I have to solve for a maximization problemwith greek letters and simplify the expression but I don't know how to proceed

Hello,

I'd like to know how to insert greek letters in the command window to solve a maximization problem and also to simplify an expression. Actually, I don't need matlab to maximize but to simplify expressions with greek letters. Could you help me please ?

Answer 1

[Andres]

To simplify expressions you need the Symbolic Math Toolbox in Matlab

https://de.mathworks.com/help/symbolic/simplify-symbolic-expressions.html

or another computer algebra system

https://en.wikipedia.org/wiki/List_of_computer_algebra_systems

A greek letter inside a variable name throws an error

>> syms β
Error using syms
Invalid variable name.

so use a valid variable name instead like

syms beta

https://de.mathworks.com/help/matlab/matlab_prog/variable-names.html

https://de.mathworks.com/matlabcentral/answers/58292-what-letters-can-be-used-in-variable-names

[Nordine Bouchelia]

Thank you,

but I encounter another difficulty,

I have to reproduce the results of an industrial organization paper and it's getting nasty to make the computation by hand, it's why I wanted to use Matlab in the first place.

It's an optimization problem, I succeed to obtain the first result by hand but others are more complicated to simplify.

Could you help me through this task or tell me how I could solve this problem using Matlab if possible?

I only want to know the process through which Matlab would allow me to get the same results as the one present in the paper.

Please consider only the third period pD3 and omegaD3, I obtained pD3 as in the paper but can't find the same omega as the one in the paper

Thanks for your time and for your help

the results in question

[Torsten]

You set the first two equations to 0 and try to solve for p_3^D and omega_3^D ?

[Nordine Bouchelia]

is there any mean to do that with Matlab ? By hand I found the same result for p_3^D* but for omega_3^D I did the maximization part but when I substitute p_3^D* into omega_3^D i don't find the same ?

Any matlab command that could help me ?

thanks for your help

[Torsten]

My question was: what are you trying to do ?

[Nordine Bouchelia]

Maximizing over 3 different period by backward induction but p_3^D and omega_3^D are the prices and dont interface with each other so first I'd like just to maximize for pi_H and Pi_G for the third period and get the optimal p_3^D* and omega_3^D* by substituting p_3^D* into omega_3^D.

The aim of this is to get the same value as the one in the last picture of the comment.

Thanks a lot

[Torsten]

I'd like just to maximize for pi_H and Pi_G for the third period and get the optimal p_3^D* and omega_3^D* by substituting p_3^D* into omega_3^D.

Sorry, I still don't get what you are trying to do. Are pi_H and Pi_G already derivatives of an objective function with respect to omega_3^D and p_3^D and you want to solve pi_H = 0 and Pi_G = 0 for omega_3^D* and p_3^D* to satisfy the necessary condition for a maximum ?

[Nordine Bouchelia]

No pi_H and pi_G are the objective functions of the whole 3 periods summed together for firm H and G

I need to derive with repect to omega_3^D and p_3^D and solve for the optimal values.

But for the expression of omega_3^D I for example, I need to get rid of the p_3^D so, substitute it inside the expression and find the same results as described above.