi Wealth Effect
Point C to B, BC and ID Curve shift out due to higher Ct+1 = [new BC intersects Endowment point]
KEY POINT: decrease in c0 from sub effect is less than increase in c0 from wealth effect [net rise in c0]
Draw the effect of increase in interest rate for Lender? [stronger positive substitution effect]
slide 27
Draw Intertemporal Choice for Borrower?
slide 29
explain steps of increase in interest rate for Borrower? [stronger positive substitution effect]
slide 30
Draw the effect of increase in interest rate for Borrower? [stronger positive substitution effect]
slide 30
explain steps of increase in interest rate for Borrower? [stronger negative substitution effect]
slide 30
Draw the effect of increase in interest rate for Borrower? [stronger positive substitution effect]
slide 31
OVERALL: Higher r for lender leads to ___ ___ …. c0 and ____ c1
depends on size of neg Sub and Pos W
both increase future consumption
OVERALL: Higher r for borrower leads to ___ c0 and ____ ___ …. c1
both increase current consumption
depends on size of neg Sub and Pos W
How does Life Cycle Hyp build on ITC? (x2) [what did ITC assume]
Both dynamic models but LCH says that income varies systematically over consumers life cycle, and that saving allows for consumer to achieve smooth consumption
unlike ITC which assumed Consumer Lifetime income exogenous
What does Euler equation mean Consumers try to achieve?
Smooth Consumption
x2 Assumptions for LCH
zero real interest rate [doesn’t affect outcome of model, only ^ savings]
consumption-smoothing is optimal
LCH:
what does Lifetime resources = ?
C over entire period = ? [consumption func]
W + RY
C = aW + bY
C = aW + bY
What does a and b mean? letters and explanation?
a = [1/T] marginal propensity to consume out of wealth b = [R/T] marginal propensity to consume out of income
LCH SR implications x2
critisms x2
- monetary mechanism - wealth in consumption func
- transitionary income taxes
- uncertainty = saving rate higher for ppl without children bc they are independant [precautionary]
- Bequest motive - leave moeny for children to inherit
LCH diagram
pg 492, sheet 5, slide36
LCH solve the Consumption Puzzle
slide 35
PIH 2 types of income? Defs of each
Permanent; av Y expected to persist for lifetime
transitionary; temp deviations form average
PIH Consumption Func
C = a x Yp [where a is fraction of permanent Y spent annually]
APC is ____ for high Y households?
lower
What type of income does Consumption (Ct) respond more to?
Show this [remember Ct = F(Yt, Yt+1, rt)]
Permanent
Slide 39
PIH vs LCH
x1 Difference for each
x32 similarities
LCH current income changes systematically (with life cycle)
PIH current income is subject to random, transitionary fluctuations
BOTH: -ppl try achieve smooth C, with changing Y0
-can explain consumption puzzle
-dynamic, 2 period models
Random-Walk Hypothesis (by?)
Additional assumption & affect on C
so only____ ____ in W or Y that alter ____ ____ will change _____
Robert Hall
rational expectations; ppl use all available info to forecast future variables like income
ie. if change in Y or W anticipated, then will be factored in
unanticipated changes, permanent income, consumption
Authors: Intertemporal choice Random - Walk Hyp PIH LCH Consumption theory
Authors: Irving Fisher Robert Hall Friedman Modigliani Keynes
EVAL of LCH & PIH
evidence of anticipated
WICOX: ^social security benefits, C not adjusted before, only after
SHAPIRO & SLEMROD: fall in tax withholding, no change in C until after policy implemented
EVAL of PIH & LCH
evidence of unanticipated
PRESTON: C reaction to permanent shocks much higher than transitionary
Studied the unanticipated change in rainfall and how this affects consumption, through the production function
EVAL of Fisher’s ITC
If individuals are subject to borrowing constraints, then cannot alter current consumption (through borrowing/lending) thus they behave as Keynes theory suggests
What is a non-binding borrowing constraint?
Where is optimal is constraint is binding
optimal c0 =< y0.
Corner point.
Diagram for non-binding and binding budget constraint following an ^y0
slide 51
How does uncertainty affect future income?
What is the assumption?
What is expected future incomce equation?
higher precautionary savings
there are only 2 states of future income [good & bad] and there probability of occuring are p & (1-p)
E(Yt+1)= [pYgood t+1] + [(1-p)Ybad t+1]
What is the Key Insight to understanding the effects of uncertainty?
in general, the function of the expected value is NOT EQUAL to the expected value of a function
Draw precautionary savings due to Uncertainty [x4 steps]
Implications of this graph?
- Draw ID and label Good and Bad States
- Label expected utility in the middle (point E)
- Connect the Good and Bad states (with straight line)
- Mid-point gives expected future Marginal utility of Ct+1 because of uncertainty.
If uncertainty is increasing, what will happen in the good/bad income state?
Good = even higher Ct Bad = even lower Ct
Does impirical evidence support Precautionary Savings model?
YES - increase in savings and fall in consumption = 40% of savings due to precautionary motive.
Estimate that 2% of household net worth is precaution savings
Psychology of Instant Gratification
what do all theories so far assume?
survey found that 76% of ppl not ___ ____ for _____
Consumer rationally try max. lifetime utility.
Saving enough , retirement
Why do ppl not save as much as they should?
In SR, ppl are impatient - want instant gratification
LR, more patient, but this decreases as time falls
