Contents

Testing function optikl

Check if starstrained k and l as generated by optikl.m move in the right direction with changing parameters phi, R, w and delta. Calls con_kl for a single combination of a and z. Plug in phi = 1 for unconstrained case.

addpath(genpath('/Users/sidhantkhanna/Documents/GitHub/BKS modified/'));

Parameter Setting

it_k_n   = 20000;
fl_phi   = 0.5;

fl_alpha = 0.4;
fl_theta = 0.79-fl_alpha;
fl_delta = 0.06;
fl_kappa = 0;
fl_r     = 0.04;
fl_w     = 1.5;

A and Z array setting

ar_a       = 2;
ar_z       = 3;
fl_ahi     = ar_a;
fl_zhi     = ar_z;
it_zgridno = 1;
it_agridno = 1;

Arrays of r and w

ar_r       = linspace(0.03, 0.06, 10);
ar_w       = linspace(1.5, 2, 8);
ar_phi     = linspace(0, 1, 10);
ar_delta   = linspace(0, 0.1, 10);
ar_alpha   = linspace(0.1, 0.7, 10);
ar_kappa   = linspace(0, 3, 10);

Test how k star reacts to different rs (fixing everything else)

as r increases, k star should fall, and l star should also fall (check with plotstarkl.m)

ar_k_star_overr = zeros(size(ar_r));
ar_l_star_overr = zeros(size(ar_r));
bl_saveimg = true;

fl_r1 = fl_r;

it_ctr = 0;
for fl_r = ar_r
    it_ctr = it_ctr + 1;

    [fl_k_star, fl_l_star] = optikl(ar_a,ar_z, ...
        fl_alpha,fl_theta,fl_delta,fl_kappa,fl_r,fl_w,fl_phi,fl_ahi,fl_zhi, ...
         it_zgridno, it_agridno);

    ar_k_star_overr(it_ctr) = fl_k_star;
    ar_l_star_overr(it_ctr) = fl_l_star;
end

% display
tb_opti_over_r = table(ar_r', ar_k_star_overr', ar_l_star_overr');
tb_opti_over_r.Properties.VariableNames = {'ar_r', 'kstar', 'lstar'};
disp(tb_opti_over_r)

fl_r = fl_r1;

      ar_r      kstar     lstar 
    ________    ______    ______

        0.03    9.9793    3.0078
    0.033333     9.899    2.9919
    0.036667    9.8201    2.9763
        0.04    9.7427    2.9609
    0.043333    9.6666    2.9457
    0.046667    9.5919    2.9307
        0.05    9.5185     2.916
    0.053333    9.4463    2.9015
    0.056667    9.3754    2.8872
        0.06    9.3057    2.8731

Test how k star reacts to different ws (fixing everything else)

as w increase, k star should fall, and l star should also fall

ar_k_star_overw = zeros(size(ar_w));
ar_l_star_overw = zeros(size(ar_w));

fl_w1 = fl_w;

it_ctr = 0;
for fl_w = ar_w
    it_ctr = it_ctr + 1;

    [fl_k_star, fl_l_star] = optikl(ar_a,ar_z, ...
        fl_alpha,fl_theta,fl_delta,fl_kappa,fl_r,fl_w,fl_phi,fl_ahi,fl_zhi, ...
         it_zgridno, it_agridno);

    ar_k_star_overw(it_ctr) = fl_k_star;
    ar_l_star_overw(it_ctr) = fl_l_star;
end

% display
tb_opti_over_w = table(ar_w', ar_k_star_overw', ar_l_star_overw');
tb_opti_over_w.Properties.VariableNames = {'ar_w', 'kstar', 'lstar'};
disp(tb_opti_over_w)

fl_w = fl_w1;

     ar_w     kstar     lstar 
    ______    ______    ______

       1.5    9.7427    2.9609
    1.5714     9.445    2.6882
    1.6429    9.1774    2.4526
    1.7143    8.9356    2.2476
    1.7857    8.7161    2.0681
    1.8571    8.5159      1.91
    1.9286    8.3326      1.77
         2     8.164    1.6454

Test how k star reacts to different phis (fixing everything else)

as phi falls, k star should fall, and l star should also fall

if(fl_phi~=1)
    fl_phi1= fl_phi;

ar_k_star_overw = zeros(size(ar_phi));
ar_l_star_overw = zeros(size(ar_phi));


it_ctr = 0;
for fl_phi = ar_phi
    it_ctr = it_ctr + 1;

    [fl_k_star, fl_l_star] = optikl(ar_a,ar_z, ...
        fl_alpha,fl_theta,fl_delta,fl_kappa,fl_r,fl_w,fl_phi,fl_ahi,fl_zhi, ...
         it_zgridno, it_agridno);

    ar_k_star_overphi(it_ctr) = fl_k_star;
    ar_l_star_overphi(it_ctr) = fl_l_star;
end

% display
tb_opti_over_phi = table(ar_phi', ar_k_star_overphi', ar_l_star_overphi');
tb_opti_over_phi.Properties.VariableNames = {'ar_phi', 'kstar', 'lstar'};
disp(tb_opti_over_phi)

fl_phi =fl_phi1;
end

    ar_phi     kstar     lstar 
    _______    ______    ______

          0      2.08    1.0757
    0.11111    2.5674    1.2349
    0.22222    3.4414    1.4965
    0.33333    4.8902    1.8842
    0.44444    7.5355    2.5019
    0.55556    13.041    3.5848
    0.66667    26.772     5.745
    0.77778    71.172    10.908
    0.88889    289.18    27.352
          1    859.74    55.883

Test how k star reacts to different deltas (fixing everything else)

as delta rises, k star should fall, and l star should also fall

ar_k_star_overdelta = zeros(size(ar_delta));
ar_l_star_overdelta = zeros(size(ar_delta));

fl_delta1 = fl_delta;

it_ctr = 0;
for fl_delta = ar_delta
    it_ctr = it_ctr + 1;

    [fl_k_star, fl_l_star] = optikl(ar_a,ar_z, ...
        fl_alpha,fl_theta,fl_delta,fl_kappa,fl_r,fl_w,fl_phi,fl_ahi,fl_zhi, ...
         it_zgridno, it_agridno);

    ar_k_star_overdelta(it_ctr) = fl_k_star;
    ar_l_star_overdelta(it_ctr) = fl_l_star;
end

% display
tb_opti_over_delta = table(ar_delta', ar_k_star_overdelta', ar_l_star_overdelta');
tb_opti_over_delta.Properties.VariableNames = {'ar_delta', 'kstar', 'lstar'};
disp(tb_opti_over_delta)

fl_delta1 = fl_delta;

    ar_delta    kstar     lstar 
    ________    ______    ______

           0    10.686    3.1458
    0.011111    10.499    3.1097
    0.022222    10.318    3.0745
    0.033333    10.143    3.0401
    0.044444    9.9727    3.0065
    0.055556    9.8075    2.9738
    0.066667    9.6469    2.9418
    0.077778     9.491    2.9105
    0.088889    9.3394    2.8799
         0.1    9.1921    2.8501

Test how k star reacts to different kappas (fixing everything else)

as kappa rises, k star should fall, and l star should also fall

ar_k_star_overkappa = zeros(size(ar_delta));
ar_l_star_overkappa = zeros(size(ar_delta));

fl_kappa1 = fl_kappa;

it_ctr = 0;
for fl_kappa = ar_kappa
    it_ctr = it_ctr + 1;

    [fl_k_star, fl_l_star] = optikl(ar_a,ar_z, ...
        fl_alpha,fl_theta,fl_delta,fl_kappa,fl_r,fl_w,fl_phi,fl_ahi,fl_zhi, ...
         it_zgridno, it_agridno);

    ar_k_star_overkappa(it_ctr) = fl_k_star;
    ar_l_star_overkappa(it_ctr) = fl_l_star;
end

% display
tb_opti_over_kappa = table(ar_kappa', ar_k_star_overkappa', ar_l_star_overkappa');
tb_opti_over_kappa.Properties.VariableNames = {'ar_kappa', 'kstar', 'lstar'};
disp(tb_opti_over_kappa)

fl_kappa = fl_kappa1;

    ar_kappa    kstar     lstar 
    ________    ______    ______

          0     9.1921    2.8501
    0.33333     8.1925    2.6428
    0.66667     7.1612    2.4196
          1     6.0875    2.1752
     1.3333     4.9528       1.9
     1.6667     3.7172     1.574
          2     2.2551    1.1342
     2.3333          0         0
     2.6667          0         0
          3          0         0

Test how k star reacts to different alpha (and theta resp) (fixing everything else)

as delta rises, k star should fall, and l star should also fall

ar_k_star_overalpha = zeros(size(ar_alpha));
ar_l_star_overalpha = zeros(size(ar_alpha));

fl_alpha1 = fl_alpha;

it_ctr = 0;
for fl_alpha = ar_alpha
    fl_theta = 0.79-fl_alpha;
    it_ctr = it_ctr + 1;

    [fl_k_star, fl_l_star] = optikl(ar_a,ar_z, ...
        fl_alpha,fl_theta,fl_delta,fl_kappa,fl_r,fl_w,fl_phi,fl_ahi,fl_zhi, ...
         it_zgridno, it_agridno);

    ar_k_star_overalpha(it_ctr) = fl_k_star;
    ar_l_star_overalpha(it_ctr) = fl_l_star;
end

% display
tb_opti_over_alpha = table(ar_alpha', ar_k_star_overalpha', ar_l_star_overalpha');
tb_opti_over_alpha.Properties.VariableNames = {'ar_alpha', 'kstar', 'lstar'};
disp(tb_opti_over_alpha)

fl_alpha = fl_alpha1;

    ar_alpha    kstar     lstar 
    ________    ______    ______

        0.1      6.474    5.1629
    0.16667     6.7324     4.175
    0.23333     7.1602    3.5903
        0.3     7.7746    3.2116
    0.36667     8.6355     2.951
    0.43333     9.8619    2.7635
        0.5     11.687    2.6224
    0.56667     14.601    2.5055
    0.63333     19.788    2.3767
        0.7     30.782    2.1206

Test how k starstriant react to different ws amd rs

as w increase, k star should fall, and l star should also fall

mt_k_star_overw = zeros(size(ar_w));
mt_l_star_overw = zeros(size(ar_w));

it_ctr_w = 0;
for fl_w = ar_w
    it_ctr_w = it_ctr_w + 1;

    it_ctr_r = 0;
    for fl_r = ar_r
        it_ctr_r = it_ctr_r + 1;

        [fl_k_star, fl_l_star] = optikl(ar_a,ar_z, ...
        fl_alpha,fl_theta,fl_delta,fl_kappa,fl_r,fl_w,fl_phi,fl_ahi,fl_zhi, ...
         it_zgridno, it_agridno);

        mt_k_star_overwr(it_ctr_w, it_ctr_r) = fl_k_star;
        mt_l_star_overwr(it_ctr_w, it_ctr_r) = fl_l_star;

    end
end

[mt_r, mt_w] = meshgrid(ar_r, ar_w);

disp('mt_k_star_overwr');
disp(mt_k_star_overwr);
disp('mt_l_star_overwr');
disp(mt_l_star_overwr);


% Graph
figure(1)
surf(mt_w, mt_r, mt_k_star_overwr);
title('k star varying over r and w (fixing a and z)');
xlabel('w');
ylabel('r');
zlabel('k star');
view(125,35);
if(bl_saveimg)
saveas(gcf, '/Users/sidhantkhanna/Documents/GitHub/BKS modified/code/Firms/figures/optikl/kstar_rw.png')
end

% Graph
figure(2)
surf(mt_w, mt_r, mt_l_star_overwr);
title(' k star varying over r and w (fixing a and z)');
xlabel('w');
ylabel('r');
zlabel('l star');
view(125,35);
if(bl_saveimg)
saveas(gcf, '/Users/sidhantkhanna/Documents/GitHub/BKS modified/code/Firms/figures/optikl/lstar_rw.png')
end

mt_k_star_overwr
  Columns 1 through 7

    8.6898    8.6382    8.5874    8.5373    8.4878    8.4391    8.3910
    8.6580    8.6067    8.5561    8.5063    8.4571    8.4087    8.3609
    8.6278    8.5768    8.5265    8.4769    8.4280    8.3798    8.3323
    8.5991    8.5483    8.4983    8.4490    8.4003    8.3524    8.3051
    8.5717    8.5212    8.4714    8.4223    8.3739    8.3262    8.2791
    8.5455    8.4953    8.4457    8.3969    8.3487    8.3012    8.2543
    8.5205    8.4705    8.4212    8.3725    8.3246    8.2773    8.2307
    8.4966    8.4468    8.3976    8.3492    8.3015    8.2544    8.2080

  Columns 8 through 10

    8.3436    8.2969    8.2507
    8.3137    8.2672    8.2214
    8.2854    8.2391    8.1935
    8.2584    8.2124    8.1670
    8.2327    8.1869    8.1417
    8.2081    8.1626    8.1176
    8.1847    8.1393    8.0945
    8.1622    8.1170    8.0724

mt_l_star_overwr
  Columns 1 through 7

    0.3930    0.3920    0.3909    0.3899    0.3889    0.3880    0.3870
    0.3728    0.3718    0.3709    0.3699    0.3690    0.3680    0.3671
    0.3545    0.3536    0.3526    0.3517    0.3508    0.3500    0.3491
    0.3378    0.3369    0.3360    0.3352    0.3343    0.3335    0.3327
    0.3225    0.3217    0.3208    0.3200    0.3192    0.3184    0.3176
    0.3085    0.3077    0.3069    0.3061    0.3053    0.3046    0.3038
    0.2956    0.2948    0.2941    0.2933    0.2926    0.2918    0.2911
    0.2836    0.2829    0.2822    0.2815    0.2808    0.2801    0.2794

  Columns 8 through 10

    0.3860    0.3851    0.3841
    0.3662    0.3653    0.3644
    0.3482    0.3474    0.3465
    0.3318    0.3310    0.3302
    0.3168    0.3161    0.3153
    0.3031    0.3023    0.3016
    0.2904    0.2897    0.2890
    0.2787    0.2780    0.2773

Published with MATLAB® R2018a