1. Assume that a country's per-worker production is y = k 1/2, where y is output...

Question

1.

Assume that a country's per-worker production is
y
=
k
^1/2, where
y
is output per worker and
k
is
capitalper worker. Assume also that 10 percent of capital depreciates per year (d = 0.10).

a.	If the saving rate (s) is 0.4, what are capital per worker, production per worker, and consumption per worker in the steady state? (Hint: Use sy = dk and y = k ^1/2 to get an equation in s, d, k, and k ^1/2, and then solve for k.)[10 points]
b.	Solve for steady-state capital per worker, production per worker, and consumption per worker with s = 0.6. [5 points]
c.	Solve for steady-state capital per worker, production per worker, and consumption per worker with s = 0.8.[5 points]
d.	Is it possible to save too much? Why or why not? [5 points]

2.

Suppose a government is able to impose controls that limit the number of children people can have.
Use the Solow growth model to graphically illustrate the impact of the slower rate of population growth on the steady-state capital–labor ratio and the steady-state level of output per worker. Be sure to label the:
a. axes; b. curves; c. initial steady-state levels; d. terminal steady-state levels; and
e. the direction curves shift.[25 points]

3.

Suppose you are an economist working for the Federal Reserve when droughts in theSoutheast and floods in the Midwest substantially reduce food production in the United States.
Use the aggregate demand–aggregate supply model to illustrate graphically
your policy recommendation to accommodate this adverse supply shock, assuming that your
top priority is maintaining full employment
in the economy.
Be sure to label: i. the axes; ii. the curves; iii. the initial equilibrium values; iv. the direction the curves shift; and v. the terminal equilibrium values.
State in words what happens to
prices and output as a combined result of the supply shock and the recommended Federal Reserve accommodation.

[25 points]

4.

Assume the economy is initially in a short-run equilibrium at a level of output below the natural rate.

a.	Use the IS–LM model to graphically illustrate: (1) how the economy will adjust in the long-run if the no policy action is taken; and (2) the long-run equilibrium if fiscal policy is used to return the economy to the natural rate of output . [15 points]
b.	Explain how investment, the interest rate, and the price level differ in the new long-run equilibrium in the two cases.[10 points]

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David · Accepted Answer

Question 1.  
Assume that a country's per-worker production is y = k
1/2
, where y is output per worker and k 
is capital per worker. Assume also that 10 percent of capital depreciates per year (= 0.10). 
a. If the saving rate (s) is 0.4, what are capital per worker, production per worker, and 
consumption per worker in the steady state? (Hint: Use sy = k and y = k
1/2
 to get an 
equation in s, , k, and k
1/2
, and then solve for k.)[10 points] 
b. Solve for steady-state capital per worker, production per worker, and consumption per 
worker with s = 0.6.[5 points] 
c. Solve for steady-state capital per worker, production per worker, and consumption per 
worker with s = 0.8.[5 points] 
d. Is it possible to save too much? Why or why not? [5 points]
Answer 1. 
a. Since sy = k and y = k
1/2 
We can said s k
1/2 
=
 
k i.e. s=  k
1/2
 i.e. k = (s/

s = 0.40 and Hence k = 16 and y = k
1/2 = 
4  
Consumption per worker is 4*(1-0.4) = 2.4 
b. Since sy = k and y = k
1/2 
We can said s k
1/2 
=
 
k i.e. s=  k
1/2
 i.e. k = (s/

s = 0.60 and Hence k = 36 and y = k
1/2 = 
6 
Consumption per worker is 6*(1-0.6) = 2.4 
c. Since sy = k and y = k
1/2 
We can said s k
1/2 
=
 
k i.e. s=  k
1/2
 i.e. k = (s/

s = 0.80 and Hence k = 64 and y = k
1/2 = 
8 
Consumption per worker is 8*(1-0.8) = 1.6 
d. 
Yes, it is possible to save too much.

1. Assume that a country's per-worker production is y = k 1/2 , where y is output per worker and k is capitalper worker. Assume also that 10 percent of capital depreciates per year (d = 0.10). a. If...

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