TERM 1: CA & endowment economy Flashcards
small economy =
taken world IR & prices as given
Cannot influence them
Choice variables for households
C1, B1* (bond holdings)
Initial wealth inherited from past
(1+r0)B0*
Period 1 BC
C1 + B1* - B0* = r0B0* + Q1
Period 2 BC
C2 + B2* - B1* = r1B1* + Q2
Transversatility condition
B2*=0
Intertemporal BC
C1 + C2/(1+r1) = (1+r0)B0* + Q1 + Q2/(1+r1)
Lifetime utility function
U = ln(C1) + ln(C2)
4 properties of ICs
- downwards sloping
- monotonic
- Ics do not cross
- ICs convex to origin
What’s does ICs convex to origin imply about preferences?
Diminishing MRS of C2 for C1
As we have more C1, only willing to give up a small amount of C2 for one extra unit C1.
Where is the optimal graphically
Where intertemporal BC tangent to IC.
Optimal C* depends on (4)
Preferences, endowments, initial wealth, IR
Wealth (exogenous) =
W = (1+r0)B0* + Q1 + Q2/(1+r1)
How do C2 and C1 relate from FOCs
C2* = (1+r1)C1*
C2* as a fucntion of W and r1
C2* = 1/2 W(1+r1)
C1* as a fucntion of W
C1* = 1/2 W
C1* as a fucntion of r0, B0*, Q1, Q2, r1
C1* = 1/2[(1+r0)B0* + Q1 + Q2/(1+r1)]
C1* is increasing in
Q1, Q2, (1+r0)B0*
C1* is decreasing in
r1
TB1 is equal to
TB1 = Q1 - C1
difference between output and consumption
IF C1 > Q1
Must import from ROW therefore TB1 < 0
IF C1 < Q1
Export to ROW therefore TB1 > 0
CA1 =
CA1 = r0B0* + TB1
TB1* formula
1/2[-(1+r0)B0* + Q1 - Q2/(1+r1)]
CA1* formula
1/2[-(1-r0)B0* + Q1 - Q2/(1+r1)]
What does free K mobility mean? Implicationfor IR too
households can borrow and lend in international financial market.
r1 = r* i.e. domestic IR = world IR
If r1 > r* what happens?
investors borrow in international markets, lend in domestic markets. Excess supply in dom = r1 falls. Excess demand in inter. = r* rises. Arbitrage opporuntities disappear.
A temporary output shock
Q1 rises, Q2 stays the same.
How does a temporary +VE output shock affect CA1*? Explain.
Housholds know shock is temporary, want to smooth consumption, so increase C1 but also increase S1 to save for period 2. Increase in Q1 > increase in C1. Therefore TB1 improves, CA1 improves as more saving.
Formula for effect of permanent output shock on CA1*. Explain.
change CA1* = 1/2 r/(1+r) change in Q1.
Smaller change in CA1 as do not need to increase saving to smooth consumption as Q2 increases too.
Difference between impact of temporary and permanent shocks
Finance tempoary shocks by running CA surpluses/deficits to smooth consumption.
Adjust to permanent shocks by changing consumption in the LR to keep CA stable.
What have we assumed so far avout the goods?
That there’s just one good which is consumed, imprted and exported.
Terms of trade = + formula
The relative price of exportable goods in terms of importable goods.
TT = Px/Pm
Now we assume bonds are denominated specifically in terms of…
Importable goods Pm
Period 1 and 2 BC including TT
C1 + B1* - B0* = r0B0* + TT1 Q1
C2 + B2* - B1* = r1B1* + TT2 Q2
Intertemporal BC including TT
C1 + C2/(1+r1) = (1+r0)B0* + TT1Q1 + TT2Q2 /(1+r1)
How are TT determined in a small open economy?
They are GIVEN
A TT shock is just like an…
endowment shock
temporary TT shock effect on CA
large effect on TB & CA to smooth consumption
permanent TT shock on CA
small effecr on TB & CA
What about the shock matters to determine impact on CA?
whether agents THINK the shock is permanent/temporary, doesnt actually matter whether it was ex-post
2 effects higher IR can have on C1 and CA1
- SE - higher r* = C2 more attractive relative to C1 = C1 falls, S1 rises = CA1 improves
- WE - higher r* = makes debtors poorer, lenders richer. C1 falls for debtors = CA improves; C1 rises for lenders. = CA worsens
Which effect dominates? Under what condition?
SE > IE. When utility preferences are log.
Explain effect of rise in r* graphically for debtor
Steeper BC = pivots around endowment point
Original equilibrium not feasible
C1 falls and C2 rises
TB1 & CA1 improve
Rationale for K controls
To curb CA deficits which arguably risk future crises and reduce C2
Strong form of K controls requires:
B1* >=0
Can lend but cannot borrow
Impact of K controls on C1 and C2 - new equilibrium
C1 falls so C1=Q1
C2 rises so C2=Q2
New equi at endowment point
What has to happen to domestic IR to make the endowment point the new optimum after K controls?
Increase domestic IR r1 above r* world IR
Encourages saving so now happy not to borrow = no longer a debtor.
formula for r1 under K controls scenario
C2=(1+r1)C1
C2 = Q2 and C1 = Q1
therefore: r1 = (Q2 / Q1) - 1
How r1 related to Q2 and Q1
The lower Q1 is relative to Q2, the more households want to borrow against future income. To make them not do this, r1 has to be even higher.
