Question
In: Economics
Consider an economy with a production function given by Y =K1/4 (EL)3/4 . The depreciation rate...
Consider an economy with a production function given by Y =K1/4 (EL)3/4 . The depreciation rate is = 0.1, the population growth rate is n = 0.02 and the technological growth rate is g = 0.03. The economy's current savings rate is s = 0.3 and the current level of capital per effective worker K0 = 1. Answer the following questions.
- What is the consumption per effective worker in the current year (C0) ?
- What is the capital per effective worker in the next period (k1) ?
- What is the steady state level of output per effective worker (y*) ?
- Find the golden rule level of output per-effective worker (yG) ?
- Compare the economy's savings rate with the golden-rule savings rate. Is the economy saving less ?
Solutions
Rahul Sunny answered 1 year agoRelated Solutions
Consider an economy with the following Cobb-Douglas production function: Y = K1/3L 2/3 .
Consider an economy with the following Cobb-Douglas production
function: Y = K1/3L 2/3 . The economy has 1,000 units of capital
and a labor force of 1,000 workers. 1a. Derive an equation describing labor demand as a function of
the real wage and the capital stock. (Hint: this is a review from
what we did in Chapter 3)b. If the real wage can adjust to equilibrate labor supply and
labor demand, what is the resulting equilibrium real wage? In this...
Consider an economy with the following production function: Y = K1/2N1/2. The economy has 1,000 units...
Consider an economy with the following production function: Y =
K1/2N1/2. The economy has 1,000 units of capital and 1,000
workers.
a) Derive the labor demand curve for this economy, (Recall that
the real wage, w = MPN. This can be used to solve for N as a
function of the other variables).
b) If the real wage can adjust to equilibrate labor supply and
labor demand, what is the real wage rate?
c) Suppose that Congress, concerned about the...
Consider the following Cobb Douglas production function: Y= K2/5L3/5. The rate of depreciation in the economy...
Consider the following Cobb Douglas production function: Y=
K2/5L3/5. The rate of depreciation in the
economy is 2% and the marginal propensity to save (mps) is 30%. Any
output that is not saved is consumed and this is a closed economy.
Population growth rate is zero.
1. Continue with the same data with the exception that mps is
unknown. Solve for the rate of investment which
will ensure golden rule of consumption per capita
2. Continue with the same data...
Suppose that the economy’s production function is Y = K1/2 (AN)1/2 , that the saving rate,...
Suppose that the economy’s production function is Y =
K1/2 (AN)1/2 , that the saving rate, s is
equal to 16%, and that the rate of depreciation, ?, is equal to
10%. Suppose further that the number of workers grows at
2% per year and that the rate of technological progress is 4% per
year.
Find the steady values of the variables listed in (i) through
(v).
The capital stock per effective worker.
Output per effective worker.
The growth rate of...
Assume that a production function is given by y = AK^1/3 L^2/3. If A = 6 and L = 1, the depreciation rate is 0.15
Assume that a production function is given by y = AK^1/3 L^2/3.
If A = 6 and L = 1, the depreciation rate is 0.15, and the savings
rate is 0.4, the steady-state level of capital is?
Consider an economy in which the production function is given by Y = 6K1/2N1/2.(a) Derive the...
Consider an economy in which the production function is given by
Y = 6K1/2N1/2.(a) Derive the per-worker production function: Y/N =
f(K/N). (Hint: A short-cut to get the per-worker production
function is to keep the constant, write the ratio (K/N) and then
raise the ratio by the same exponent on capital (K).Assume that the
depreciation rate is 15% per year and the savings rate is 10% per
year.(a) Solve for the steady-state level of capital per worker
(K/N).(b) Solve for...
QUESTION Consider the following Cobb Douglas production function: Y= K2/5L3/5. The rate of depreciation in the...
QUESTION
Consider the following Cobb Douglas production function: Y=
K2/5L3/5. The rate of depreciation in the
economy is 2% and the marginal propensity to save (mps) is 30%. Any
output that is not saved is consumed and this is a closed economy.
Population growth rate is zero.
Continue with the same data with the exception that mps is
unknown. Solve for the rate of
investment which will ensure golden rule of
consumption per capita . Show
all the steps covered...
Suppose that output (Y ) in an economy is given by the following aggregate production function:...
Suppose that output (Y ) in an economy is given by the following
aggregate production function: Yt = Kt + Nt where Kt is capital and
Nt is the population. Furthermore, assume that capital depreciates
at rate δ and that savings is a constant proportion s of income.
You may assume that δ > s. 1. Suppose that the population
remains constant. Solve for the steady-state level of capital per
worker. 2. Now suppose that the population grows at rate...
Suppose that output (Y ) in an economy is given by the following aggregate production function:...
Suppose that output (Y ) in an economy is given by the following
aggregate production function: Yt = Kt + Nt where Kt is capital and
Nt is the population.
Furthermore, assume that capital depreciates at rate δ and that
savings is a constant proportion s of income. You may assume that δ
> s.
1. Suppose that the population remains constant. Solve for the
steady-state level of capital per worker.
2. Now suppose that the population grows at rate...
Consider the Solow model for an economy with a population growth rate of 4%, a depreciation...
Consider the Solow model for an economy with a population growth
rate of 4%, a depreciation rate of 12%, a savings rate of 20%, and
a production function of Y=5K1/2N1/2
What would the golden-rule savings rate be? Explain what the
golden-rule savings rate achieves.
Explain what policymakers can do in order to achieve the
golden-rule savings rate.
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