Question

Use the Solow model to solve. Suppose, you are the chief
economic advisor to a small African country with an aggregate per
capita production function
of y=2k^{1/2.} Population grows at a
rate of 1%. The savings rate is 12%, and the rate of depreciation
is 5%.

(a) At the steady-state level of output, what is the numerical value of consumption? Identify the amount of consumption in your graph in part a. Show your work.

(b) Say that population growth decreases in this economy. What do you expect to happen to the growth rate of income per capita in the short run and long run?

(c) Say that this economy was in its steady state when a cyclone destroyed half of its capital stock. How does this change the steady state value of income per capita? Explain.

(d) On a graph show what happens to steady-state capital per worker and income per worker in response to a change in consumer preferences increases the savings rate.

Answer #1

Use the Solow model to solve. Suppose, you are the chief
economic advisor to a small African country with an aggregate per
capita production function
of y=2k1/2. Population grows at a
rate of 1%. The savings rate is 12%, and the rate of depreciation
is 5%.
(a) On a graph, show the output, break-even investment, and
savings functions for this economy (as a function of capital per
worker). Denote steady-state capital per worker k* and
steady-state output per worker y*. Label...

Question #1: The Basic Solow Model
Consider an economy in which the population grows at the rate of
1% per year. The per worker production function is y = k6, where y
is output per worker and k is capital per worker. The depreciation
rate of capital is 14% per year. Assume that households consume 90%
of their income and save the remaining 10% of their income.
(a) Calculate the following steady-state values of
(i) capital per worker
(ii) output...

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...

Use the H-augmented Solow model to determine the a)
instantaneous impact on GDP per capita, b) instantaneous impact on
consumption per capita, c) long-run impact on GDP per capita, d)
long-run impact on consumption per capita, e) impact on long-run
GDP per capita growth rate, and f) impact on long-run GDP growth
rate of a permanent and instantaneous increase in the fraction of
national resources devoted to investment in human capital, sh.
Assume the country begins at its steady state...

Answer the following questions using the basic Solow growth
model, without population growth or technological progress.
(a) Draw a diagram with per worker output, y, consumption, c,
saving, s and investment, i, on the vertical axis and capital per
worker, k, on the horizontal condition. On this diagram, clearly
indicate steady-state values for c, i, and y. Briefly outline the
condition that holds in the steady- state (i.e. what is the
relationship between investment and the depreciation of
capital?).
(b)...

Consider a version of the Solow model where population grows at
the constant rate ? > 0 and labour efficiency grows at rate ?.
Capital depreciates at rate ? each period and a fraction ? of
income is invested in physical capital every period. Assume that
the production function is given by:
?t =
?ta(?t?t
)1-a
Where ??(0,1), ?t is output, ?t is
capital, ?t is labour and ?t is labour
efficiency.
a. Show that the production function exhibits constant...

Suppose, in the Solow growth model, that learning by doing is
captured as a cost of installing new capital. In particular,
suppose that for each unit of investment, r units of goods are used
up as a cost to firms.
(a) Determine how r affects the steady state quantity of capita per
worker, and per capita income.
(b) Now suppose that r differs across countries. How
will these countries differ in the long run? Discuss.

1. In the Solow model without exogenous technological change,
per capita income will grow in the long term as
long as the country has an initial level of capital below the
steady state level of capital (k o < k ⋅)
TRUE OR FALSE?
2. In the Solow model without exogenous technological change, per
capita income will grow in the short term as long
as the country has an initial level of capital below the steady
state level of capital...

Which of the following statements about the Solow growth model
is FALSE?
A. The higher steady-state capital per capita, the higher the
output/income per capita.
B. The higher output/income per capita, the higher consumption
per capita.
C. Golden-rule capital per capita must be a steady state, but
not all steady-state is also a golden-rule.
D. Golden-rule capital per capita can be achieved by setting
the saving rate at the appropriate level.

QUESTION 1
Suppose an economy can be characterized by a Cobb-Douglas
production function with capital share of 1/3, and A =
200. The investment rate is 0.12 (12%), the annual rate of growth
of the labor force is 0.02 (2%), and the annual depreciation rate
of capital is 0.04 (4%). According to the Solow growth model, this
economy's steady state capital/labor ratio (capital per worker,
k) is
4,000
8,000
10,000
12,000
None of the above.
QUESTION 2
The steady state...

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