Yaobin's Comments:
My answers to all questions 1-6 can be found in the .m file named "PS4_Aiyagari_Yaobin".
Answer to question 1 and 2 about FOCs for the firm, defining the Hh's problem, etc. are typed as comment lines in the .m file.
For question 3, I discretize the exogeneous state variable z into 5 grid points;
For quesrion 4, I discretize the endogenous state variable into 500 grid points;
For question 5, I solve the model numerically with VFI and report the time elapsed;
For question 6, I compare the interest rate here with the interest rate under complete market;
I plot the policy functions for each exogeneous state;
I also draw the lorenze curve for wealth and calculated the wealth Gini coeff.;
And finally, I draw the distribution of wealth;
My answers to question 7 can be found in the .m file named "PS4_PFI_Yaobin".
For question 7, I used PFI in addition to VFI to slove the model numerically and report the time elapsed;
I also do the same analysis and plots about interest rate, policy function, Lorenze curve, wealth Gini coeff., and wealth distribution;
The PFI boost up the program and the results are consistent with those using the VFI method alone;