I am attempting to solve my model’s steady state analytically. My understanding that these equations must be solved simultaneously and thus I can’t take two equations of two unknowns and solve them independently using fsolve to determine , say C and K, and use the results to determine rest of variables. Is my understanding correct ?
In the meantime, I am able to write all my 17 variables in terms of two variables (C,K), after substantiation, to get 17 variable in terms C & K but not sure how to proceed from there. Any suggestions ?
My answer to your first question is no, you can first solve two equations for only K and C and then use these two values to solve the rest of equations. The key is to use blocks. DSGE models’ steady state values are typically solved by blocks. Imagine like a chain of events where one policy affects one block, say, an interest rate policy from central bank affects all equations that relate to financial sector, then the values obtained from solving the financial sector equations are fed into the second block of equations that relate to real economy etc.. (An example: central bank changes its policy rate which affects the financial sector, and changes in financial sector cause the cost of financing for firms, which spills over into product pricing and so on..)
My answer to your second question is that there are two ways for you to proceed. The first one is a pure linear algebra where you are basically solving a system of 17 non-linear equations. If you can, I suggest you to proceed and express all equations either in terms of C or K. If you cannot, then sure, fsolve is the way to go.
The second option is the approach I strongly suggest you to do and that you solve your 17 equations consecutively by blocks. The main advantage is that from economic perspective, you get to see the real causal relationship, which is not that obvious from a purely linear algebraic approach.