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a ) Consider the following Neoclassical growth model. Capital depreciates at an annual rate of 25%...

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) Consider the following Neoclassical growth model. Capital depreciates at an annual rate of 25% and population grows at an annual rate of 5%. There is noproductivity growth. The economy saves 10% of its income. Currently, each worker uses $2000 of capital and produces $5000 of output. We can conclude that the amount of investment per worker needed to break-even is ___ and capital per worker will __ from this year to the next.

(A) $600; decrease by $100.

(B) $600; increase by $100.

(C) $500; decrease by $100.

(D) $500; increase by $100

I know the correct answer is A, but I have no idea why, can someone explain this question in graph please?

Don't have to use graph to explain

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Answer #1

d = .25, n = .05, s = .1

K = 2000, Y = 5000

At eqm , in steady state

sY = (d+n)*K

(d+n)*K = (.25+.05)*2000

= .3*2000

= 600

.

K= 2000,

From capital accumulation eqn

So, Kt+1 = Kt - (d+n)*Kt + s*Yt

= 2000 - (.3)*2000 + .1*5000

= .7*2000 + 500

= 1400+500

= 1900

So next year , capital per worker will decrease by (2000-1900) = $ 100

So pption A)

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