Question

How do I find the system of differential equations in p and u:
P=a-T-betaU+hn
n(dot)=1(P-n)
U(dot)=-k(m-p)

Answer 1

is it time dependent?

Answer 2

yes n(dot) and U(dot) are. and I assume that the result should be time dependent too.

Answer 3

and a, T and h are constants??

Answer 4

yes. a,beta, T bigger than 0 and h lies between 1 and 0, k bigger than 0

Answer 5

I am not sure where to start. should I just shift the equations first that I have u= and p= on the left hand side?

Answer 6

this one right??
\[ P = a-T-\beta U+hn \]

Answer 7

yes. So should I just take this equation and derive P with respect to time. but than we want a small p in the result. Do you think it has to be adjusted?

Answer 8

in the first task we have to find the system of differential equation in p and u, and in the second task we need to draw a phase diagram, but this is less of a problem.

Answer 9

what is it related to??

Answer 10

I have difficulties to find the system of differential equations, but if I have it tho draw a phase diagram wont be difficult

Answer 11

i meant the system? kinda looks like physics!!

Answer 12

ouuu no it is just mathematics for economist. and the task is without any implications to an economical problem, that is why I m kinda stucked...and not sure where to start..

Answer 13

\[ P = a-T-\beta U+hn \]
\[ \dot{n}=1(P-n)\]
\[ \dot{U}=-k(m-p) \]

any relation between P and p??

Answer 14

there is nothing about that in the task. So probably not

Answer 15

and n is actually a pi

Answer 16

so it could be that P stand for normal price, U-utility, and pi- profit

Answer 17

so that p is real price...but there is nothig about in the task and just a guess

Answer 18

\[ \dot{P} = -\beta \dot{U} + h \dot{\pi} = -k(m-p)+(P-\pi)\]

there is still \( \pi \) ... i must be function of of P .. i.e \( \pi(P) \) if it is not then .. it might be incorrect.

also is \( -k(m-p) \) all constants??

Answer 19

no p is not a constant, we have to find the system of differential equation in p and u, so p and u must be dependent on time

Answer 20

is it a partial differential equation??

Answer 21

it must be total

Answer 22

are you sure this does not involve partial derivative??
\[ \dot{\pi}=1(P-\pi)\]
solving this equation, you get, \( \pi = C_1 e^{\int dt} + e^{\int +P dt} \int P e^{\int dt} dt\)

You can substitute the value of \( \pi\) in above equation ...
But I am not sure ...
http://www.codecogs.com/latex/eqneditor.php
Try using latex

Answer 23

I m really not sure

Answer 24

can you rewrite all equations?? in latex?? ..
also make sure if one quantity is dependent on other variables or not??

Answer 25

I am not familiar with latex. but the 3 equations you tiped in before where correct, and those three equations are all I have to solve this task. I wish I would have more hints.

Answer 26

from these 3 equations I have to find the system of differential equations in p and u.

Answer 27

Ops sorry ... no P there,
\[ \pi = C_1 e^{\int dt} + e^{\int dt} \int P e^{\int dt} dt\]
This is getting difficult .. P is again functio of pi

Answer 28

hmm but what is the system of differential equation? and shouldt there be a solution for p and u?

Answer 29

let's google it ... what is the name of this equation??

Answer 30

Sorry ... i guess i can't help it!!

Answer 31

I tried to google it and links to this side are shown. But thanks though, I ll try to solve it. maybe it works somehow ;)

Answer 32

k ..