Question
In: Economics
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 n. Solve for the steady-state level of capital per worker. 3. Based on your answer to part 2) above, solve for the steady-state growth rates (in terms of n) of the following: (a) capital per worker (b) output per worker (c) capital (d) output
Solutions
Rahul Sunny answered 2 years agoRelated Solutions
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 the production function for output in an economy is given by Yt=Kt0.25N0.75 The number...
Suppose that the production function for output in an economy is
given by
Yt=Kt0.25N0.75
The number of workers, N, is constant. The saving rate
is s, and the depreciation rate of physical capital is
δ.
a) Write down the equation showing the
evolution of physical capital stock over time. Explain in
words.
b) Derive the steady
state levels of capital per worker and output per worker in terms
of the saving rate (s) and the depreciation rate
(δ).
Suppose the aggregate production function is given by Y = K0.5L0.5. Does it have increasing, decreasing...
Suppose the aggregate production function is given by Y =
K0.5L0.5. Does it have increasing, decreasing or constant returns
to scale? Show that the marginal products of capital and labour are
declining. Show that they are increasing in the input of the other
factor.
Consider an economy described by the aggregate production function Y=f(K,L)=KEL^(1/2) Where Y is the total output,...
Consider an economy described by the aggregate production
function
Y=f(K,L)=KEL^(1/2) Where Y is the total output, K is the total
capital stock, E is the efficiency of labour, and L is the total
labour force.
Assume this economy has a population growth of 5%, a
technological growth rate of 10%, and a depreciation rate of 20%.
Use the Solow model with population growth and labour-augmenting
technological progress to answer the following questions:
Assume this economy has a population growth of...
Consider an economy described by the aggregate production function Y=f(K,L)=(KEL)^(1/2) Where Y is the total output,...
Consider an economy described by the aggregate production
function Y=f(K,L)=(KEL)^(1/2) Where Y is the total output, K is the
total capital stock, E is the efficiency of labour, and L is the
total labour force. Assume this economy has a population growth of
5%, a technological growth rate of 10%, and a depreciation rate of
20%. Use the Solow model with population growth and
labour-augmenting technological progress to answer the following
questions: Assume this economy has a population growth of...
Suppose that an economy's production function is given as Y=A·K2-L1/2, and the price of output, nominal...
Suppose that an economy's production function is given as
Y=A·K2-L1/2, and the price of output, nominal wage rate, and the
rental price of capital are given as P, W, and R, respectively.
i) Derive the demand for labor (Lº) as a function of real wage
(W/P), using a representative firm's profit maximization. That is,
solve the problem of Max [P·Y– (W-L + R:K)] for L.
(ii) If the capital stock doubles (from 'K' to '2K'), how much
is the demand...
Suppose a country has the production function Y = 2 √?, where Y = output and...
Suppose a country has the production function Y = 2 √?, where Y
= output and K = physical capital. People devote 30% of output to
producing new capital goods ( = 0.30). Further assume that capital
depreciates at the rate of 3 percent per period (δ = 0.03).
a. Suppose that the country invested in 6 units of new capital
in the current period. By how many units will output change in the
next period?
b. What are the...
Suppose Canada’s aggregate production function is given by the following: Y = (K*1^3)(N*2^3) Variables are defined...
Suppose Canada’s aggregate production function is given by the
following:
Y = (K*1^3)(N*2^3)
Variables are defined as they were in class. Suppose the savings
rate in Canada is 33.33% (s = 1 3) and the depreciation rate is 15%
(δ = 0.15). Assume that Canada is not currently experiencing any
technological change.
a) Calculate the steady-state level of capital per worker
and output per worker in Canada’s economy.
b) Determine the annual growth rate of output per
worker in Canada....
Suppose that the production function for the economy is Y = AK0.25L0.75, A = 2, K...
Suppose that the production function for the economy is Y =
AK0.25L0.75, A = 2, K = 100,000, and L = 60,000. What are the
values of real GDP, the real wage, and the real rental cost of
capital? Show this data using graphs of the aggregate production
function, the aggregate capital market, and the aggregate labor
market. Really need help on this ASAP!!
Suppose a closed economy has an aggregate consumption function given by C = 200 + 0.50Yd and generates $2400 output and income in equilibrium
2Suppose a closed economy has an aggregate consumption function
given by C = 200 + 0.50Yd and generates $2400 output and income in
equilibrium. Suppose also that the government collects a lump-sum
tax of 100.How much will the private sector be saving total in
equilibrium?3Suppose a closed economy generates $2500 output and income in
equilibrium. Suppose also that the government spends 350 and
imposes a lump-sum tax of 100.By how much is the government in deficit?
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