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ffs_abz_fibs_set_functions.m
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ffs_abz_fibs_set_functions.m
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%% Set Model Functions (ABZ FIBS)
% *back to <https://fanwangecon.github.io Fan>'s
% <https://fanwangecon.github.io/CodeDynaAsset/ Dynamic Assets Repository>
% Table of Content.*
%%
function [f_util_log, f_util_crra, f_util_standin, f_inc, f_coh, f_cons_coh_fbis, f_cons_coh_save, f_bprime] = ...
ffs_abz_fibs_set_functions(varargin)
%% FFS_ABZ_SET_FIBS_FUNCTIONS setting model functions
% Define functions for the abz problem with formal and informal borrowing
% and savings. See here:
% <https://fanwangecon.github.io/CodeDynaAsset/m_abz/paramfunc/html/ffs_abz_set_functions.html
% ffs_abz_set_functions> for *abz* function settings without without formal
% and informal considerations.
%
% @param fl_crra float crra utility
%
% @param fl_c_min float minimum consumption
%
% @param fl_r_fbr float formal borrowing interest rate
%
% @param fl_r_fsv float savings interest rates
%
% @param fl_w float wage rate
%
% @return f_util_log handle log utility
%
% @return f_util_crra handle crra utility general
%
% @return f_util_standin handle log utility with coh for testing graphing codes
%
% @return f_inc income handle equation wage and interests
%
% @return f_coh_fbis handle cash on hand equation given current period
% shock and formal and informal borrowing and savings choices.
%
% @return f_cons_coh_fbis handle consumption given cash on hand and formal
% and informal borrowing and savings choices.
%
% @return f_bprime handle aggregate borrowing and savings principles
%
% @example
%
% [f_util_log, f_util_crra, f_util_standin, f_inc, f_coh_fbis, f_cons_coh_fbis] = ...
% ffs_abz_set_functions(fl_crra, fl_c_min, fl_r_fbr, fl_r_fsv, fl_w);
%
%% Default
[fl_crra, fl_c_min] = deal(1, 0.001);
[fl_r_fbr, fl_r_fsv, fl_w] = deal(0.035, 0.025, 1.28);
bl_display_setfunc = false;
bl_b_is_principle = false;
default_params = {fl_crra fl_c_min fl_r_fbr fl_r_fsv fl_w bl_display_setfunc};
%% Parse Parameters
% numvarargs is the number of varagin inputted
[default_params{1:length(varargin)}] = varargin{:};
[fl_crra, fl_c_min, fl_r_fbr, fl_r_fsv, fl_w, bl_display_setfunc] = default_params{:};
%% Define Utility Functions
f_util_log = @(c) log(c);
f_util_crra = @(c) (((c).^(1-fl_crra)-1)./(1-fl_crra));
%% Define Income Equation
if (bl_b_is_principle)
f_inc = @(ar_z, fl_r_inf, ar_for_borr, ar_inf_borr, ar_for_save) ...
(ar_z*fl_w ...
+ (ar_for_borr.*(fl_r_fbr) ...
+ ar_inf_borr.*(fl_r_inf) ...
+ ar_for_save.*(fl_r_fsv)));
else
f_inc = @(ar_z, fl_r_inf, ar_for_borr, ar_inf_borr, ar_for_save) ...
(ar_z*fl_w ...
+ ((ar_for_borr./(1+fl_r_fbr))*fl_r_fbr ...
+ (ar_inf_borr./(1+fl_r_inf))*fl_r_inf ...
+ (ar_for_save./(1+fl_r_fsv))*fl_r_fsv));
end
if (bl_display_setfunc)
disp('f_inc')
disp(f_inc)
[ar_z, fl_r_inf, ar_for_borr, ar_inf_borr, ar_for_save] = deal(1, 0.06, -1, -0.33, 0);
fl_inc = f_inc(ar_z, fl_r_inf, ar_for_borr, ar_inf_borr, ar_for_save);
fprintf('fl_inc=%.3f\nwith fl_r_inf:%.3f, ar_for_borr:%.3f, ar_inf_borr:%.3f, ar_for_save:%.3f',...
fl_inc, fl_r_inf, ar_for_borr, ar_inf_borr, ar_for_save);
end
%% Define Cash on Hand Current Period
if (bl_b_is_principle)
f_coh = @(ar_z, fl_r_inf, ar_for_borr, ar_inf_borr, ar_for_save) ...
(ar_z*fl_w ...
+ (ar_for_borr.*(1+fl_r_fbr) ...
+ ar_inf_borr.*(1+fl_r_inf) ...
+ ar_for_save.*(1+fl_r_fsv)));
else
f_coh = @(ar_z, ar_b) (ar_z*fl_w + ar_b);
end
if (bl_display_setfunc)
disp('f_coh_fbis')
disp(f_coh)
if (bl_b_is_principle)
[ar_z, fl_r_inf, ar_for_borr, ar_inf_borr, ar_for_save] = deal(1, 0.06, -1, -0.33, 0);
fl_coh_fbis = f_coh(ar_z, fl_r_inf, ar_for_borr, ar_inf_borr, ar_for_save);
fprintf('fl_coh_fbis=%.3f\nwith fl_r_inf:%.3f, ar_for_borr:%.3f, ar_inf_borr:%.3f, ar_for_save:%.3f',...
fl_coh_fbis, fl_r_inf, ar_for_borr, ar_inf_borr, ar_for_save);
end
end
%% Define Consumption
if (bl_b_is_principle)
% ar_for_borr, ar_inf_borr, ar_for_save are choices
f_cons_coh_fbis = @(coh, fl_r_inf, ar_for_borr, ar_inf_borr, ar_for_save) ...
(coh + (ar_for_borr + ar_inf_borr + ar_for_save));
f_cons_coh_save = @(coh, ar_for_save) (coh - ar_for_save);
f_bprime = @(fl_r_inf, ar_for_borr, ar_inf_borr, ar_for_save) ...
(ar_for_borr + ar_inf_borr + ar_for_save);
else
% ar_bprime_in_c: array of b prime choice in current consumption units
f_cons_coh_fbis = @(coh, ar_bprime_in_c) (coh + ar_bprime_in_c);
f_cons_coh_save = @(coh, ar_for_save) (coh - ar_for_save./(1+fl_r_fsv));
f_bprime = @(fl_r_inf, ar_for_borr, ar_inf_borr, ar_for_save) ...
(ar_for_borr./(1+fl_r_fbr) ...
+ ar_inf_borr./(1+fl_r_inf) ...
+ ar_for_save./(1+fl_r_fsv));
end
if (bl_display_setfunc)
disp('f_cons_coh_fbis')
disp(f_cons_coh_fbis)
if (bl_b_is_principle)
% current period states
[ar_z, fl_r_inf, ar_for_borr, ar_inf_borr, ar_for_save] = deal(1, 0.06, -1, -0.33, 0);
fl_coh_fbis = f_coh(ar_z, fl_r_inf, ar_for_borr, ar_inf_borr, ar_for_save);
% current period choices
[ar_for_borr, ar_inf_borr, ar_for_save] = deal(-1, -0.33, 0);
fl_cons_coh_fbis = f_cons_coh_fbis(fl_coh_fbis, fl_r_inf, ar_for_borr, ar_inf_borr, ar_for_save);
% display
fprintf('fl_cons_coh_fbis=%.3f\nwith fl_r_inf:%.3f, ar_for_borr:%.3f, ar_inf_borr:%.3f, ar_for_save:%.3f',...
fl_cons_coh_fbis, fl_r_inf, ar_for_borr, ar_inf_borr, ar_for_save);
end
end
%% Defome Stand-in Utility for Testing
f_coh_simple = @(ar_z, ar_b) (ar_z*fl_w + ar_b);
f_util_standin = @(z, b) f_util_log(f_coh_simple(z, b).*(f_coh_simple(z, b) > 0) + fl_c_min.*(f_coh_simple(z, b) <= 0));
end