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