Solutions to Midterm ExamSolutions to Midterm Exam

Part I

Question 1: (b),    Question 2: (c),    Question 3: (d),    Question 4: (b),
Question 5: (d)


Question 6

When a young and an old person trade together, the lender has no way to enforce the contract. If a young lends to an old in period t, the old never pays off its debt since he is dead in period t+1. If an old lends to a young, the old will not enjoy the payoff from his lending since he will be dead next period.


Question 8

The competitive equilibrium is the set of interest rates

{r(1), r(2), r(3), r(4), ... } = {1.0714, 1.4286, 1.0714, ... },
the consumption allocation
{ch1(1), ch2(2), ch3(3), ... } = { 4, 3, 4, ... }    for  h = 1, ..., 100
{ch0(1), ch1(2), ch2(3), ... } = { 3, ... }    for  h = 1, ..., 100,
and the government policy
{G(1), G(2), G(3), ... } = {0, 100, 0, ... }
{th1(1), th2(2), th3(3), ... } = { 0, 1, 0, ... }    for  h = 1, ..., 100,
{th0(1), th1(2), th2(3), ... } = { 0, ... }    for  h = 1, ..., 100.


Question 9

The competitive equilibrium is the set of interest rates

{r(1), r(2), r(3), r(4), ... } = {1.0714, 1.7647, 1.3636, 1.1115, 1.0714, ... },
the consumption allocation
{ch1(1), ch2(2), ch3(3), ... } = { 4, 3, 3.2942, 3.8557, 4, ... }    for h = 1, ..., 100
{ch0(1), ch1(2), ch2(3), ... } = { 3, 3, 3.7059, 3.1443, 3 ... }    for h = 1, ..., 100,
and the government policy
{G(1), G(2), G(3), ... } = {0, 100, 0, ... }
{B(1), B(2), B(3), ... } = {0, 70.5841, 14.4316, 0 ... }
{th1(1), th2(2), th3(3), ... } = { 0, 0.6, 0.60, 0.1443, 0 ... }    for  h = 1,..., 100,
{th0(1), th1(2), th2(3), ... } = { 0, ... }    for  h = 1, ..., 100.


Question 10

There are many ways to answer that question. Here is what I would have done.
utilityconsu question 8 question 9
Q8 Q9
ch0(1) 3 3
uh1 2.1553 2.1553
uh2 1.8676 2.0156
uh3 2.1553 1.9941
uh4 2.1553 2.1186
uh5 2.1553 2.1553

On the one hand, policy in Q8 imposes large utility losses on generation 2 but the following generations get the maximum utility they can get.

On the other hand, policy in Q9 spreads the utility losses over three generations.

Personally I prefer policy Q9. The people born in period 2 are not responsible in any way for the disaster so I don't think they should be the only one to absorb all the costs. You may argue that people in period 4 should not have to suffer from the disaster that occurred 2 periods ago.


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