Set Model Functions (Interpolated + Percentage + Risky + Safe Asset + FIBS + RShock)

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Contents

function [f_util_log, f_util_crra, f_util_standin, f_util_standin_coh, ...
    f_prod, f_inc, f_coh, f_coh_fbis, f_coh_save, f_cons] = ffs_ipwkbzr_fibs_set_functions(varargin)

FFS_IPWKZR_FIBS_SET_FUNCTIONS setting model functions

Default

[fl_crra, fl_c_min, fl_b_bd] = deal(1.5, 0.001, -20);
[fl_Amean, fl_alpha, fl_delta] = deal(1, 0.36, 0.08);
[fl_w, fl_r_fbr, fl_r_fsv] = deal(1.28, 0.035, 0.025);
bl_display_setfunc = false;

default_params = {fl_crra fl_c_min fl_b_bd ...
    fl_Amean fl_alpha fl_delta fl_w fl_r_fbr fl_r_fsv bl_display_setfunc};

Parse Parameters

% numvarargs is the number of varagin inputted
[default_params{1:length(varargin)}] = varargin{:};
[fl_crra, fl_c_min, fl_b_bd, fl_Amean, fl_alpha, fl_delta, ...
    fl_w, fl_r_fbr, fl_r_fsv, bl_display_setfunc] = default_params{:};

Equations Utility

f_util_log = @(c) log(c);
f_util_crra = @(c) (((c).^(1-fl_crra)-1)./(1-fl_crra));

Equations Production

f_prod = @(z, k) ((fl_Amean.*(z)).*(k.^(fl_alpha)));

Equations Income

f_inc = @(z, k, fl_r_inf, ar_for_borr, ar_inf_borr, ar_for_save) ...
    (f_prod(z, k) - (fl_delta)*k + fl_w + ...
        (ar_for_borr.*(fl_r_fbr) + ar_inf_borr.*(fl_r_inf) + ...
         ar_for_save.*(fl_r_fsv)));

Equations Cash-on-Hand

b_cons_cost: For borrowing, given the overall b choice, function ffs_fibs_min_c_cost_bridge finds the optimal formal and informal joint choices, and we obtain the consumption cost of borrowing from that

Unlike for the abz (fibs) problem, where the equations below are in terms of consumption, here we know b is principle due to two stage solution method.

% coh, where the b_with_r include various formal and informal choices with
% interest rate.
f_coh = @(z, b_with_r, k) (f_prod(z, k) + k*(1-fl_delta) + fl_w + b_with_r);

% If borrowing overall, various files in
f_coh_fbis = @(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));

% If saving overall
f_coh_save = @(b) (b.*(1+fl_r_fsv));

Equations Consumption (b=principle)

Note this is different from ffs_abz_fibs_set_functions, here only need to deal with b = principle, otherwise two stage solution does not work. So from today's perspective, choosing k and b for next period in principles.

f_cons = @(coh, bprime, kprime) (coh - kprime - bprime);

Equations Stand-in Fake Utility for Graphs

Utility for graphing with random data, note that when we graph with coh as the state variable using this equation here, there is no effect of shock on utility, it is fully captured by the coh.

f_util_standin = @(z, b, k) f_util_log((f_coh(z,b,k)-fl_b_bd).*((f_coh(z,b,k) - fl_b_bd) > fl_c_min) + ...
                                        fl_c_min.*((f_coh(z,b,k) - fl_b_bd) <= fl_c_min));

f_util_standin_coh = @(coh, fl_r_borr) f_util_log((coh-fl_b_bd).*( (coh > 0) & (((coh - fl_b_bd)./(1)) > fl_c_min)) + ...
                                                  ((coh-fl_b_bd)./(1)).*( (coh <= 0) & (((coh - fl_b_bd)./(1)) > fl_c_min)) + ...
                                                  (fl_c_min./(1+fl_r_borr)).*( (((coh - fl_b_bd)./(1)) <= fl_c_min)));

end

ans =

  function_handle with value:

    @(c)log(c)

Published with MATLAB® R2019a