housing subsidy by qKQ55N

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 Overview               Overview                Overview



                        Overview
     Specify these values.
          PHOUSING =       $1.00                                Utility Maximization
                M=     $4,000.00              6000
 Values below are determined.                                                   Budget Line
                                              5000
               H* =       1000.0
                                                                                Highest Attainable Indifference Curve
                Y* =      3000.0
                                              4000
               U* =     2279.507




                                     Good Y
Spent on housing:      $1,000.00              3000

                                              2000

On Solver                                     1000

                                                0
                                                     0   1000          2000          3000            4000
                                                                              Housing


         The axes are fixed. If your select a much different value for either M or P HOUSING, you might want to
         select new maximum values. For the Y axis select a value about 50 percent larger than the value for M.
         For the H axis, select a value at least as large as M/PHOUSING.

         To make these changes, right-click on the relevant axis (on any of the numbers). Select "Format Axis"
         and then "Scale." Enter the appropriate value in the "Maximum" cell.
Attainable Indifference Curve




             4000           5000




    , you might want to
rger than the value for M.


rs). Select "Format Axis"
X
       0
     100
     200
     300
     400
     500
     600
     700
     800
     900
  1000.0
1137.931
1275.862
1413.793
1551.724
1689.655
1827.586
1965.517
2103.448
2241.379
 2379.31
2517.241
2655.172
2793.103
2931.034
3068.966
3206.897
3344.828
3482.759
 3620.69
    4000
Budget Line Indifference Curve X* & Y*
       4000                         3000
       3900         6463.30407      3000
       3800         5129.92784      3000
       3700       4481.404747       3000
       3600       4071.626425       3000
       3500         3779.76315      3000
       3400       3556.893304       3000
       3300       3378.743641       3000
       3200       3231.652035       3000
       3100       3107.232506       3000
       3000               3000      3000
 2862.06897       2873.531357     -99999
 2724.13793       2766.007453     -99999
  2586.2069       2672.961079     -99999
 2448.27586       2591.292369     -99999
 2310.34483       2518.770283     -99999
 2172.41379       2453.740498     -99999
 2034.48276       2394.945503     -99999
 1896.55172       2341.409138     -99999
 1758.62069       2292.359895     -99999
 1620.68966       2247.178428     -99999
 1482.75862       2205.360715     -99999
 1344.82759       2166.491614     -99999
 1206.89655       2130.225509     -99999
 1068.96552       2096.271897     -99999
 931.034483       2064.384479     -99999
 793.103448       2034.352801     -99999
 655.172414       2005.995753     -99999
 517.241379       1979.156465     -99999
 379.310345       1953.698251     -99999
           0      1889.881575     -99999
        Select the value below.
       Percentage rebate =              40                         Utility Maximization, Subsidy

                Initial Values New Values                                         Real Budget Line
                                                       6000
   PHOUSING =             $1.00       $0.60                                       Highest Indifference Curve, No Subs
         M=           $4,000.00   $4,000.00                                       Apparent Budget Line
                                                       5000
        H* =           1000.000    1666.670                                       Highest Indifference Curve, w/Subsi
         Y* =          3000.000    2999.998
        U* =           2279.507    2590.020            4000




                                              Good Y
Subsidy =                          $666.67             3000


                                                       2000
                              About reset
                                                       1000


                                                         0
                                                              0   1000   2000   3000     4000
                                                                                  Housing
ation, Subsidy
Real Budget Line
Highest Indifference Curve, No Subsidy
Apparent Budget Line
Highest Indifference Curve, w/Subsidy Alone




       4000        5000      6000        7000
1222.223
1259.261
1296.298
1333.335
1370.372
 1407.41
1444.447
1481.484
1518.521
1555.559
1592.596
1629.633
1666.670
1777.781
1888.893
2000.004
2111.115
2222.226
2333.337
2444.448
2555.559
 2666.67
2777.781
2888.893
3000.004
3111.115
3222.226
3333.337
3444.448
3555.559
 3666.67
3777.781
3888.893
4000.004
4111.115
4222.226
4333.337
4444.448
4555.559
 4666.67
4777.781
4888.893
5000.004
5111.115
5222.226
6666.667
X          Budget_1    IC_1        IC_2        X* & Y*     Budget2     X**&Y**
       0        4000                                3000        4000    2999.998
111.1111    3888.889    6240.251    7398.636        3000    3933.333    2999.998
222.2222    3777.778    4952.891    5872.301        3000    3866.667    2999.998
333.3333    3666.667    4326.749    5129.928        3000        3800    2999.998
444.4444    3555.556    3931.112    4660.849        3000    3733.333    2999.998
555.5556    3444.444    3649.321    4326.749        3000    3666.667    2999.998
666.6667    3333.333    3434.143    4071.626        3000        3600    2999.998
777.7778    3222.222    3262.141    3867.696        3000    3533.333    2999.998
888.8889    3111.111    3120.126    3699.318        3000    3466.667    2999.998
1000.000        3000        3000    3556.893        3000        3400    2999.998
1037.037    2962.963    2963.852    3514.035      -99999    3377.778    2999.998
1074.074    2925.926    2929.385     3473.17      -99999    3355.555    2999.998
1111.112    2888.888    2896.468    3434.142      -99999    3333.333    2999.998
1148.149    2851.851    2864.982    3396.811      -99999    3311.111    2999.998
1185.186    2814.814    2834.822    3361.053      -99999    3288.888    2999.998
1222.223    2777.777    2805.893    3326.754      -99999    3266.666    2999.998
1259.261    2740.739     2778.11    3293.813      -99999    3244.444    2999.998
1296.298    2703.702    2751.395     3262.14      -99999    3222.221    2999.998
1333.335    2666.665     2725.68    3231.651      -99999    3199.999    2999.998
1370.372    2629.628    2700.899     3202.27      -99999    3177.777    2999.998
 1407.41     2592.59    2676.996     3173.93      -99999    3155.554    2999.998
1444.447    2555.553    2653.917    3146.567      -99999    3133.332    2999.998
1481.484    2518.516    2631.614    3120.124      -99999     3111.11    2999.998
1518.521    2481.479    2610.043    3094.548      -99999    3088.887    2999.998
1555.559    2444.441    2589.161     3069.79      -99999    3066.665    2999.998
1592.596    2407.404    2568.933    3045.807      -99999    3044.442    2999.998
1629.633    2370.367    2549.322    3022.555      -99999     3022.22    2999.998
1666.670     2333.33    2530.296    2999.998      -99999    2999.998    2999.998
1777.781    2222.219    2476.444    2936.149      -99999    2933.331      -99999
1888.893    2111.107    2426.902     2877.41      -99999    2866.664      -99999
2000.004    1999.996      2381.1    2823.106      -99999    2799.998      -99999
2111.115    1888.885    2338.571    2772.683      -99999    2733.331      -99999
2222.226    1777.774    2298.927    2725.679      -99999    2666.664      -99999
2333.337    1666.663    2261.841    2681.709      -99999    2599.998      -99999
2444.448    1555.552    2227.038    2640.446      -99999    2533.331      -99999
2555.559    1444.441    2194.283     2601.61      -99999    2466.664      -99999
 2666.67     1333.33    2163.373    2564.963      -99999    2399.998      -99999
2777.781    1222.219    2134.135    2530.297      -99999    2333.331      -99999
2888.893    1111.107    2106.416    2497.432      -99999    2266.664      -99999
3000.004    999.9963    2080.083    2466.211      -99999    2199.998      -99999
3111.115    888.8852    2055.019    2436.495      -99999    2133.331      -99999
3222.226    777.7741    2031.122    2408.161      -99999    2066.664      -99999
3333.337     666.663    2008.298    2381.101      -99999    1999.998      -99999
3444.448    555.5519    1986.467    2355.217      -99999    1933.331      -99999
3555.559    444.4408    1965.555    2330.424      -99999    1866.664      -99999
 3666.67    333.3297    1945.497    2306.642      -99999    1799.998      -99999
3777.781    222.2186    1926.234    2283.803      -99999    1733.331      -99999
3888.893    111.1074    1907.711    2261.842      -99999    1666.664      -99999
4000.004    -0.00366    1889.881    2240.702      -99999    1599.998      -99999
4111.115    -111.115    1872.699    2220.331      -99999    1533.331      -99999
4222.226    -222.226    1856.126    2200.681      -99999    1466.664      -99999
4333.337   -333.337   1840.124   2181.708   -99999   1399.998   -99999
4444.448   -444.448    1824.66   2163.374   -99999   1333.331   -99999
4555.559   -555.559   1809.703    2145.64   -99999   1266.664   -99999
 4666.67    -666.67   1795.225   2128.475   -99999   1199.998   -99999
4777.781   -777.781   1781.199   2111.845   -99999   1133.331   -99999
4888.893   -888.893   1767.602   2095.724   -99999   1066.664   -99999
5000.004      -1000    1754.41   2080.083   -99999   999.9978   -99999
5111.115   -1111.11   1741.604     2064.9   -99999   933.3311   -99999
5222.226   -1222.23   1729.163    2050.15   -99999   866.6645   -99999
6666.667   -2666.67   1593.988   1889.882   -99999          0   -99999
   Effects of a Cash Transfer       w/subsidy
PHOUSING =         $1.00      $1.00       $0.60                       Utility Maximization, Cash Transfer
      M=       $4,000.00  $4,666.67   $4,000.00
     H* =       1000.000   1166.667    1666.670                                             Real Budget Line
                                                           6000
      Y* =      3000.000   3500.001    2999.998                                             Apparent Budget Line
     U* =       2279.507   2659.426    2590.020                                             Highest Indifference Cu
                                                           5000
                                                                                            Highest Indifference Cu
Subsidy =                  $666.67     $666.67
                                                           4000




                                                  Good Y
                                                           3000


                                                           2000


                                                           1000


                                                             0
                                                                  0       1000       2000
                                                                                            Housing
ximization, Cash Transfer
            Real Budget Line
            Apparent Budget Line
            Highest Indifference Curve, No Subsidy
            Highest Indifference Curve, w/Cash Transfer




     2000            3000           4000             5000
            Housing
X
       0
      50
     100
     150
     200
     250
     300
     350
     400
     450
     500
     550
     600
     650
     700
     750
     800
     850
     900
     950
1000.000
1016.667
1033.333
    1050
1066.667
1083.334
    1100
1116.667
1133.334
    1150
1166.667
1216.667
1266.668
1316.668
1366.668
1416.669
1466.669
1516.669
 1566.67
 1616.67
1666.670
1744.448
1822.226
1900.004
1977.782
2055.559
2133.337
2211.115
2288.893
2366.671
2444.448
2522.226
2600.004
2677.782
 2755.56
2833.337
2911.115
2988.893
3066.671
3144.449
6666.667
Budget_1    IC_1        IC_2        X* & Y*     Budget2     X**&Y**
     4000                                3000    4666.668    3500.001
     3950    8143.253    10001.39        3000    4616.668    3500.001
     3900    6463.304    7938.111        3000    4566.668    3500.001
     3850    5646.216    6934.579        3000    4516.668    3500.001
     3800    5129.928    6300.483        3000    4466.668    3500.001
     3750    4762.203     5848.85        3000    4416.668    3500.001
     3700    4481.405    5503.979        3000    4366.668    3500.001
     3650     4256.95    5228.308        3000    4316.668    3500.001
     3600    4071.626    5000.696        3000    4266.668    3500.001
     3550    3914.868    4808.168        3000    4216.668    3500.001
     3500    3779.763    4642.235        3000    4166.668    3500.001
     3450    3661.567    4497.069        3000    4116.668    3500.001
     3400    3556.893    4368.511        3000    4066.668    3500.001
     3350    3463.247    4253.496        3000    4016.668    3500.001
     3300    3378.744    4149.711        3000    3966.668    3500.001
     3250    3301.927    4055.366        3000    3916.668    3500.001
     3200    3231.652    3969.055        3000    3866.668    3500.001
     3150    3167.002    3889.653        3000    3816.668    3500.001
     3100    3107.233    3816.246        3000    3766.668    3500.001
     3050    3051.734    3748.084        3000    3716.668    3500.001
     3000        3000    3684.545        3000    3666.668    3500.001
 2983.333    2983.516    3664.299      -99999    3650.001    3500.001
 2966.667    2967.389    3644.492      -99999    3633.335    3500.001
     2950    2951.604    3625.106      -99999    3616.668    3500.001
 2933.333    2936.151    3606.126      -99999    3600.001    3500.001
 2916.666    2921.015    3587.537      -99999    3583.335    3500.001
     2900    2906.188    3569.326      -99999    3566.668    3500.001
 2883.333    2891.657    3551.479      -99999    3550.001    3500.001
 2866.666    2877.412    3533.984      -99999    3533.335    3500.001
     2850    2863.443    3516.828      -99999    3516.668    3500.001
 2833.333    2849.742    3500.001      -99999    3500.001    3500.001
 2783.333    2810.157    3451.383      -99999    3450.001      -99999
 2733.332    2772.684    3405.359      -99999        3400      -99999
 2683.332    2737.133    3361.696      -99999        3350      -99999
 2633.332    2703.337    3320.189      -99999        3300      -99999
 2583.331    2671.151    3280.659      -99999    3249.999      -99999
 2533.331    2640.446    3242.947      -99999    3199.999      -99999
 2483.331    2611.105    3206.911      -99999    3149.999      -99999
  2433.33    2583.026    3172.425      -99999    3099.998      -99999
  2383.33    2556.117    3139.376      -99999    3049.998      -99999
  2333.33    2530.296    3107.663      -99999    2999.998      -99999
 2255.552    2492.118    3060.773      -99999     2922.22      -99999
 2177.774    2456.144    3016.591      -99999    2844.442      -99999
 2099.996    2422.162    2974.854      -99999    2766.664      -99999
 2022.218    2389.985    2935.335      -99999    2688.887      -99999
 1944.441    2359.453    2897.836      -99999    2611.109      -99999
 1866.663    2330.423    2862.183      -99999    2533.331      -99999
 1788.885    2302.771    2828.221      -99999    2455.553      -99999
 1711.107    2276.387    2795.817      -99999    2377.775      -99999
 1633.329    2251.172    2764.848      -99999    2299.998      -99999
 1555.552    2227.038    2735.207      -99999     2222.22      -99999
1477.774   2203.907   2706.798   -99999   2144.442   -99999
1399.996   2181.708   2679.533   -99999   2066.664   -99999
1322.218   2160.377   2653.335   -99999   1988.886   -99999
 1244.44   2139.857   2628.132   -99999   1911.109   -99999
1166.663   2120.094   2603.861   -99999   1833.331   -99999
1088.885   2101.042   2580.461   -99999   1755.553   -99999
1011.107   2082.657   2557.881   -99999   1677.775   -99999
933.3292   2064.899   2536.071   -99999   1599.997   -99999
855.5514   2047.732   2514.986   -99999    1522.22   -99999
-2666.67   1593.988   1957.706   -99999      -2000   -99999
       Percentage rebate =         40
                                                                      Utility Maximization, Tax = Subsidy
PH =                 $1.00       $0.60                                             Real Budget Line
M=               $4,000.00   $3,428.57                   3200                      Highest Indifference Curve, No Subsidy
H* =              1000.000    1428.571                                             Apparent Budget Line
Y* =              3000.000    2571.429                   3100
                                                                                   Highest Indifference Curve, w/Subsidy&Ta
U* =              2279.507    2220.017
                                                         3000

          Tax = subsidy =     $571.43                    2900




                                                Good Y
                                                         2800
To see the nature of the equilibrium requires
                                                         2700
focusing on the range of values involving the
two equilibria. For different values of s,               2600
different ranges of values will be required.
                                                         2500
To change the axis range, right-click on the
relevant axis and select "Format Axis."                  2400
Click on the "Scale" tab. Then type the                         700        900        1100        1300
appropriate values into the dialog box.                                                   Housing
ation, Tax = Subsidy
eal Budget Line
ighest Indifference Curve, No Subsidy
pparent Budget Line
ighest Indifference Curve, w/Subsidy&Tax




              1300         1500         1700
      Housing
                                                                   Housing     Budget_1
                                                                           0       4000
                                                                          50       3950
                                                                         100       3900
For full equilibrium, the taxpayer/subsidy recipient must pay            150       3850
and receive the same amount. The "apparent" (subsidy and                 200       3800
tax) budget line must intersect the real budget line at the              250       3750
selected consumption bundle.                                             300       3700
                                                                         350       3650
Y = M - PH -- real budget line                                           400       3600
(P is the price of housing. The subscript is omitted to simplify
                                                                         450       3550
notation.)
Y = M' - P(1-s)H -- apparent budget line                                 500       3500
Rearranging terms,                                                       550       3450
Y = M' - PH + PsH                                                        600       3400
M' - PH + PsH = M - PH because the lines must intersect.                 650       3350
M' = M - PsH.                                                            700       3300
We do not know M', but with the Cobb-Douglas utility                     750       3250
function, H = 0.25M'/(P(1-s)), so                                        800       3200
M' = M - (0.25)M's/(1-s), so                                             850       3150
M' (1 + 0.25s/(1-s)) = M                                                 900       3100
M' = M/(1 + .25s/(1-s))                                                  950       3050
                                                                    1000.000       3000
                                                                    1100.000       2900
                                                                    1200.000       2800
                                                                    1300.000       2700
                                                                    1400.000       2600
                                                                    1500.000       2500
                                                                    1600.000       2400
                                                                    1700.000       2300
                                                                    1800.000       2200
                                                                    1900.000       2100
                                                                    2000.000       2000
                                                                    2100.000       1900
                                                                    2200.000       1800
                                                                    2300.000       1700
                                                                    2400.000       1600
                                                                    2500.000       1500
                                                                    2600.000       1400
                                                                    2700.000       1300
                                                                    2800.000       1200
                                                                    2900.000       1100
                                                                    3000.000       1000
                                                                    3100.000         900
                                                                    3200.000         800
                                                                    3300.000         700
                                                                    3400.000         600
                                                                    3500.000         500
                                                                    3600.000         400
                                                                    3700.000         300
                                                                    3800.000         200
                                                                    3900.000         100
                                                                    4000.000           0
4100.000    -100
4200.000    -200
4300.000    -300
4400.000    -400
4500.000    -500
4600.000    -600
4700.000    -700
4800.000    -800
4900.000    -900
5000.000   -1000
IC_1        IC_2        X* & Y*     Budget2     X**&Y**
                             3000   $3,428.57    2571.429
 8143.253    7861.133        3000   $3,398.57    2571.429
 6463.304    6239.385        3000   $3,368.57    2571.429
 5646.216    5450.605        3000   $3,338.57    2571.429
 5129.928    4952.203        3000   $3,308.57    2571.429
 4762.203    4597.218        3000   $3,278.57    2571.429
 4481.405    4326.148        3000   $3,248.57    2571.429
  4256.95     4109.47        3000   $3,218.57    2571.429
 4071.626    3930.566        3000   $3,188.57    2571.429
 3914.868    3779.238        3000   $3,158.57    2571.429
 3779.763    3648.814        3000   $3,128.57    2571.429
 3661.567    3534.714        3000   $3,098.57    2571.429
 3556.893    3433.666        3000   $3,068.57    2571.429
 3463.247    3343.264        3000   $3,038.57    2571.429
 3378.744    3261.688        3000   $3,008.57    2571.429
 3301.927    3187.533        3000   $2,978.57    2571.429
 3231.652    3119.693        3000   $2,948.57    2571.429
 3167.002    3057.282        3000   $2,918.57    2571.429
 3107.233    2999.583        3000   $2,888.57    2571.429
 3051.734    2946.008        3000   $2,858.57    2571.429
     3000    2896.066        3000   $2,828.57    2571.429
 2906.188    2805.504      -99999   $2,768.57    2571.429
 2823.108    2725.302      -99999   $2,708.57    2571.429
 2748.781     2653.55      -99999   $2,648.57    2571.429
 2681.711    2588.804      -99999   $2,588.57    2571.429
 2620.741    2529.947      -99999   $2,528.57      -99999
 2564.964    2476.102      -99999   $2,468.57      -99999
 2513.651    2426.566      -99999   $2,408.57      -99999
 2466.212    2380.771      -99999   $2,348.57      -99999
 2422.163    2338.248      -99999   $2,288.57      -99999
 2381.102    2298.609      -99999   $2,228.57      -99999
  2342.69    2261.528      -99999   $2,168.57      -99999
 2306.643     2226.73      -99999   $2,108.57      -99999
 2272.717    2193.979      -99999   $2,048.57      -99999
 2240.702    2163.074      -99999   $1,988.57      -99999
 2210.419     2133.84      -99999   $1,928.57      -99999
 2181.709    2106.124      -99999   $1,868.57      -99999
 2154.435    2079.795      -99999   $1,808.57      -99999
 2128.475    2054.735      -99999   $1,748.57      -99999
 2103.723     2030.84      -99999   $1,688.57      -99999
 2080.084     2008.02      -99999   $1,628.57      -99999
 2057.472    1986.192      -99999   $1,568.57      -99999
 2035.813    1965.283      -99999   $1,508.57      -99999
 2015.038    1945.228      -99999   $1,448.57      -99999
 1995.086    1925.967      -99999   $1,388.57      -99999
 1975.901    1907.447      -99999   $1,328.57      -99999
 1957.434    1889.619      -99999   $1,268.57      -99999
 1939.638     1872.44      -99999   $1,208.57      -99999
 1922.472    1855.869      -99999   $1,148.57      -99999
 1905.898    1839.869      -99999   $1,088.57      -99999
 1889.882    1824.407      -99999   $1,028.57      -99999
 1874.39   1809.452   -99999   $968.57   -99999
1859.394   1794.976   -99999   $908.57   -99999
1844.867   1780.952   -99999   $848.57   -99999
1830.784   1767.357   -99999   $788.57   -99999
1817.121   1754.167   -99999   $728.57   -99999
1803.856   1741.362   -99999   $668.57   -99999
1790.971   1728.924   -99999   $608.57   -99999
1778.447   1716.833   -99999   $548.57   -99999
1766.265   1705.073   -99999   $488.57   -99999
1754.411    1693.63   -99999   $428.57   -99999

								
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