hi all, i have been struggling with these problems for a couple of days and would appreciate any help?:confused::confused::confused:

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- Jul 26th 2007, 12:51 PMbobby87Thrre sector model and a production fuction question
hi all, i have been struggling with these problems for a couple of days and would appreciate any help?:confused::confused::confused:

- Jul 26th 2007, 01:02 PMtopsquark
- Jul 26th 2007, 01:14 PMbobby87
Hi sorry dan the problems are there now

many thanks:D - Jul 26th 2007, 01:33 PMtopsquark
The first part of 2 isn't as much hard as it is long.

$\displaystyle Y= C + I$

So

$\displaystyle Y = (aY_d + b) + (cr + d)$

$\displaystyle Y = aY_d + b + cr + d$

Then

$\displaystyle Y =a(Y - T) + b + cr + d$

$\displaystyle Y = aY - aT + b + cr + d$

Then

$\displaystyle Y = aY - a(tY + T^*) + b + cr + d$

$\displaystyle Y = aY - atY - aT^* + b + cr + d$

Now

$\displaystyle Y - aY + atY = -aT^* + b + cr + d$

$\displaystyle Y(1 - a + at) = -aT^* + b + cr + d$

$\displaystyle Y = \frac{-aT^* + b + cr + d}{1 - a + at}$

$\displaystyle Y = \frac{-aT^* + b + cr + d}{1 - a(1 - t)}$

-Dan - Jul 26th 2007, 01:39 PMtopsquark
For the partial derivatives:

$\displaystyle Y = \frac{-aT^* + b + cr + d}{1 - a(1 - t)}$

$\displaystyle \frac{\partial Y}{\partial c} = \frac{r}{1 - a(1 - t)}$

since all other terms are considered to be constant.

Also

$\displaystyle \frac{\partial Y}{\partial a} = \frac{(-T^*)(1 - a(1 - t)) - (-aT^* + b + cr + d)(-(1 - t))}{(1 - a(1 - t))^2}$ <-- By the quotient rule

And I'll let you clean this up yourself.

-Dan