ABCDEFGHIJKLMNOPQRSTUVWXYZ
1
Disproof of First Fundamental Welfare Theorem
2
The excel version of this spreadsheet can be copied by
clicking here.
3
4
Assumptions:
5
1
Each person is endowed with 10 units of effort per day.
6
2
One unit of effort produces one banana.
7
3
The size of your house is H = sqrt(10 Eh), where Eh is the daily effort to build and maintain the house.
8
4
Each person's utility is U = H + B + Pride, where B = bananas/day.
9
5
Pride = 0.9*[H − Average(H)]
10
6
People can trade bananas for house-building effort.
11
12
13
14
Find Neoclassical (Optimal) Equilibrium
15
EhHBPrideU
16
2.44.907.6012.499
17
2.55.007.5012.500
18
2.65.107.4012.499
19
20
Unilateral Deviation from Optimal Outcome
21
EhHBPrideU
22
57.0752.0714.142
23
24
Competitive Equilibrium
25
EhHBPrideU
26
8.99.431.1-0.04810.4864
27
99.4910.00010.4868
Equilibrium
28
9.19.540.90.04710.48670.1
= Deviation
29
Change the Green "House Effort" (Eh) until
30
Neither higher nor lower Eh provides more utility for the individual
31
32
Note that the Competitive Equilbrium provides less utility (10.5) than the Neoclassical equilibrium (12.5)
33
So the Neoclassical equilibrium is inefficient, which contradicts the First Fundamental Welfare Theorem
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100