Set Model Functions (Interpolated + Percentage + Risky + Safe Asset + Save + Borrow + R Shock)
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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_cons] = ffs_ipwkbzr_set_functions(varargin)
FFS_IPWKBZR_SET_FUNCTIONS setting model functions
define functions here to avoid copy paste mistakes. This function is identical to the ffs_akz_set_functions file.
@param fl_crra float crra utility
@param fl_c_min float minimum consumption
@param fl_Amean float mean productivity level
@param fl_alpha float Cobb-Douglas elasticity crs if = 1 and is risky financial investment like stocks, if decreasing return to scales, could be interpreted as risky physical capital investment.
@param fl_delta float risky capital depreciation if this is risky financial investment, deprecitation could be full, there is no additional return from risky financial investment except for its production function earnings. If we are looking are risky capital investment, there is a production function return, output. Then we can also sell the risky capital with some depreciation. fl_delta = 0.1 means 10 percent depreciation.
@param fl_r_save float savings interest rate, the borrowing interest rate is a paramter for the coh and inc functions, not a parameter for the overall function here.
@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 handle cash on hand equation given current period shock
@return f_cons handle consumption equation given coh and asset choice
@example
[f_util_log, f_util_crra, f_util_standin, f_inc, f_coh, f_cons] = ... ffs_akz_set_functions(fl_crra, fl_c_min, fl_Amean, fl_alpha, fl_delta, ... fl_r_save, fl_r_borr, fl_w);
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_r_save, fl_w] = deal(0.02, 1.23);
default_params = {fl_crra fl_c_min fl_b_bd ...
fl_Amean fl_alpha fl_delta fl_r_save fl_w};
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_r_save, fl_w] = default_params{:};
Equations Utility
f_util_log = @(c) log(c); f_util_crra = @(c) (((c).^(1-fl_crra)-1)./(1-fl_crra));
Equations Production
production function, z already exp, possible decreasing return to scale. if fl_alpha = 1, crs. That means we have a risky asset like stocks vs safe asset like bond. If we have decrease return to scale, can be interpreted as capital investments.
f_prod = @(z, k) ((fl_Amean.*(z)).*(k.^(fl_alpha)));
Equations Income
z here refers to z_wage. Income equation now based on b = interest + principles, fl_w is fixed wage, shock now on risky capital. Three sources of income, production income minus depreciation, wage income (could be zero), also interest income or interest costs dependong on borrowing or savings
% f_inc = @(z, b, k) (f_prod(z, k) - (fl_delta)*k ... % + fl_w ... % + (b./(1+fl_r_save)).*fl_r_save.*(b>0) + (b/(1+fl_r_borr)).*(fl_r_borr).*(b<=0)); % z already exp f_inc = @(fl_r_borr, z, b, k) (f_prod(z, k) - (fl_delta)*k ... + fl_w ... + b.*(fl_r_save).*(b>0) + b.*(fl_r_borr).*(b<=0)); % z already exp
Equations Cash-on-Hand
z here refers to z_wage. Cash on Hand, b is principle and interest. Very important to include fl_w in the COH equation, with fl_w > 0, there will be an income floor, lowest coh that we will solve for will not be 0. with fl_w > 0, the c_min parameter is only there to reset invalid choice grid values, have no effects on value func. f_coh = @(z, b, k) (f_prod(z, k) + k*(1-fl_delta) + fl_w + b);
f_coh = @(fl_r_borr, z, b, k) (f_prod(z, k) + k*(1-fl_delta) + fl_w + b.*(1+fl_r_save).*(b>0) + b.*(1+fl_r_borr).*(b<=0));
Equations Consumption
Simple Consumption given cash-on-hand f_cons = @(coh, bprime, kprime) (coh - kprime - ((bprime./(1+fl_r_save)).*(bprime>0)) - ((bprime./(1+fl_r_borr)).*(bprime<=0)));
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 = @(fl_r_borr, z, b, k) f_util_log((f_coh(fl_r_borr,z,b,k)-fl_b_bd).*((f_coh(fl_r_borr,z,b,k) - fl_b_bd) > fl_c_min) + ... fl_c_min.*((f_coh(fl_r_borr,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_r_borr)) > fl_c_min) ) + ... % ((coh-fl_b_bd)./(1+fl_r_borr)).*( (coh <= 0) & (((coh - fl_b_bd)./(1+fl_r_borr)) > fl_c_min) ) + ... % fl_c_min.*( (((coh - fl_b_bd)./(1+fl_r_borr)) <= fl_c_min) )); % fl_r_borr does not need to matter explicitly here for testing to work. 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)