How do I solve this for Y/P? | Mathematics | Page 1

broken boneBOT Feb 2, 2024, 3:32 AM

#

candid tinsel Feb 2, 2024, 3:33 AM

#

try divding by P on both sides

#

$T^\alpha P^{1-\alpha} P^{-1}$

mystic sealBOT Feb 2, 2024, 3:35 AM

#

HSF

candid tinsel Feb 2, 2024, 3:35 AM

#

remember dividing is just multiplication by reciprocal

#

yes, because we multiplied both sides by P^{-1}

#

now do you remember exponent rules?

#

like $a^b a^c = a^{b+c}$

mystic sealBOT Feb 2, 2024, 3:37 AM

#

HSF

candid tinsel Feb 2, 2024, 3:38 AM

#

yes!

#

now you can simplify that with like 2 extra steps more

#

hint: remember the 2nd rule
\newline $(a^b)^c=a^{bc}$

mystic sealBOT Feb 2, 2024, 3:40 AM

#

HSF

candid tinsel Feb 2, 2024, 3:41 AM

#

ok so you ended up with T^a * P^-a right?

#

the exponents (a, -a) are all factors of a

#

now remember the hint i said above

#

applies for 2 exponents at once

#

wait no that part doesn't make sense in this context

#

but still the earlier hint applies

#

try taking the ath root

#

(taking power to the 1/a)

#

yes

#

close: remember you have to take root on both sides

#

also, you did a small typo

#

Y/P = T^a * P^-a =/= T^a * P ^{1-a}

#

well you do what Y/P equals, but it's in a slightly messy form

#

remove the second ath root and you did it

#

so Y/P = (T/P)^a

#

oh alright let me see

#

alright we solved a right?

#

now we need to solve b

#

actually

#

yeah

#

it has to be 1

#

so P_(t+1)=P_t

#

so (1+g(Y/P))=0

#

yes

#

given that g(Y/P)=Y/P - c = 0

#

what do you know about Y/P?

#

yes!

#

i'm not sure if it's neccessary on this part

#

you can just put 1/P = c/Y then multiply numerator x denominator

#

so what's P in terms of those 2 constants?

#

and the reciprocal of a fraction is just switching numerator and denominator, so you get

#

Y/c = P

#

yeah, i think we solved it

#

any other questions or nah?

#

alright

#

i'm kinda bored now

#

so sure

#

wow that's long

#

it depends on the earlier question, right?

#

agh wait i don't know how to do economics at all

#

i'll try to see if i can help a bit, but i'm not sure i can do a lot

#

alright

#

wait how did you get that?

#

shouldn't it be (T/P)^a= c/(1-t)?

#

yeah

#

you can multiply both sides by P^a

#

yeah

#

it's

#

$P^a * (\frac{T}{P})^a$

mystic sealBOT Feb 2, 2024, 4:03 AM

#

HSF

candid tinsel Feb 2, 2024, 4:03 AM

#

and the P's cancel out

#

by exponent rules

#

T^a

#

yes

#

you can take the ath root

#

wait how did it end up for you?

#

cause there's a part that may need a little simplifying

#

yes!

#

wait 2 small details:

#

1/(c(1-t)) can be written as (1-t)/c

#

well as multiplying by (1-t)/c

#

and 2nd small detail:

#

you can distribute the root to get the ath root of ((1-t)/c) * T

#

but yeah that's pretty much it

#

i saw that the problem used calculus too

#

so if you wanna ask about that you can

#

wait imma search up what is per capita income to help

#

oh i get it now

#

imma re-read problem

#

wait i'm getting answers that don't make sense

#

sorry you gotta get another helper for this, my economics skills suck

#

i suppose that was all the algebra left

#How do I solve this for Y/P?