# bankers

Document Sample

```					       0.1 rho, rate of time discounting per period (up to retirement period after n-period career)    good is better than gad
10 n, number of periods in banker's career                                                      bad is bad, even at r_1
0.95 alpha, proby of success for good project                                                   r_max for bad to be bad
0.05 gamma, fraction of investment that entrepreneur can divert in bad project                gamma_max for bad @r_1
0 eta, fraction of investment that banker spends evaluating the project
0.142857 E, entrepreneurs required bonus when succeed, per unit invested
0.387755 B, bankers required rewards when succeed, per unit invested                       0
1.339527 r in steady-state equilibrium, for given n
for n=infinity                     0.232515 investment at r_1
1.300752 r_infinity, steady state r 1.688507 r_1, steady state r for n=1
Parameters for an linear investment-demand function. Workers (one unit required per successful investment) have utility = wage-.5*pi*labor^2
1.74 Psi, maximal returns (r) at zero wage
0.233117 pi, rate of wage increase as employment increases
1.983408 investment at r_infinity, largest possible amount of good investment at any time 1.300752 R(I)

n      10
steady state                1            2          3          4          5           6          7          8          9
For eqm:            1.364341     1.358813   1.352732   1.346043   1.338685    1.330591   1.321688   1.311895   1.301122
-5.7E-09   =0, 0<= 0.063589     0.058061    0.05198   0.045291   0.037933    0.029839   0.020936   0.011143    0.00037
1.717902            1.611461     1.635175    1.66126   1.689954   1.721517    1.756237   1.794428   1.836439    1.88265
0.400473            0.375659     0.381187   0.387268   0.393957   0.401315    0.409409   0.418312   0.428105   0.438878
0.687973             0.60536     0.623308   0.643353    0.66577   0.690871    0.719019   0.750631   0.786189   0.826254
0.245415            0.230209     0.233596   0.237323   0.241422   0.245931    0.250891   0.256347   0.262348    0.26895
0.066613            0.102471     0.094939   0.086352   0.076539   0.065302    0.052405   0.037568   0.020463   0.000696
0.93804     0.951844   0.967028   0.983731   1.002104    1.022315   1.044546   1.069001   1.095901
0.180832            0.169627     0.172124   0.174869    0.17789   0.181212    0.184867   0.188887   0.193309   0.198174
0.909091     0.826446   0.751315   0.683013   0.620921    0.564474   0.513158   0.466507   0.424098
0.078843     0.078843   0.078843   0.078843   0.078843    0.078843   0.078843   0.078843    0.27595
0            1          2          3          4           5          6          7          8
0<= 0.317698 0.090771      0.090771   0.090771   0.090771   0.090771    0.090771   0.090771   0.090771   0.090771
0 1.673582 1.696275    1.721237    1.748695    1.778899   1.812123      1.84867   1.888872   1.933093   1.981737
1.696275   1.721237    1.748695    1.778899   1.812123      1.84867   1.888872   1.933093   1.981737
( 0.090771   0.090771    0.090771    0.090771   0.090771    0.090771    0.090771   0.090771   0.090771
0.224536   0.270618    0.313776    0.352663   0.385626    0.410647    0.425274   0.426527   0.410799
0.294636      0.5698   0.827365    1.069045     1.29641   1.510898    1.713832   1.906428     2.08981
0.049351   0.086902    0.113623    0.130384   0.137967    0.137067    0.128305   0.112228   0.089319
0.275622   0.220704    0.170561    0.125669   0.086554    0.053794    0.028024   0.009943   0.000319
0.058992   0.042944      0.03017   0.020208   0.012653    0.007149    0.003386   0.001092   3.19E-05
0.214033   0.194576    0.176887    0.160806   0.146187    0.132898    0.120816   0.109833   0.099848
0           0.053508   0.048644    0.044222    0.040202   0.036547    0.033224    0.030204   0.027458   0.024962
0.214033   0.194576    0.176887    0.160806   0.146187    0.132898    0.120816   0.109833   0.099848
0<=         0           0           0          0           0           0          0          0           0
0           0           0          0           0           0          0          0           0
0    young 0.090771    0.090771    0.090771    0.090771   0.090771    0.090771    0.090771   0.090771   0.090771

0.267541   0.243219    0.221109 0.201008 0.182734 0.166122 0.15102               0.137291 0.12481
0.080635   0.065159    0.051831 0.040388 0.030597 0.022252 0.015172              0.009195 0.00418
0.301391   0.267904    0.234416 0.200928 0.16744 0.133952 0.100464               0.066976 0.033488
0.343986   0.656701    0.940988 1.19943 1.434377 1.647966 1.842137               2.018656 2.179129
1.4
1.3
1.2                                                                  interest on investment
1.1
1                                                                  banking profits
0.9
0.8                                                                  entrepreneurs' income
0.7
wages
0.6
0.5
0.4
0.3
0.2
0.1
0
steady   1   2   3     4        5       6     7   8   9   10
state               10-period credit cycle
-0.22146 -0.22146 -0.22146 -0.22146 -0.22146 -0.22146 -0.22146 -0.22146 -0.22146
0.00069        0        0        0        0        0        0        0 0.000627
0        0        0        0        0        0        0        0    -0.001
0.091461 0.090771 0.090771 0.090771 0.090771 0.090771 0.090771 0.090771 0.091398

1.696275 1.721237 1.748695 1.778899 1.812123 1.84867 1.888872 1.933093 1.980737
1.696275 1.721237 1.748695 1.778899 1.812123 1.84867 1.888872 1.933093 1.981637
-5.7E-09     1.79E-12 1.97E-12 2.17E-12 2.38E-12 2.62E-12 2.88E-12 3.17E-12 3.49E-12   0.0001

-0.22146 -0.22146 -0.22146 -0.22146 -0.22146 -0.22146 -0.22146 -0.22146   -0.22146
1.1    1.21    1.331   1.4641 1.61051 1.771561 1.948717 2.143589   2.357948
0.0011        0        0        0       0        0        0        0          0
-1.1E-19     -0.00011 -0.00012 -0.00013 -0.00015 -0.00016 -0.00018 -0.00019 -0.00021   -0.00024
0.091871 0.090771 0.090771 0.090771 0.090771 0.090771 0.090771 0.090771   0.090771

1.696165 1.721116 1.748562 1.778752 1.811962 1.848493 1.888677 1.932879 1.981501
1.577713 1.645069 1.71916 1.80066 1.89031 1.988925 2.097402 2.216726 2.347983
-5.7E-09     0.118561 0.076168 0.029535 -0.02176 -0.07819 -0.14025 -0.20853 -0.28363 -0.36625

-0.22146 -0.22146 -0.22146 -0.22146 -0.22146 -0.22146 -0.22146 -0.22146 -0.22146
0.00069        0        0        0        0 0.000627 -0.00069        0        0
0            0        0        0        0        0    -0.001       0        0        0

steady state          0        1        2        3        4        5        6        7        8
0.113464     0.090771 0.090771 0.090771 0.090771 0.090771 0.090771 0.090771 0.090771 0.090771
0.12481     0.349468 0.099848 0.099848 0.099848 0.099848 0.099848 0.099848 0.099848 0.099848
0.137291      0.109833   0.384415    0.109833   0.109833     0.109833   0.109833   0.109833    0.109833      0.109833
0.15102      0.120816   0.120816    0.422856   0.120816     0.120816   0.120816   0.120816    0.120816      0.120816
0.166122      0.132898   0.132898    0.132898   0.465142     0.132898   0.132898   0.132898    0.132898      0.132898
0.182734      0.146187   0.146187    0.146187   0.146187     0.511656   0.146187   0.146187    0.146187      0.146187
0.201008      0.160806   0.160806    0.160806   0.160806     0.160806   0.562822   0.160806    0.160806      0.160806
0.221109      0.176887   0.176887    0.176887   0.176887     0.176887   0.176887   0.619104    0.176887      0.176887
0.243219      0.194576   0.194576    0.194576   0.194576     0.194576   0.194576   0.194576    0.681014      0.194576
0.267541      0.214033   0.214033    0.214033   0.214033     0.214033   0.214033   0.214033    0.214033      0.749116

1.696275 1.721237 1.748695 1.778899 1.812123               1.84867 1.888872 1.933093 1.981737
0        0        0        0        0                     0        0        0        0

2.2
2.0
1.8
1.6
1.4                                                                                            old bankers'
investments
1.2
1.0                                                                                            middle-aged
0.8                                                                                            bankers' investments

0.6
young bankers'
0.4
investments
0.2
0.0
steady   0      1       2         3        4       5       6       7      8       9
state
10-period credit cycle
TRUE            steady state polynomials const     over n    over n^2
TRUE                           r             1.301     0.388     0.000                            1.689
1.75 0.061493              I             1.983    -1.751     0.000                            0.233
-0.00015                        Y             1.097    -0.968     0.000                            0.129
0.055008                        entrepr       0.269    -0.238     0.000                            0.032
bankers       0.000     0.731    -0.645                            0.086
workers       0.828    -1.461     0.645                            0.011
n             0         0          0
1         1         1          1

have utility = wage-.5*pi*labor^2
1.75 PsiMax(pi) to guarantee investment can be positive only where bad projects are not worthwhile
0.233117 pi_1 to make netProduct =1 at r_infinity

old investment at n-1
shortfall of stabilization subsidy needed at n
1.355884                 0.338971 -0.10277 1.694855
10   t+1           FALSE        TRUE steady state
1.369366    r(t+1)                                 1.339527
0.068614    surplus for bankers, sigma(t+1)        0.038776
1.589903    employment                             1.717902
0.370634    wage, w(t+1)                           0.400473 0.343986 workers' welfare
0.589272    workers' earnings         0.143467 0.687973               0
0.227129    managers' earnings                     0.245415
0.10909   banking profits                        0.066613
0.925491    net product (less cost of inputs) at time t+1 1                                  0
0.167358    interest                               0.180832
0.385543    discount@0                                ..    Consider a stabilization by recapitalization grants at n-1, financed by govt bonds that are repa
0.078843    old banker's consumption at t+1 0.098553 0.07027 cost at n of capital needed for stabilization at n-1
9   t                                         ..      0.104514 overall workers' long-run gains at n from stabilization at n-1
0.317698    young bankers' investments, J(t) 0.113464 TRUE stabilization worthwhile for workers?
1.673582 total investment by banks at t        1.808318
1.673582 total project investment at t         1.808318
0.317698 equivalent J(t), without excess)      0.113464
0.31941
0.176626 capital of all bankers for investment at time t 0.098701 wage gains at time n alone from stabilization
2.265016 welfare at n of future wages for workers born at t1.354324 existing workers welfare at n of future wages in cycle
0.059996 gains at n from stabilization at n-1 for workers born at t 2.265016 welfare at n of future wages in cycle including unborn workers'
0 capital/investment at time n-1 for bankers born at t                             0             1.627454 factor for all cycles
0 capital held by bankers born at t for investment at time n-1            1.35E-11               1.627454
0.317698 investment at time n-1 by bankers born at t
investment shortfall at time n-1 by bankers born at t, from 0.063882 stabilization cost at n-1, funds needed at n-1 to expand investment to steady state
pattern of investments at n-1                                                   0
deviation from pattern in investment at n-1
subsidy at n-1 needed to deviate from pattern                       0 cost of deviating from pattern at n-1
young pattern      0.8 fraction of steady state             1.354324 maximize for optimal intervention paid by lump-sum tax on workers
0.113464 investment at time n-1 by bankers born at t
0 capital for investment at time n-1 held by bankers born at t
0 capital/investment at time n-1 for bankers born at t
at t
2.325012 welfare at n of future wages for workers born 1.458838
solverA                                                   values at time n
FALSE                                                                workers n-1  wage stabilizatn
cost of stabilizatn atvalue of gains at n alone
1                                            0.8 0.07027 0.104514 0.098701
TRUE                                             0.999 0.000351 0.000543 0.000512
100                                           0.99 0.003514 0.005424 0.005116               0.4
0.98 0.007027 0.010828 0.010214
0.35
solverB                                              0.95 0.017568 0.026913 0.025391
1.354324                                             0.9 0.035135 0.053303 0.050305               0.3
10                                           0.85 0.052703 0.07917 0.074742 0.25
FALSE                                                0.8 0.07027 0.104514 0.098701
TRUE                                               0.75 0.087838 0.124007 0.120063               0.2
TRUE                                                0.7 0.105405 0.139655 0.139433 0.15
100                                           0.65 0.122973 0.153381 0.157735
0.1
0.6 0.14054 0.163434 0.173788
0.55 0.158108 0.172656 0.189262 0.05
0.5 0.175675 0.181141 0.204126                 0
0.4 0.21081 0.19245 0.229444                      0   0.5
0.3 0.245945 0.20309 0.254081
0.2 0.28108 0.20914 0.273807
0.1 0.316215 0.214605 0.292906
-0.22146    R'(I_{n-1})                                          0.01 0.347837 0.219162 0.30971
0.336385    subsidy cost per unit of small balanced short-term stimulus at n-1
0.275622 cost of fiscal stimulus using old one-term bankers
0.060764 cost of stimulating the regular banking system, to keep young bankers
0.704204    wage benefits at n per unit of short-term investment stimulus at n-1
0.3038   net discounted wage benefits less subsidy cost at n-1
0.044471 net benefits of new work                      0
0.259329 net benefits of higher wages for work from old banks
-0.22146 R'(I_t)                  epsilon
-0.00132 Delta(J_t) vector             0.001
0.001 Delta(I_t) vector
0.316381

1.674582
1.673682 values here
-1E-04

-0.22146    R'(I_t)
1   growth from time n-1, or -10.001 epsilon
-0.0011   Delta(J_t) vector         0.0011 delta        0.0001
0.001494    Delta(I_t) vector              0              0.0001
0.316598    new J vector                   0             -0.0001
0.001594
1.675076
1.516641 values here
0.156941

-0.22146 R'(I_t)                      0.001 epsilon
-0.00063 Delta(J_t) vector
0.001 Delta(I_t) vector

9t
0.317698
0.099848
0.109833
0.120816
0.132898
0.146187
0.160806
0.176887
0.194576
0.214033

1.673582
0
ents
1                               0.1
1.1                                10
1.21                              0.95
1.331                                0.6
1.4641                               0.05
1.61051                                   0
1.771561
1.948717
2.143589
2.357948 2.357948

1.74
0.233117
0.105494 hyperKeynesian J, young bankers' investment in steady state
0.127021 subsidized short-term investment G
0.042111 subsidy from taxes
0

n-1, financed by govt bonds that are repaid from wage taxes at n.
1.48732
om stabilization at n-1
0
1.458838       1.277697 0.076627
2.325012
n cycle including unborn workers'
factor for all cycles

n-1 to expand investment to steady state

y lump-sum tax on workers
cost
workers gains long-run
wage gains period n

0.5   1   1.5
0.1 rho, rate of time discounting per period (up to retirement period after n-period career)    good is better than gad
10 n, number of periods in banker's career                                                      bad is bad, even at r_1
0.95 alpha, proby of success for good project                                                   r_max for bad to be bad
0.05 gamma, fraction of investment that entrepreneur can divert in bad project                gamma_max for bad @r_1
0 eta, fraction of investment that banker spends evaluating the project
0.142857 E, entrepreneurs required bonus when succeed, per unit invested
0.387755 B, bankers required rewards when succeed, per unit invested                       0
1.339527 r in steady-state equilibrium, for given n
for n=infinity                     0.232515 investment at r_1
1.300752 r_infinity, steady state r 1.688507 r_1, steady state r for n=1
Parameters for an linear investment-demand function. Workers (one unit required per successful investment) have utility = wage-.5*pi*labor^2
1.74 Psi, maximal returns (r) at zero wage
0.233117 pi, rate of wage increase as employment increases
1.983408 investment at r, largest possible amount of good investment at any time              1.300752 R(I)

n    10
steady state              1              2          3          4          5           6          7          8          9
For eqm: 1.354242 1.349114       1.344786   1.341218   1.338348   1.336102    1.334396   1.333142   1.332259   1.331668
-1.4E-08 =0, 0<= 0.048362       0.044034   0.040466   0.037596    0.03535    0.033644   0.032391   0.031507   0.030916
1.765031       1.784573   1.800685   1.813642   1.823785    1.831491   1.837149   1.841139   1.843809
1.717902           1.67678       1.695345   1.710651    1.72296   1.732596    1.739916   1.745292   1.749082   1.751618
0.400473          0.390886       0.395214   0.398782   0.401652   0.403898    0.405604   0.406858   0.407741   0.408332
0.687973           0.65543       0.670024   0.682177    0.69203   0.699792    0.705718   0.710085   0.713173   0.715242
0.245415           0.23954       0.242192   0.244379   0.246137   0.247514    0.248559   0.249327   0.249869   0.250231
0.066613          0.081092       0.074653   0.069223   0.064777   0.061248    0.058537   0.056531   0.055108   0.054153
0.976062       0.986869   0.995779   1.002944   1.008553    1.012814   1.015944    1.01815   1.019626
0.180832          0.176503       0.178457   0.180069   0.181364   0.182378    0.183149   0.183715   0.184114   0.184381
0.909091       0.826446   0.751315   0.683013   0.620921    0.564474   0.513158   0.466507   0.424098
0.085544       0.088478   0.091076   0.093316   0.095197    0.096732   0.097951   0.098887    0.15604
0              1          2          3          4           5          6          7          8
0<= 0.094767    0.098486   0.101864   0.104855   0.107434    0.109599    0.111367   0.112769   0.113848
1E-10             1.765031   1.784573   1.800685   1.813642   1.823785    1.831491    1.837149   1.841139   1.843809
0.287281   0.311557   0.328887   0.339923   0.345377    0.345965    0.342367   0.335184   0.324923
0.319173   0.617096   0.893966   1.150231   1.386563    1.603821    1.803001   1.985194   2.151544
0.024813   0.039605   0.047022   0.049199   0.047814    0.044144    0.039136   0.033463   0.027585
0.288684   0.246917   0.208887   0.173939     0.14147     0.11094   0.081884   0.053911      0.0267
0.223455   0.211114   0.198504   0.185757   0.173023    0.160464    0.148229   0.136451   0.125233
0.064508   0.052127   0.041465    0.03231   0.024478    0.017802    0.012138   0.007356   0.003344
capital pattern 0.064508    0.052127   0.041465    0.03231   0.024478    0.017802    0.012138   0.007356   0.003344
diff -4.2E-11   -4.9E-11   -5.8E-11     -7E-11   -8.6E-11    -1.1E-10    -1.5E-10   -2.3E-10   -4.5E-10

0.267541    0.243219   0.221109 0.201008 0.182734 0.166122 0.15102              0.137291 0.12481
0.080635    0.065159   0.051831 0.040388 0.030597 0.022252 0.015172             0.009195 0.00418
0.301391    0.267904   0.234416 0.200928 0.16744 0.133952 0.100464              0.066976 0.033488
0.343986    0.656701   0.940988 1.19943 1.434377 1.647966 1.842137              2.018656 2.179129
1.3
1.2
1.1                                                                                                interest on investment        1
1                                                                                                                         TRUE
banking profits             100
0.9
0.8
entrepreneurs' income
0.7
0.6                                                                                                wages
0.5
0.4
0.3
0.2
0.1
0
steady   1      2        3       4        5       6         7       8         9        10
state                         10-period credit cycle

steady state          0          1          2          3             4          5              6            7           8
0.113464     0.094767   0.098486   0.101864   0.104855      0.107434   0.109599       0.111367     0.112769    0.113848
0.12481     0.197613   0.104243   0.108335   0.112051       0.11534   0.118177       0.120559     0.122504    0.124046
0.137291     0.137756   0.217374   0.114668   0.119168      0.123256   0.126874       0.129995     0.132615    0.134754
0.15102     0.150096   0.151531   0.239111   0.126134      0.131085   0.135581       0.139562     0.142994    0.145876
0.166122     0.163052   0.165106   0.166685   0.263022      0.138748   0.144193       0.149139     0.153518    0.157294
0.182734      0.17651   0.179358   0.181616   0.183353      0.289325   0.152623       0.158613     0.164053     0.16887
0.201008      0.190326 0.194161 0.197293 0.199778 0.201688   0.318257   0.167885    0.174474 0.180458
0.221109      0.204332 0.209358 0.213577 0.217023 0.219756   0.221857   0.350083    0.184673 0.191921
0.243219      0.218355 0.224766 0.230294 0.234935 0.238725   0.241731   0.244043    0.385091 0.203141
0.267541      0.232225 0.24019 0.247242 0.253323 0.258429    0.262598   0.265904    0.268447    0.4236

1.765031 1.784573 1.800685 1.813642 1.823785 1.831491 1.837149 1.841139 1.843809
0        0        0        0        0        0        0        0        0

2.0
1.8
1.6
1.4
old bankers'
1.2                                                                                 investments

1.0
middle-aged
0.8                                                                                 bankers' investments
0.6
0.4                                                                                 young bankers'
investments
0.2
0.0
steady   0      1     2      3       4        5    6    7      8       9
state
10-period credit cycle
TRUE            steady state polynomials const     over n    over n^2
TRUE                           r             1.301     0.388     0.000                             1.689
1.75 0.061493              I             1.983    -1.751     0.000                             0.233
-0.00015                        Y             1.097    -0.968     0.000                             0.129
0.055008                        entrepr       0.269    -0.238     0.000                             0.032
bankers       0.000     0.731    -0.645                             0.086
workers       0.828    -1.461     0.645                             0.011
n             0         0          0
1         1         1          1

have utility = wage-.5*pi*labor^2
1.75 PsiMax(pi) to guarantee investment can be positive only where bad projects are not worthwhile
0.233117 pi_1 to make netProduct =1 at r_infinity                 0.439248 pi_1 to make employment alpha*I(r_infinity)=1

old investment at n-1
shortfall of stabilization subsidy needed at n
1.562229                  0.132625 -0.04212 1.694855
10   t+1            FALSE        TRUE steady state
1.354242                                            1.339527
r(t+1), returns to successful investments, per unit invested
0.05349   surplus for bankers, sigma(t+1)         0.038776
1.741877                                            1.808318
good investment in previous period, I(r(t+1))
1.654783    employment                              1.717902
0.385758    wage, w(t+1)                            0.400473 0.343986 workers' welfare
0.638347    workers' earnings          0.072134 0.687973               0
0.236398    managers' earnings                      0.245415
0.088514    banking profits                         0.066613
0.963258    net product (less cost of inputs) at time t+1 1                                   0
0.174188    interest                                0.180832
0.385543    discount@0                                 ..    Consider a stabilization by recapitalization grants at n-1, financed by govt bonds that are repa
0.082313    old banker's consumption at t+1 0.098553 0.07027 cost at n of capital needed for stabilization at n-1
9   t                                          ..      0.037458 overall workers' long-run gains at n from stabilization at n-1
0.113464 J(t)
0.179648 young bankers' investments in previous period, FALSE stabilization worthwhile for workers?
1.741877 total investment at t                 1.808318
0.31941
0.255528 capital of all bankers for investment at time t 0.049626 wage gains at time n alone from stabilization
t
2.30321 welfare at n of future wages for workers born at 1.42138 existing workers welfare at n of future wages in cycle
0.021802 gains at n from stabilization at n-1 for workers born at t    2.30321 welfare at n of future wages in cycle including unborn workers'
0 capital/investment at time n-1 for bankers born at t                                         1.627454 factor for all cycles
0.179648 investment at time n-1 by bankers born at t                                    0 investment sums correctly
0 capital held by bankers born at t for investment at time n-1          3.44E-11 capital sums correctly
capital pattern 0.8 fraction of steady state
diffs        1.98E-16 1.97E-16
0.113464 investment at time n-1 by bankers born at t
0 capital for investment at time n-1 held by bankers born at t
0 capital/investment at time n-1 for bankers born at t
at t
2.325012 welfare at n of future wages for workers born 1.458838
solver
FALSE
1
TRUE
100

9t
0.179648
0.125233
0.136451
0.148229
0.160464
0.173023
0.185757
0.198504
0.211114
0.223455

1.741877
0
0.1
10
0.95
0.6
0.05
0

1.74
ha*I(r_infinity)=1                                            0.233117

n-1, financed by govt bonds that are repaid from wage taxes at n.
0.533061
om stabilization at n-1
2.325012
n cycle including unborn workers'
factor for all cycles

```
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