Question

Consider the following Cobb-Douglass production function?≡??(?,?):?=??1/3?2/3

where Y is output, the constant z measures productivity, K is physical capital, and N is labor. Suppose ?=2, ?=0.16, ?=0.06, and ?=0.02.

a. What are the steady-state (numerical) values of ?, ?, and ??

b. What is the golden-rule (numerical) level of capital per worker?

c. If the government wants to achieve the golden rule level of k, should savings increase, decrease or remain unchanged? Solve for/obtain its (numerical) value. Explain briefly.

Answer #1

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?

Assuming the following Cobb-Douglas production
function is given for a closed economy without government.
i. Where returns to capital = 0.5; and rate of
depreciation of physical capital
Determine the steady-state level of capital per worker. What is the
savings rate at which the steady-state level of capital is
achieved?
[6marks]
ii Prove that the steady-state level of output is the
ratio of the saving rate to the rate of
depreciation
[6 marks]
iii. Assuming that , what will be...

A closed economy has the following Cobb-Douglas production
function: F(KL) = K2/5 (EL)3/5, where the notation is as in class.
The depreciation rate is 1.5% and the saving rate is 20%. The
economy is in steady state, where the population decreases at a
rate 1% and capital K increases at a rate 1%. (a) Find the growth
rates of the following variables (i) labor efficiency, E (ii) the
number of workers per machine, L/K (iii) the average productivity
of capital,...

Suppose an economy is described by the following production
function:
Y = K1/2 (EL)1/2
The savings rate in the economy is 0.40, population is growing
at a rate of 0.01, technological progress is growing at a rate of
0.01, and the depreciation rate is 0.02.
What is the Golden Rule level of capital per effective worker?
(Use two decimal places)

Consider the following production function:
Y = output = AK1/2N1/2, A = productivity, K = capital, N =
labor.
a) (3 pts.) Suppose that Y = 1331, K =121, and N = 121. Find
A.
b) (4 pts.) Find the marginal product of capital (MPK), measured
as the additional output that arises when the capital stock is
increased by 1 unit. (Start with the values of A, K and N that you
found in part (a).)
c) (4 pts.) Suppose...

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