I'm actually a little upset that I got so focused on one side of the equation that I forgot I could manipulate both sides at once... putting both sides to the negative power of three would certainly solve the equation, but the answer is far from what I got in my little mathematical endeavor. That comes out to 27826 and some odd decimal.
The full problem, as you asked for is as follows.
- Begin Question -
A country has the per-worker production function:
Where y is out put per worker and k is the capitol-labor ratio. The depreciation rate is .1 and the population growth rate is .1.
The total saving function is
Where S is total national saving and Y is total output.
A. What is the steady state value of the capitol-labor ratio?
B. What is the steady state value of output per worker?
C. What is the steady state value of consumption per worker?
- End Question -
Part A is solving for k; lower and upper case are different in that lower case is per capita and upper is the aggregate value. The depreciation rate and population growth rate fit together in the equation
and the steady state is where
What is s?
Take some substitution for
(this is what I started to simplify in my first post here).
I'll stop here briefly to say I messed up, and you probably caught it. There is a .1 missing from my substitutions... The equation I should have come up with was
Not that it makes a difference for the operation of what I was asking originally.
Anyway, I progress awkwardly and incorrectly as stated, but it just shows how much math my professor is willing to do while correcting tests.
I don't know how much more of my work you would like, but the next two parts are rather irrelevant as my question is about part A.
Part B is just plugging in the value of k into
Part C needed some more number flipping, but I felt confident in this one. My math reads
which is an irrelevant number now, so I'm going to act like it's not there.
More irrelevant numbers due to my missed .1 in the beginning; I'm not overly willing to do the math for it as long as the process was right (which it seemed to be since the .1 was all I was marked off for), and this took me forever to type out as well.
If you do see any more flaws, feel free to let me know; should help me on my final.