Dynamics of Supply and Inputs, Present Value and Interest Rates Flashcards
(17 cards)
What is the S=I procedure and what does it imply?
- Individuals decision of saving and work can be determined in the life cycle model
- We can combine these individual decisions to determine aggregate or national savings
- Using the fundamental macroeconomic identity, we get national savings (S) = national investment (I)
- In a closed economy this implies that a decline in savings means a decline in investment
What occurs in period t+1?
- Agents invest their savings in assets at the beginning of period t + 1
- Agents consumer the principal plus interest at the end of t + 1 and they die
What is N?
The population of each generation, total pop = 2N
What is the lifetime BC?
- cyt + (cot+1)/(1 + rt+1) = wt
What is the PV with a fixed interest rate?
- PV = (1/1+r)^(T-t0) FV$
What is the PV of a maturity dependent interest rate?
- PV = (1/1+r1) x (1/1+r2) x (1/1+rx) FV$
- i.e. disentangle the fixed discount factor
What are the optimal consumptions for a Cobb Douglas Utility?
- ct = αwt
- ct+1 = (1-α)wt(1+rt+1)
What is optimal savings for a Cobb Douglas utility?
s = (1-α)wt
What utility functions have equivalent optimal s and c’s?
CD and (α),(1-α)log
What is optimal savings for a (1),(α)log utility?
s = (α/(1+α))w
How are taxes integrated into optimal consumption and savings?
(1-t) affecting every w in optimal conditions
It =
Kt+1 - Kt
Yt = in terms of input prices?
Yt = Nwt + rtKt
What is S in terms of input prices and how does this demonstrate the fundamental macroeconomic identity?
- St = Nwt + rtKt - Ncyt - Ncot
- St = N(wt - cyt) + (rtKt - cot)
- St = Nat+1 + (rtNat - Nat(1+rt))
- St = Nat+1 - Nat = Kt+1 - Kt = It
at+1 =
at+1 = (wt - cyt)
What is at?
at : assets that the old generation in period t have brought from the previous period
What is at+1?
number of assets that the young in period t bring into the next period t +1, hence at+1 = (wt - cyt)
