Question

Consider an economy described by the production function:

*Y = F(K, L) = K ^{0.3}L^{0.7}.*

**Assume that the depreciation rate is 5 percent per year.
Make a table showing steady-state capital per worker, output per
worker, and consumption per worker for saving rates of 0 percent,
10 percent, 20 percent, 30 percent, and so on. Round your answers
to two decimal places. (You might find it easiest to use a computer
spreadsheet then transfer your answers to this table.)**

Steady State Values for Various Saving Rates | ||||

s | k* | y* | c* | |

Depreciation Rate: | 0.0 | |||

(0.05) | 0.1 | |||

0.2 | ||||

0.3 | ||||

0.4 | ||||

0.5 | ||||

0.6 | ||||

0.7 | ||||

0.8 | ||||

0.9 | ||||

1.0 |

**What saving rate maximizes output per worker? What
saving rate maximizes consumption per worker?**

A saving rate of percent maximizes output per worker. A saving rate of percent maximizes consumption per worker.

Answer #1

Y = K^{0.3}L^{0.7}

Output per worker (y) = Y / L = (K/L)^{0.3} =
k^{0.3} where k = K/L

When s: Savings rate, in steady state,

s / = k / y

s /
= k / k^{0.3}

s /
= k^{0.7}

Capital per worker (k*) = [s /
]^{(1/0.7)} = [s /
]^{1.43}

Output per worker (y*) = k^{0.3} = [s /
]^{(0.3/0.7)} = [s /
]^{0.43}

Consmption per worker (c*) = yY - sy* = y* x (1 - s) = [s /
]^{0.43} x (1 - s)

When = 0.05,

k* = (s / 0.05)^{1.43}

y* = (s / 0.05)^{0.43}

c* = (s / 0.05)^{0.43} x (1 - s)

Therefore:

s | k* | y* | c* |

0 | 0 | 0 | 0 |

0.1 | 2.69 | 1.35 | 1.21 |

0.2 | 7.26 | 1.82 | 1.45 |

0.3 | 12.96 | 2.16 | 1.51 |

0.4 | 19.56 | 2.45 | 1.47 |

0.5 | 26.92 | 2.69 | 1.35 |

0.6 | 34.93 | 2.91 | 1.16 |

0.7 | 43.55 | 3.11 | 0.93 |

0.8 | 52.71 | 3.29 | 0.66 |

0.9 | 62.38 | 3.47 | 0.35 |

1 | 72.52 | 3.63 | 0.00 |

**A savings rate of 100% maximizes output per
worker.**

**A savings rate of 30% maximizes consumption per
worker.**

Assume that an economy is described by the Solow growth model as
below:
Production Function: y=50K^0.4 (LE)^0.6
Depreciation rate: S
Population growth rate: n
Technological growth rate:g
Savings rate: s
a. What is the per effective worker production function?
b. Show that the per effective worker production function
derived in part a above exhibits diminishing marginal returns in
capital per effective worker
C.Solve for the steady state output per effective worker as a
function of s,n,g, and S
d. A...

Assume that an economy described by the Solow model has the
production function Y = K 0.4 ( L E ) 0.6, where all the variables
are defined as in class. The saving rate is 30%, the capital
depreciation rate is 3%, the population growth rate is 2%, and the
rate of change in labor effectiveness (E) is 1%.
For this country, what is f(k)? How did you define lower case
k?
Write down the equation of motion for k....

Portugal has the following per-worker production function:
y=3k^0.05
Depreciation rate is 0.08, population growth rate is 0.02.
Saving is S=0.2Y, where S is national saving and Y is national
output.
(a) what are the steady state value of capital-labour ratio,
output per worker and consumption per worker?
(b) Suppose that national saving increases to 0.4, what are the
steady state value of capital-labour ratio, output per worker and
consumption per worker?
(c) Suppose depreciation rate increases to 0.20, what are...

Consider an economy described by the following production
function: ? = ?(?, ?) = ?^1/3 ?^2/3
depreciation rate is 5 percent (? = 0.05)
the population grows at 2 percent (n = 0.02)
savings rate is 20 percent (s = 0.20)
f) At what rates do the following grow at in the steady state:
[3 points]
a. Capital per worker, k:
b. Output per worker, y:
c. Total output, Y:

Consider the production function Y = F (K, L) = Ka *
L1-a, where 0 < α < 1. The national saving rate is
s, the labor force grows at a rate n, and capital depreciates at
rate δ.
(a) Show that F has constant returns to scale.
(b) What is the per-worker production function, y = f(k)?
(c) Solve for the steady-state level of capital per worker (in
terms of the parameters of the model).
(d) Solve for the...

17. Solow growth The production function in your country is: Y =
K^0.5(LE)^0.5.
Your economy saves 24% of output each period, and 5% of the
capital stock depreciates each period. The population grows 2%
annually. Technology grows 1% annually. You begin with 1000 workers
and 1 unit of capital, and a tech- nology level equal to 1.
a) Write the production function in per-eective-worker terms, so
that per-effective-worker output (y = Y/LE ) is a function of
per-effective-worker capital (k=...

Assume that the production function in an economy is given by
y=k1/2, where y and k are the per-worker levels of output and
capital, respectively. The savings rate is given by s=0.2 and the
rate of depreciation is 0.05. What is the optimal savings rate to
achieve the golden-rule steady state level of k?

Answer the following
Y = f(k) = ka, where a = 0.25
S = 0.3
δ = 0.2
n = 0.05
g= 0.02
a. Find the steady state capital per effective worker, output
per effective worker, investment per effective worker, and
consumption per effective worker.
b. Find the steady state growth rate of capital per worker,
output per worker, investment per worker, and consumption per
worker.
c. Find the steady state growth rate of capital, output,
investment, and consumption.
d....

Use information to answer questions below.
Y = f(k) = ka, where a = 0.25
S = 0.3
δ = 0.2
n = 0.05
g= 0.02
a. Find the steady state capital per effective worker, output
per effective worker, investment per effective worker, and
consumption per effective worker.
b. Find the steady state growth rate of capital per worker,
output per worker, investment per worker, and consumption per
worker.
c. Find the steady state growth rate of capital, output,
investment,...

2. Consider a numerical example using the Solow growth model:
The production technology is Y=F(K,N)=K0.5N0.5 and people consume
after saving a proportion of income, C=(1-s)Y. The capital per
worker, k=K/N, evolves by (1+n)k’=szf(k)+(1-d)k.
(a) Describe the steady state k* as a function of other
variables
(b) Suppose that there are two countries with the same steady
state capital per worker k* and zero growth rate of
population(n=0), but differ by saving rate, s and depreciation
rate, d. So we assume...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 51 seconds ago

asked 51 seconds ago

asked 51 seconds ago

asked 2 minutes ago

asked 5 minutes ago

asked 6 minutes ago

asked 14 minutes ago

asked 15 minutes ago

asked 15 minutes ago

asked 15 minutes ago

asked 17 minutes ago

asked 19 minutes ago