Week 5 Uncertainty

Question 1

Why add uncertainty into the 2 period model for economy?

Answer 1

As it is not true that agents know how much endowment they will receive in the next period.

Question 2

How do you measure uncertainty?

Answer 2

You look at macro indicators and look at stdeviation.

Question 3

What is the great moderation?

Answer 3

After the mid 1980s macreconomic volatility decreased.

Question 4

How do we add uncertainty into the model?

Answer 4

There are two states that both happen with p(1/2)
-Q - stdv bad state
-Q + stdv good state

Question 5

1. How does the utility function change?
2. How does the budget constraint change?

Answer 5

1. ln(c1) + Eln(c2)
   The second period is an expectation operator.
2. BC good state =

Question 6

What implication does uncertainty have on C, TB and CA?

Answer 6

-As we are evaluating utility through a concave logarithm function

-Any negative state is extremely costly even if the expected value this is the same.

-Therefore, you will consume less than the endowment in period 1 in case you get the bad scenario you have more resources in the second period.

-Consumption decreases

-TB increases

-CA increases

Question 7

What phenomena is caused by having uncertainty?

What does uncertainty do to trade balance and current account?

Answer 7

-Pre-cautionary saving.

-Trade balance increases

-Current account increases.

Question 8

Does symmetric probability cause symmetric effects?

Answer 8

even though probability is symettric and expectation may be the same in uncertainty.

-As it makes you evaluate bad and good outcomes differently.

-As utility is measured through a non-linear concave logarithm function, bad states are evaluated as even worse.

Question 9

Set up the utility maximisation problem with uncertainty.

Find the F.O.C and explain it

Answer 9

U function ln(c1) + Eln(c2)

BC good state: C2 = Q1 + stdv + C1
BC bad state C2 = Q1 - Stdv - C1

Then ln(c1) + 1/2ln(C2 = Q1 + stdv - C1) + 1/2ln(Q1 - Stdv - C1)

FOC W.R.T C1

1/C1 = 1/2[ 1/ Q1 +stdv - C1 + 1/ Q1 - Stdv -C1]

LHS is the MU of consuming in period 1
RHS is the MU of not consuming in p1

Question 10

What does the F.O.C imply

Answer 10

if you sub in Q= C1 into the FOC

The F.O.C only holds if sigma = 0

Hence in uncertainty:
they consume less than endowment.

You want to lower consumption in period 1 in order to equate the marginal utilities as it is so costly to get a bad outcome in period 2.

-So even if worst scenario happens you still have resources to consume in period 2