Week 3 Endowment

Question 1

What is the two period budget constraint for a small open economy which has no production.

Explain each part of equation

Answer 1

C1 + B1 -B0 = r0B*0 + Q1

RHS is income created in period 1
Q1 is endowment (resources falling)
r0B*0 is Net Investment Income (Can be negative or positive depending if has debt or not).

LHS is expenditure
Consumption (use them)
B1 - B0 (you either increase or decrease amount of assets)

Question 2

1. What does a small and open economy mean?

Give examples of developed small open economies?

Answer 2

1. Small means:
   A country that has little role on world prices and interest rate.

Open means:
Economy is open when it trades with the rest of the world.

2. Switzerland

Question 3

1. What are the sequential budget constraints for small open economy with no production and how do we get intertemporal?

2 .What is an important assumption and why does this hold?

Answer 3

C1 + B1 - B0 = r0B0 + Q1
C2 + B2 - B1 = r1B1 + Q2

2. Then assume transversality condition B*2 = 0. As the world ends in period 2 no one would save and as you can’t pay the debt back no one will loan.

Then eliminate B*1 from both equations .

Yields IBC

C1 + C2 / 1+r1 = (1+r0)B*0 + Q1 + Q2 /1+r1

Question 4

Explain the aspects of the IBC for small open economy with no production?

Answer 4

C1 + C2 / 1+r1 = (1+r0)B*0 + Q1 + Q2 /1+r1

LHS is presented discounted value of consumption
RHS = Given and exogenous to household. Present discounted value of initial wealth.

Question 5

What is the gradient of the IBC of small open economy no production?

Answer 5

• -(1+r)

-This is the relative price of consuming 1 more unit in the 2nd period.
-As if you sacrifice 1 period of consumption in period 1 you can put it in the bank and get 1+r1 next period.

Question 6

1. Draw the IBC small open economy with no production graph.
   Outline all labels
2. What does it show?

Answer 6

1. X axis = C1. Q1 + Q2 / 1+r
   Y axis = C2. (1+r)Q1 + Q2

Downward sloping straight line

2. All the bundles below the line are feasible given the IBC.

Question 7

What properties would the lifetime utility function lnC1 + lnC2 have?

Answer 7

Additive - you would like to consume in both periods.

Concave - averages are better than extremes.

Question 8

Graphically do you always consume endowment, if not why is this?

Answer 8

No, as you could borrow and be on a higher indifference curve within the feasible set.
-You get some debt in period 1 that you repay in period 2.

Question 9

Graphically how does a consumer optimise lifetime utility.

Answer 9

Indifference curves are tangent to IBC

MRS = (1+r)

Question 10

1. With a simple lifetime utility function of lnC1 + lnC2 and IBC of C1 + C2 / 1+r1 = w how do you derive optimal consumption?
2. Comment on answer
3. What if you want it in terms of exogenous variables

Answer 10

1. First make IBC in terms of C1

Then do MU = (1+r)

Then sub C1 or C2 to eliminate.

Then you get

C1 = 1/2w

2. This answer is intuitive as they would want to smooth consumption.

C2 = 1/2w (1+r1) This is also intuitive as they get the other 1/2w and put it back in the bank and earn it for consumption next period.

3. C1 = 1/2 [ (1+r0)B*0 + Q1 + Q2/ 1+r1]

Question 11

Thinking about C1 = 1/2[ (1+r0)B*0 + Q1 + Q2/1+r1].

Can you explain how changes in this variables would impact consumption?

What if Q1 only increases?

What if Q1 and Q2 increase in the same magnitude?

Answer 11

To find response of C1 to Q1 it is 1/2 this follows intuition as increase in endowment in period 1 not followed in period 2 makes you want to smooth consumption due to log utility function.

-Derivative 1+r1/2 / 1+r which is close to 1 so they will consume extra endowment in both periods.

Question 12

What is the interest rate in a small open economy and why is this?

Answer 12

r1 = r*

As any difference between r1 and r* would give rise to arbitrage opportunity.

if r1 > r*

Could make infinite profits from borrowing in international and lending in domestic.

if r* > r1 you could make infinite profits from borrowing in domestic and saving in international.

These infinite profits are not possible when r1 = r*

Question 13

1. What would happen to the current account if there is a temporary output shock in period 1.

(Small open economy with no production).

2. What does this tell us about the usage of a current account?

Answer 13

1.
Means change in Q1> 0 and Change in Q2 = 0

Change in CA = 1/2 Change Q1

As household’s know that the change in output is temporary they save half for next period

This improves the CA as it is Saving - Investment.

2. CA is a way to move consumption between periods.

Question 14

1. What would happen to the CA in a temporary decrease in output in period 1

Also explain grahpcially

Answer 14

This would shift the IBC inwards.

The consumer would decrease consumption but not 1 to 1 with the decrease in output.

They use the CA as an asset to transfer consumption through periods as they know output in not affected in period 2.

Rather than decreasing across the horizontal line this would be 1 to 1 but you want to decrease less than 1 to 1.

Question 15

What would happen to the CA if there is a permanent increase in output?

Answer 15

• Change in Q1 = Change in Q2 > 0

Change in CA = 1/2 [ change in Q1 - Change in Q2 / 1+r*]

Sub in Q1 = Q2

Change in CA1 = 1/2 r* / 1+r* change in Q1

As the interest rate is small number will be close to 0.

This shows when output is permanent the CA is not used to transfer resources from one period to another.

Question 16

How can you explain the usage of the CA in real life terms.

Answer 16

If you forget your lunch money one day you borrow from a friend and still eat.

However, if your lunch allowance gets completely cut you reduce spending accordingly.

Therefore, you use current account to finance temproary shocks and change spending to react to permanent shocks.

Question 17

What is terms of trade and why is it important in terms of shocks?

• Give formula

Answer 17

-Some countries like Norway mainly export Oil and must import food from countries like italy (Pizza).

This means if the relative price of oil changes compared to pizza this impacts them.

If the relative price of Oil decreased compared to pizza it would have shock on TB, CA and consumption.

-TT = PX / PM

Question 18

1. How do you compute the IBC for terms of trade shock?

2.

Answer 18

1. Start with
   PM . C1 + PM . B1 - PM . B0 = PM . r0B0 + PX . TT1
   Then shift a period forward
   PM . C2 + PM . B2 - PM . B1 = PM . r1B1 + PX . TT2

Then due to transversality condition we can eliminate B2
Then eliminate B1 from both sides.

This gives C1 + C2 / 1+r1 = (1+r0)B*0 + TT1 Q1 + TT2Q2/ 1+r1

2. Terms of trade is given.

Question 19

1. How can we think of terms of trade in no production economy?

How does this link to endowment?

Answer 19

1. Terms of trade simply shifts endowment.

Even if country has the same amount of oil, if the price increases it will increase wealth.

Therefore, changes in terms of trade are exactly the same as changes in endowment.

2. You can think of it exactly like an increase in endowment.

Question 20

How does terms of trade link to the current account?

Answer 20

-We can finance temporary terms of trade shocks by using the CA.
-We can adjust to permanent terms of trade shocks by permanently adjusting spending.

Question 21

What does the Chile Copper Case study teach us about Terms of Trade and CA?

Answer 21

Sometimes there may be a permanent terms of trade shock but it may be interpreted as a temporary one and hence CA will improve as they will save to smooth consumption.

Question 22

What is the impact of an interest rate shock?

(Increase in interest rate)

Answer 22

• Substitution effect
• Reward for saving increases so C down
  -TB goes up
  -CA goes up.

Income effect
debtor - C1 down, TB up, CA up
creditor - C1 up, TB down, TB down.

Question 23

What effect dominates between substitution effect and income effect?

Answer 23

Substitution effect dominates:

Question 24

How does the income effect vary?

Answer 24

An increase in interest rate makes creditors richer and debtors poorer.

Creditors:
If interest rate increases, this means repayment increases so income increases

Debtors:
Interest repayment increases so wealth decreases.

Question 25

In a log model with IBC how can we see from the equations the impact of the interest rate on consumption TB, CA.

Answer 25

C1 = 1/2 [ (1+r0)B0 + Q1 + Q2/ (1+r) ]
TB = 1/2 [ -(1+r0)B0 + Q1 -Q2/ (1+r) ]
CA = 1/2 [ [ -(1+r0)B0 + Q1 -Q2/ (1+r)] ]

As 1 +r os the denominator of Q2 an increase in interest rate decreases consumption

For TB as it is a negative term

Question 26

Graphically how is an increase in world interest shock shown with log preferences and IBC?

Answer 26

• The increase in interest rate will change the gradient of the IBC and therefore, make the new IBC more steeper.

-However, both the new and the old IBC go through endowment point.

-This means what was originally feasible is no longer feasible as borrowing is more costly.

-Therefore, welfare decreases as they are forced to consume on a lower utility level.

Question 27

Graphically how can the wealth effect and income effect be presented with an increase in the interest rate?

Answer 27

• Wealth effect is represented that the initial feasible set is no longer affordable.

-Substitution effect, increase r makes future consumption more attractive.

Question 28

What are capital controls?

What could be an example of a strict capital control?

Answer 28

-Efforts to limit borrowing to reduce CA deficits.

-B*1 or equaled to 0.

Question 29

What is the implication of borrowing contraints?

Answer 29

• Leads to a welfare loss as before the constraint you are on a higher level of utility.
  You can only borrow at a constrained point.

Question 30

What is something else that an economy can do if they have borrowing contraints and what impact does this have to the graph?

Answer 30

If borrowing constraints are there it means that the economy can control domestic interest rate

-Graphically they can keep increasing domestic interest rate (tilting) to the point which is tangential to A.

-We can make the constrained equilblrium an optimal one from the point of view of the household.