Question

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= K/LE ).

b) Compute the initial levels of output and per-worker output. Will
per-effective worker output rise or fall next period?

c) Compute steady state capital-per-eective worker,
output-per-eective worker,

and consumption-pe-effective worker

d) In the steady-state, at what rate does output grow? At what rate
does

output-per-worker grow?

e) Compute the Golden rule level of capital-per-eective worker, and
saving

rate needed to achieve that steady-state. Should more or less
saving be

encouraged?

Answer #1

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...

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production technology is Y=F(K,N)=K0.5N0.5 and people consume after
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k=K/N, evolves by (1+n)k’=szf(k)+(1-d)k.
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