1

. Assume an economy has a product

i

on function of:

Y = AK.

3

5L.65 with: A = 1, K = 1

0

0 and L =

4

0. There is no labor force growth and technology remains constant.

(a) Find the level of Y for this economy. Find the levels of y and k.

(b) Assume that the capital stock in this economy depreciates at 10%/year and the savings rate out of GDP is

2

5%. What would be the steady state level of y, k, c and i?

(c) Find the golden rule savings rate for this economy. What would be the new level of steady state y, k, c and i if the economy moved to the golden rule savings rate? What would be the values for y, c, s, and k if the economy increased its savings rate by 5% above the golden rule savings rate?

(Round all answers to 2 decimal places)

Fill in as table and show calculations separately.

Steady State

Golden Rule

Steady State with Savings

Savings Rate

Savings Rate

Five Percent Over Golden Rule

y

k

c

i

2. Taylor Rule

Assume an economy with an AE curve with a slope of 1 where a one percent change in real interest rates changes real GDP by 1 percent with a one year lag. This economy is also characterized by an ouput gap Phillips curve where a one percentage point change in the output gap affects inflation with a one year lag. From Okun’s law for this economy a 1 percent change in real GDP changes the unemployment rate by .5%. The natural rate of unemployment for this economy is 5%. The neutral real rate of interest rn = 3.0 %/ and the target rate of inflation ΠT = 2%.

Assumes that policy makers inherit an economy at its natural rate of unemployment (5%), 6 percent inflation in year 0, and decide to use an aggressive Taylor rule of:

r = 3% + 1.0 (Y-Y*/Y*) + 1.0 (Π – 2%)

Fill in the following table assuming that policy makers have a correct model of the economy, follow the aggressive Taylor rule, and the economy has the two one period lags. Remember that in each year the policy choice for the real interest rate changes. (Your policy choice in year 0 affects GDP in Y in year 1 and how that policy affects GDP in year 1 affects inflation in year 2.

Hint. Use the Taylor rule to pick r in period 0 based on information in table. That r chosen for year 0 will have an impact on Y (and u based on Okun’s law) in year 1, but will have no impact on inflation until year 2 depending on the output gap that opens up in year 1.

0

Yea r |
r |
Π |
Y |
(Y-Y*/Y* |
Π-ΠT |
u |
i |

(policy) |
ouptut gap |
nominal |
|||||

interest rate |
|||||||

0 |
6.0 |
100.0 |
4.0 |
5.0 |
|||

1 | |||||||

2 | |||||||

3 | |||||||

4 |