Partial Solutions to Assignment 3
Partial Solutions to Assignment 3
Complete solutions on reserve in Stauffer Library

Question 1

(a)

There are 10 bonds issued in period 2. 7 more bonds are issued in period 3 so that the total number of bonds is 17. 3 more bonds are issued in period 4 so that the total is 20.


(b)

r(5) = 1.2987


(c)

r(4) = 1.3633, p1(4) = 0.7335, G(4) = 2.2006.


(d)

r(3) = 1.3110, p2(3) = 0.5595, G(3) = 3.9165.


(e)

r(2) = 1.2633, p3(2) = 0.4429, G(2) = 4.4288.


(f)

r(1) = 1.2245


(g)

The perfect foresight competitive equilibrium for this economy is the set of interest rates

{r(1), r(2), r(3), ... } = {1.2245, 1.2633, 1.3110, 1.3633, 1.2987, 1.2245, ... },
the set of government bonds prices
{p3(2), p2(3), p1(4), p0(5)} = {0.4429, 0.5595, 0.7335, 1}
the consumption allocation

for h even

{ch1(1), ch2(2), ... } = { 3.7941, 3.7498, 3.699, 3.6474, 3.5941, 3.7941, ... }
{ch0(1), ch1(2), ... } = { 3, 3.2521, 3.3161, 3.3946, 3.4807, 3.2674, 3.2521, ... }

for h odd

{ch1(1), ch2(2), ... } = { 3.2059, 3.1616, 3.1108, 3.0591, 3.0059, 3.2059, ... }
{ch0(1), ch1(2), ... } = { 3, 2.7480, 2.7958, 2.8548, 2.9194, 2.7326, 2.7479, ... }
and the government policy
{G(1), G(2), G(3), ... } = {0, 4.4288, 3.9165, 2.2006, 0, ... }
{B3(2), B2(3), B1(4)} = {10, 17, 20 }
{th1(1), th2(2), th3(3), ... } = { 0, 0, 0, 0, 0.2, 0,... }    "h
{th0(1), th1(2), th2(3), ... } = { 0, ... }    "h.


(h)

As we move from period 1 to 4, more and more bonds are sold each period. Therefore savings must increase so that agents are able to buy the bonds supplied.

The savings market pushes the interest rate up over time make sure more and more savings are generated by the private sector.


(i)

In period 3, the government issues [^(B)]2(3) bonds. Therefore agents must save p2(3) [^(B)]2(3) to be able to buy these bonds. However, people who where young in period 2 bought B3(2) bonds in period 2. Since they die at the end of period 3, they want to sell their B3(2) bonds in period 3. To be able to buy these bonds, period 3 young must save p2(3) B3(2). Therefore, total savings in period 3 must satisfy

S3(r(3)) = p2(3) B3(2)+p2(3) ^
B
 
2 
 (3) = p2(3)[B3(2)+ ^
B
 
2 
 (3)] = p2(3) B2(3).

Question 2

(a)

The TSIR in period 1 is

{r1(1), r1(2), r1(3)} = {1.0742, 1.0773, 1.08}

(b)

Using the formula given, the prediction for r(3) is 1.0854. This is to be compared to the value for r(3) = r1(3) in the data which is 1.08.


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