Need to implement a parameter that grows at a specific rate over time

The context is a computational general equilibrium (economic) model

I want to have a parameter that is geometric growth.

The growth in time is G(+1) = (1+I)*G, however, I don't know how to set the value of G at t=0?

(I is percent growth of G for each time period)

I looked in help and found the following equation form

y=C*exp(k*t)

where C is the value of y at t=0 and k can be derived by knowing the value of y at a different time

However, I'm a nube and I'm not sure how to implement this equation in the context of my model.

[Mathieu NOE]

hello

does it mean you know G for t > 0 ? but not at t = 0 ?

[Michael Reed]

i know G(0) for example G(0) = 2.0, and I also know I (0.3). I want these two values to be input parameters

In algabraic form the equation is

G(t) = G(0)*(1+I)^t

Im not sure how to implement t in the exponent

Answer 1

[Star Strider]

Perhaps this —

G0 = 2;
I0 = 0.3;
Gfcn = @(t,G,I) G.*(1+I).^t;

t = linspace(0,5, 25);

figure
plot(t, Gfcn(t,G0,I0))
grid
xlabel('t')
ylabel('G(t)')

.

[Michael Reed]

This is progress and shows the function of interest but...

I need to be able to implement this function in the context of other equations that form a general equilibrium model

ex:

K(+1)= function of K

D(+1) = function of K,G, ...

***

my initial thought of implmenting my G function was

G(+1) = (1+I)*G+G_bar where G_bar is G(0), but this doesn't work because G_bar gets added at every time step.

Is it possible to implement the Gfcn from above in this context?

[Star Strider]

I do not understand what you want to do.

(I need to be away for a few minutes. I will check back in later.)

[Michael Reed]

I may have a solution. I will implement it later today and let you know my results.

Thanks for the info in above answers. It is useful

[Star Strider]

My pleasure!