# Thrre sector model and a production fuction question

• Jul 26th 2007, 01:51 PM
bobby87
Thrre 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, 02:02 PM
topsquark
Quote:

Originally Posted by bobby87
hi all, i have been struggling with these problems for a couple of days and would appreciate any help?:confused::confused::confused:

What problems?

-Dan
• Jul 26th 2007, 02:14 PM
bobby87
Hi sorry dan the problems are there now
many thanks:D
• Jul 26th 2007, 02:33 PM
topsquark
The first part of 2 isn't as much hard as it is long.

$Y= C + I$

So
$Y = (aY_d + b) + (cr + d)$

$Y = aY_d + b + cr + d$

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

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

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

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

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

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

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

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

-Dan
• Jul 26th 2007, 02:39 PM
topsquark
For the partial derivatives:
$Y = \frac{-aT^* + b + cr + d}{1 - a(1 - t)}$

$\frac{\partial Y}{\partial c} = \frac{r}{1 - a(1 - t)}$
since all other terms are considered to be constant.

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

And I'll let you clean this up yourself.

-Dan