# housing subsidy by qKQ55N

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```									            Menu. The buttons below provide navigation.
Cells below them contain brief comments regarding the destinations.

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
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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