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In class there was an argument that if people could accumulatehuman as well as physical Capital, the production function wouldlook like the "AK" production function.

(A)If the production function is AK and the savings rate is theconstant rate "S", and the rates of depreciation and populationgrowth are d and n respectively, what would the growth rate of theeconomy be?

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Yusra Anees
Yusra AneesLv10
28 Sep 2019

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Related questions

a) Is it true that if people could accumulate human as well as physical capital, the production function would look like the "AK" production function?
b) What would be the consequences of a decrease in fertility in this economy?

Consider an economy with the following production function:

Y = AK.5L.5
The labor force is constant. The rate of depreciation is รŽยด = .1, the savings rate is s = .3.

a. Has this production function constant returns to scale? Why?

b. Write the production function in per worker variables.

c. Does the per worker production function have diminishing marginal returns to capital? Why?

d. Write the fundamental Solow equation in per worker variables.

e. Depict the steady state of this economy.

f. What are the growth rates of per worker output and capital in steady state?

g. Calculate the steady state level of capital, output, consumption and savings.

h. Redraw the initial equilibrium and show what happens when the savings rate increases. Do the growth

rates change?

i. Redraw the initial equilibrium and show what happens when there is a one time increase in population.

. Do the growth rates change?

j. Redraw the initial equilibrium and show what happens when there is a one time innovation that increases

productivity. Do the growth rates change?

k. Redraw the initial equilibrium and show what happens when there is constant productivity growth. Do

the growth rates change?

Consider an economy with the following production function:

Y = AK0.5 L0.5

The labor force is constant. The rate of depreciation is รŽยด=0.1, the savings rate is s=0.3

a) Has this production function constant returns to scale? Why?

b) Write the production function in per worker variables.

c) Does the per worker production function have diminishing marginal returns to capital? Why?

d)Write the fundamental Solow equation in per worker variables.

e) Depict the steady state of this economy.

f) What are the growth rates of per worker output and capital in steady state?

g) Calculate the steady state level of capital, output, consumption, and savings.

h) Redraw the initial equilibrium and show what happens when the savings rate increases. Do the growth rates change?

i) Redraw the initial equilibrium and show what happens when there is a one time increase in populatikon. Do the growth rates change?

j) Redraw the initial equilibrium and show what happens when there is a one time innovation that increases productivity. Do the growth rates change?

k) Redraw the initial equilibrium and show what happens when there is constant productivity growth. Do the growth rates change?

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