Hall and Jorgenson uses the integral to find the present value...
z = [integral from 0 to infinite] exp(-r s) D(s) ds
Find z, so it's a function of t, when...
D(s) = 2(t - s) / t^2 for 0 <= s <= t, D(s) for s > t. (Linear decrease)
It would be appreciated a whole lot, if anyone could take a look at the above...
Good evening,
Simon DK
Hey, thanks for taking time to look at it...
But - I'm quite sure it's supposed to be ' r '...
Notes on the assignment says...
"Hall and Jorgenson uses the integral
z = [integral from 0 to infinite] exp(-r*s)*D(s) ds
to find the discounted present value, to rate r, by a time-dependent flow of depreciations."
I actually have the answer, but it's getting there I'm uncertain of...
z = (2 / (r*t)) * (1 - (1/(r*t))*(1-exp(-r*t)))
Maybe this helps? But - how do I get there?
Any help is still appreciated...
Thanks though...
Well, it wouldn't completely surprise me that I goofed up somewhere, but I don't like the form of your answer and it doesn't match my work. Even if I made a mistake somewhere I don't see how you could have a factor that includes .
Since the integration is independent of t:
The first integral is trivial:
We may do the second integral using integration by parts:
=
=
So we get:
-Dan
Hi,
Thanks for all the help... It has been a great journey, but I think I have to give in... I'll have to talk to my math teacher later today... I have a lecture in 2 hours, so - maybe he can clarify this mystery and ease the pain?
I hope I'll come back to this forum with answers...
Simon DK
Hi there...
I talked with my lecturer and he left me with a little idea of how to proceed...
It's for a math project, which is due till next Friday, so I have a little time to figure it out... I'll be attending another class tomorrow with a different teacher, so I'm hoping to solve the mystery tomorrow...
But - I'll continue with other parts of the project for now...
I'll be back with news. : o )
Simon DK