1. A country has the per-worker production function: Y. = where y, is output per worker and k, is the capital-labor ratio. The depreciation rate is 0.1 and the population growth rate is 0.1. The saving function is S = 0.1Y, where S, is total national saving and Y, is total output. a) What is the steady-state value of capital-labor ratio? b) What is the steady-state value of output per worker? c) What is the steady-state value of consumption per worker? Answer:

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1. A country has the per-worker production function:
Yt =
6k/3
where y, is output per worker and k, is the capital-labor ratio. The depreciation rate is 0.1 and the
population growth rate is 0.1. The saving function is
S; = 0.1Y,
where S, is total national saving and Y, is total output.
a) What is the steady-state value of capital-labor ratio?
b) What is the steady-state value of output per worker?
c) What is the steady-state value of consumption per worker?
Answer:
2. What happens in the steady state to the capital-labor ratio, output per worker, and consumption per
worker when each of the following events occur? You should assume that the steady-state capital-labor
ratio is below the Golden Rule level.
k
y
a) Productivity falls
b) Population growth falls
c) The saving rate falls
d) The depreciation rate falls
Transcribed Image Text:1. A country has the per-worker production function: Yt = 6k/3 where y, is output per worker and k, is the capital-labor ratio. The depreciation rate is 0.1 and the population growth rate is 0.1. The saving function is S; = 0.1Y, where S, is total national saving and Y, is total output. a) What is the steady-state value of capital-labor ratio? b) What is the steady-state value of output per worker? c) What is the steady-state value of consumption per worker? Answer: 2. What happens in the steady state to the capital-labor ratio, output per worker, and consumption per worker when each of the following events occur? You should assume that the steady-state capital-labor ratio is below the Golden Rule level. k y a) Productivity falls b) Population growth falls c) The saving rate falls d) The depreciation rate falls
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