Solving an Algebraic Headache: Proving Kt+1 = 1.15 * K

[Flummoxed]

I have an algebra problem which is giving me headaches.

L_t = S_t
L_t = K_t+1 - K_t
S_t = s * Y_t
K_t = k * Y_t

K₀ = 200, s = 0.3, k = 2

Prove that K_t+1 = 1.15 * K

Thanks.

 

[Flummoxed]

I have an algebra problem which is giving me headaches.
L_t = S_t
L_t = K_t+1 - K_t
S_t = s * Y_t
K_t = k * Y_t
K₀ = 200, s = 0.3, k = 2
Prove that K_t+1 = 1.15 * K
Thanks.

Now I'm not sure if this is correct, but I started off by subsituting in the known values.

Lt = St
Lt = Kt+1 - Kt
St = 0.3 * Yt
Kt = 2 * Yt

-----------------

Lt = St
Lt = Kt+1 - Kt
St = 0.3 * (0.5 * Kt)
0.5 * Kt = Yt

 

[HallsofIvy]

I have an algebra problem which is giving me headaches.
L_t = S_t
L_t = K_t+1 - K_t
S_t = s * Y_t
K_t = k * Y_t
K₀ = 200, s = 0.3, k = 2
Prove that K_t+1 = 1.15 * K
Thanks.

Since the very first equations says L_t= S_t, you can simplify slightly by writing that third equation as L_t= 0.3Y_t. You now have 3 equations:
L_t= K_t+1- K_t
L_t= s Y_t
K_t= k Y_t

Also, You say you want to prove "K_t+1= 1.15*K" which makes no sense. I imagine it must be either "K_t+1= 1.15*k" or "K_t+1= 1.15*K_t". I suspect it is the latter.

Since, however, you want K_t+1= something, I suggest rewriting that first equation as K_t+1= L_t + K_t (add K_t to both sides). Now, it looks to me like you just need to replace that L_t with something!

You know that L_t= sY_t. do you see that Y_t= (1/k) K_t? That should make it clear!

 

[Flummoxed]

The sheet I was given says "Prove that K_t+1 = 1.15 x K" with the K in upper case.

 

[VietDao29]

The sheet I was given says "Prove that K_t+1 = 1.15 x K" with the K in upper case.

I think that's a little typo. The sheet should read:
K_{t + 1} = 1.15 K_t.
---------------
You can follow HallsofIvy's post, and you'll soon arrive at the answer,
or you may also want to try a slightly different way:
S_t = L_t
<=> s Y_t = K_{t + 1} - K_t.
What's K_{t + 1}? What's K_t?
Can you go from here?

 

[matrixx333]

I have also been able to confirm that the equation:

K_t+1 = 1.15 * K

should read:

K_t+1 = 1.15 * K_t

From the help that HallsofIvy and VietDao29 provided, you should come to the answer.

I came to the answer a different way, but want to find out if you can use their help before I make another post.