ECON7520-econ7520代写
时间:2023-03-31
ECON7520: World Interest Shocks and
Import Tariffs in an Endowment Economy
Semester 1, 2023
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ECON7520
Recap: Current Account Determination in an Endowment
Economy
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Recap: Key Economic Mechanism
Last week, we introduced a small open economy model.
The key is the household’s optimal intertemporal
allocation of consumption: The household
makes intertemporal consumption and saving decisions.
smoothes consumption over time by borrowing and lending.
The household’s consumption and savings decisions
determine TB and CA.
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Recap: Setup
Two-period small open economy: periods 1 and 2.
The single consumption good in the economy is
perishable, i.e. cannot be stored across periods.
The single asset traded in the financial market is a bond.
There is a representative household (HH) in the
economy endowed with
B0 units of the bond at the beginning of period 1,
Q1 units of the good in period 1,
Q2 units of the good in period 2.
Interest Rates:
r0 for the initial bond holdings,
r1 for the bonds held at the end of period 1.
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Recap: Intertemporal Budget Constraint
C1 + B1 = (1+ r0)B0 + Q1, (1)
C2 = (1+ r1)B1 + Q2. (2)
By combining the budget constraints (1) and (2) we obtain
the HH’s intertemporal budget constraint
C1 +
C2
1+ r1︸ ︷︷ ︸
Consumption Values
= (1+ r0)B0 + Q1 +
Q2
1+ r1︸ ︷︷ ︸
Inital Assets + Total Income Values
.
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Recap: Intertemporal Budget Constraint
The above graph assumes B0 = 0.
The slope of the budget constraint is −(1+ r1).
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Recap: The Optimal Intertemporal Allocation
The above graph assumes B0 = 0.
The optimal consumption path is point B.
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Recap: Equilibrium
Exogenously given are r0,B0, r
∗,Q1 and Q2. An equilibrium is
a consumption path (C1,C2) and an interest rate r1 such that:
1 Feasibility of the intertemporal allocation
C1 +
C2
1+ r1
= (1+ r0)B0 + Q1 +
Q2
1+ r1
.
2 Optimality of the intertemporal allocation
U1(C1,C2) = (1+ r1)U2(C1,C2).
3 Interest rate parity condition
r1 = r

.
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Recap: Trade Balance and Current Account Balance
In this economy,
TB1 = Q1 −C1,
TB2 = Q2 −C2.
And
CA1 = r0B0 + TB1,
B1 = B0 + CA1
CA2 = r1B1 + TB2.
Also, since we don’t have investments in this economy
(I1 = I2 = 0),
S1 = CA1,
S2 = CA2.
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ECON7520
World Interest Rate Shocks
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World Interest Rate Shocks
What is the effect of an increase in the world interest rate
from r∗ to r∗ +∆?
There are two potentially opposing effects:
1 Substitution effect (SE)
An increase in the interest rate makes C1 relatively more
expensive and C2 relatively cheaper.
Saving in period 1 becomes more attractive.
2 Income effect (IE)
An increase in interest rate changes the HH’s purchasing
power.
Overall, an increase in the interest rate makes debtors
poorer and creditors richer.
The total effect (TE) equals SE plus IE.
Assume B0 = 0 and that C1 and C2 are normal goods.
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Adjustment to a World Interest Shock
r∗ ↑, HH = debtor
slope of black line = (1+ r∗)
slope of blue line = (1+ r∗ +∆)
C1
C2
b
b
b
b
A
CA1
CA2
C
CC1
CC2
B
CB1
Q1
Q2
SEIE
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Adjustment to a World Interest Shock
r∗ ↑, HH = creditor
slope of black line = (1+ r∗)
slope of blue line = (1+ r∗ +∆)
C1
C2
b
b
b
b
A
CA1
CA2
C
CC1
CC2
B
CB1
CB2
Q1
Q2
SE
IE
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World Interest Rate Shocks
Substitution effect:
Change in period 1 consumption C1 due to change in
relative “price”.
A = (CA1 ,C
A
2 ) = originally optimal path
B = (CB1 ,C
B
2 ) = path that is optimal given budget line that
passes through A and has slope (1+ r∗ +∆)
SE = CB1 − CA1
SE < 0 (by revealed preference argument).
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World Interest Rate Shocks
Income effect:
Change in C1 due to change in purchasing power.
B = (CB1 ,C
B
2 ) = path from previous slide
C = (CC1 ,C
C
2 ) = new optimal path
IE = CC1 − CB1
r∗ ↑ has two opposing effects on HH’s purchasing power.
The HH can purchase more on a fixed budget since the
“price” 1
1+r∗ of C2 falls.
The present value Q2
1+r∗ of endowment Q2 decreases.
Netting these effect, r∗ ↑ makes
debtors (for whom Q1 < C1 and thus C2 < Q2) poorer,
creditors (for whom C1 < Q1 and thus Q2 < C2) richer.
Since C1 is a normal good,
IE < 0 if purchasing power decreases (debtor),
IE > 0 if purchasing power increases (creditor).
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World Interest Rate Shocks
Overall, if the interest rate increases:
If the country is a debtor (Q1 < C1):
IE < 0 as budget line shift that determines IE is to the left.
TE = SE + IE < 0 as SE < 0 and IE < 0.
Therefore, HH’s savings increase after the shock.
If the country is a creditor (Q1 > C1):
It remains a creditor after the interest rate rise (by a
revealed preference argument).
IE > 0 as budget line shift that determines IE is to the right.
TE = SE + IE R 0 depending on which of SE and IE
dominates.
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ECON7520
Import Tariffs
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Import Tariffs: Setup
Question: Does an increase in import tariffs reduce
imports and therefore improve TB?
Consider the two-goods economy from Slides 3 which
exports endowments of oil (Q1,Q2) and
imports food for consumption (C1,C2).
Assume that in each period t ∈ {1,2}, the government
imposes an import tariff τt ≥ 0, and
returns the revenue from τt via a lump-sum transfer Lt .
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Import Tariffs: Budget Constraints
Then, the HH’s budget constraints for period 1 and 2 are
(1+ τ1)C1 + B1 = (1+ r0)B0 + TT1Q1 + L1,
(1+ τ2)C2 = (1+ r1)B1 + TT2Q2 + L2.
Important: The HH treats τt and Lt as exogeneously given.
The HH’s intertemporal budget constraint is
(1 + τ1)C1 +
(1 + τ2)C2
1+ r1
= (1+ r0)B0 + TT1Q1 + L1 +
TT2Q2 + L2
1+ r1
. (3)
It has a slope of
[
−1+τ11+τ2 (1+ r1)
]
.
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Import Tariffs: Optimality, Resource Constraint
The optimality condition (tangency of IC and IBC) becomes
U1(C1,C2) =
1+ τ1
1+ τ2
(1+ r1)U2(C1,C2).
If τ1 = τ2, then there is no change from τ1 = τ2 = 0.
If τ1 > τ2, then C1 becomes relatively more expensive and,
assuming diminishing marginal utilities, C1 ↓ and C2 ↑.
If τ1 < τ2, then C1 becomes relatively cheaper and,
assuming diminishing marginal utilities, C1 ↑ and C2 ↓.
Plugging τ1C1 = L1 and τ2C2 = L2 (= government BCs)
into (3) yields the economy’s resource constraint
C1 +
C2
1+ r1
= (1+ r0)B0 + TT1Q1 +
TT2Q2
1+ r1
.
τ1 and τ2 do not enter this constraint because the import
tariff revenues are returned to the HH.
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Import Tariffs: Equilibrium
Exogenously given are r0,B0, r
∗,Q1,Q2, τ1 and τ2.
An equilibrium is a consumption path (C1,C2) and an interest
rate r1 such that:
1 Feasibility of the intertemporal allocation
C1 +
C2
1+ r1
= (1+ r0)B0 + TT1Q1 +
TT2Q2
1+ r1
.
2 Optimality of the intertemporal allocation
U1(C1,C2) =
1+ τ1
1+ τ2
(1+ r1)U2(C1,C2).
3 Interest rate parity condition
r1 = r

.
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Adjustment to Changes in Import Tariffs
B is optimal if τ1 = τ2; C is optimal if τ1 > 0, τ2 = 0;
D is optimal if τ1 = 0, τ2 > 0
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Import Tariffs: Setup
Question: Does an increase in import tariffs reduce
imports and therefore improve TB?
TB1 = TT1Q1 − C1.
Answer: An increase in import tariffs leads to
TB ↑ if (present import tariff > expected future import tariff)
TB → if (present import tariff = expected future import tariff)
TB ↓ if (present import tariff < expected future import tariff)
Additional observation: In our model, τ1 6= τ2 leads to
lower welfare than τ1 = τ2 = 0 (no import tariffs).
τ1 6= τ2 distorts the HH’s optimal intertemporal allocation.
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ECON7520: Current Account Determination
in a Production Economy
Semester 1, 2023
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Motivation
So far we abstracted from the production side of the
economy.
The household received endowments Q1 and Q2
(endowment economy).
Question 1: How does our analysis change if we consider
firms that produce output?
Question 2: Does firms’ investment behavior affect the
current account?
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Key Points
We will assume that there is a representative firm in the
economy.
The firm is owned by the household.
We will analyze the firm’s optimal investment decision.
Similar to the household’s decisions, the firm’s decision
also significantly affects TB and CA.
Also, the following shocks change the firm’s investment
decisions.
Productivity shocks.
World interest rate shocks (next lecture).
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Setup
Two-period small open economy: periods 1 and 2.
The single consumption good is perishable.
The single asset traded in the financial market is a bond
(measured in units of the consumption good).
There is a representative household (HH) endowed with
Bh0 units of the bond at the beginning of period 1.
There is a representative firm. The household owns the
firm and obtains the firm’s profits
Π1 in period 1,
Π2 in period 2.
Interest Rates:
r0 for the initial bond holdings,
r1 for the bonds held at the end of period 1.
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Firm
What does the firm do? The firm
makes investments in period t that lead to output in t + 1.
finances its investments in period t by issuing debt in t.
Production: The production in periods 1 and 2 is given by
Q1 = A1F (I0)
Q2 = A2F (I1)
where
F is a function,
At > 0 (t = 1, 2) are technology parameters,
I0 is the investment in period 0 and exogeneously given,
I1 is the investment in period 1 and chosen by the firm.
Debt: The firm issues debt Dft in period t = 0,1:
D
f
0 = I0 (exogenous; to be repaid in period 1),
D
f
1 = I1 (to be repaid in period 2) (4)
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Investment Decision
How does the firm choose the investment level I1?
The firm maximizes its profits
Π2 = A2F (I1)− (1+ r1)Df1 where Df1 = I1
or
Π2(I1) = A2F (I1)− (1+ r1)I1.
The first-order condition for profit maximization is
Π′2(I1) = 0
⇔ A2F ′(I1) = 1+ r1
d [A2F (I1)]
dI1
= A2F
′(I1) = Marginal Product of Capital (MPK)
(1+ r1) = Marginal Cost of Capital (MCK).
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Production Function
Optimal Investment Condition
Marginal Product of Capital = Marginal Cost of Capital
A2F
′(I1) = (1+ r1)
We assume that F has the following properties:
1 F (0) = 0.
2 Positive MPK: F ′(I) = dF (I)
dI
> 0 for all I > 0.
3 Diminishing MPK: F ′′(I) = dF
′(I)
dI
< 0 for all I > 0.
4 limI→0 F
′(I) =∞.
Example: F (I) =

I.
Properties 1-4 guarantee that
the optimal investment condition has a unique solution and
that unique solution also maximizes profit.
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Graph: Production Function
Firm’s Production Function A2F (I1)
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Graph: Marginal Product of Capital (MPK)
Marginal Product of Capital A2F
′(I1)
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Graph: Firm’s Optimal Investment Decision
The firm chooses I1 so that A2F
′(I1) = (1+ r1).
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Household
Since the HH owns the firm, it receives the latter’s profits
Π1 = A1F (I0)− (1+ r0)Df0, (5)
Π2 = A2F (I1)− (1+ r1)Df1. (6)
The HH’s budget constraint in period 1 is:
C1 + B
h
1 = (1+ r0)B
h
0 + Π1, (7)
The HH’s budget constraint in period 2 is:
C2 + B
h
2 = (1+ r1)B
h
1 + Π2. (8)
We assume the transversality condition
B
h
2 = 0. (9)
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Intertemporal Budget Constraint, NIIP
By combining (7), (8) and (9) we obtain the HH’s
intertemporal budget constraint
C1 +
C2
1+ r1
= (1+ r0)B
h
0 + Π1 +
Π2
1+ r1
. (10)
The economy’s net foreign asset positions are
B0︸︷︷︸
NIIP
= Bh0︸︷︷︸
Domestic Supply
− Df0︸︷︷︸
Domestic Demand
, (11)
B1 = B
h
1 − Df1.
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Intertemporal Resource Constraint
By combining (4), (5), (6), (10) and (11), we obtain the
economy’s intertemporal resource constraint:
C1 +
C2
1+ r1
+ I1 = (1+ r0)B0 + A1F (I0) +
A2F (I1)
1+ r1
.
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Equilibrium
Exogenously given are r0,B
h
0 , r
∗, I0,D
f
0,A1 and A2. An
equilibrium is (C1,C2, I1, r1) such that:
1 Feasibility of the intertemporal allocation
C1 +
C2
1+ r1
+ I1 = (1+ r0)B0 + A1F (I0) +
A2F (I1)
1+ r1
.
2 Optimality of the intertemporal allocation
U1 (C1,C2) = (1+ r1)U2 (C1,C2) .
3 Interest rate parity condition
r1 = r

.
4 Optimal investment condition
A2F
′(I1) = (1+ r1).
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Analysis: Productivity Shocks
Now we can analyze the effect of productivity shocks.
Next slides: Positive Anticipated Future Productivity
Shock: Assume ∆ > 0 and that the period 2 technology
parameter changes to
A

2 = A2 +∆
while A1 remains unchanged.
1 How does this shock alter the firm’s optimal investment
decision?
2 How does the household react?
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Positive Productivity Shocks: Optimal Investment
Effect of a Positive Shock to A2 on the Production Function
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Positive Productivity Shocks: Optimal Investment
Effect of a Positive Shock to A2 on MPK
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Positive Productivity Shocks: Optimal Investment
Effect of a Positive Shock to A2 on the Optimal Investment
Productivity shocks affect the firm’s optimal investment.
Positive productivity shock: I1 ↑, output ↑, Π2 ↑.
Negative productivity shock: I1 ↓, output ↓, Π2 ↓.
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Household’s Reaction
Positive Anticipated Future Productivity Shock: HH’s Reaction
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Positive Anticipated Future Productivity Shocks
1 Change in optimal investment:
A2 ↑→ I1 ↑.
2 HH’s reaction, assuming that C1 is a normal good:
A2 ↑→ Π2 ↑→ S1 ↓.
Therefore, assuming that C1 is a normal good,
CA1 = S1 − I1
deteriorates following a positive anticipated future
productivity shock.
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Other Productivity Shocks
Other productivity shocks such as
negative anticipated future productivity shocks
temporary productivity shocks (A′1 6= A1, A′2 = A2)
permanent productivity shocks ([A′1 > A1, A

2 > A2] or
[A′1 < A1, A

2 < A2])
can be analyzed similarly.
The HH’s reaction to such a shock depends on
1 whether the shock is positive or negative,
2 whether the shock is temporary or permanent,
3 whether the shock is anticipated or not.
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Summary and Conclusion
Today, we studied:
1 Endowment economies.
Analysis of the effect of world interest rate shocks.
Policy analysis: import tariffs.
2 Production economies: Current account determination.
The firm’s optimal investment decision is a key aspect.
3 Production economies: Analysis of the effect of productivity
shocks on the CA.
Next week, we will study fiscal deficits and current
account imbalances.
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