Department

EconomicsCourse Code

ECON 402Professor

Maciej DudekLecture

9This

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A numerical Example:

Production function

= = = 1/2 1/2

( , )

Y F K L K L K L

Per-worker production function

Y/L = K^1/2*L^1/2/ L = (K/L)^1/2

And we can substitute y = Y/L and k = K/L

y = f(k) = k^1/2

Prediction:

Solow model predicts with higher rates of saving will have higher level of capital and

income per-worker in long run.

However, this may not match with real work condition.

The golden Rule:

Different values of s lead to different states and we need to find out the best state.

The best steady state per person given:

c* = (1–s) f(k*).

With increase in s

1. Higher k* and y* and raises c*

2. Reduces consumption’s share of income (1–s),

and lowers c*.

The golden Rule:

Lets define

k*gold = the steady state of k that maximizes consumption.

c* = y* − i*

= f (k*) − i*

= f (k*) − δk*

The transition to the Golden Rule State:

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