9.1

2020-11-01 created. 2020-11-02 revised. 2021-07-18 add.

by hand

新しい仕事の給与 x の期待効用 E[U(x)] は、

x = [80000 90000 100000 110000 120000 130000 140000]
U(x) = x1/4
E[U(x)] = (800001/4 + ... + 1400001/4) / 7
        = 18.1538

確実同値額 C の効用 U(C) と期待効用 E[U(x)] を等置し、Cについて解く。

U(C) = E[U(x)]
C1/4 = E[U(x)]
C = E[U(x)]4
C = 18.15384 = 108160($)108610($) (2024-11-02)

Julia

code

# 9.1.jl
# 2020-11-01

x = [8e4 9e4 10e4 11e4 12e4 13e4 14e4]
u(x) = x ^ (1 / 4)
eux = sum(map(u, x)) / 7
c = eux ^ 4

println("9.1.jl")
println("x ", x)
println("E[U(x)] ", eux)
println("C ", round(c))
# eof

output

9.1.jl
x [80000.0 90000.0 100000.0 110000.0 120000.0 130000.0 140000.0]
E[U(x)] 18.15379770791559
C 108610.0

Julia part2

code

# 9.1.part2.jl
# 2021-07-18
        
x = [80e3 90e3 100e3 110e3 120e3 130e3 140e3]
u(x) = x ^ (1 / 4)
eux = sum(u, x) / length(x)
c = eux ^ 4
        
println("9.1.part2.jl")
println("x= $x")
println("E[U(x)]= $eux")
println("C= ", round(Int, c))
# eof

output

9.1.part2.jl
x= [80000.0 90000.0 100000.0 110000.0 120000.0 130000.0 140000.0]
E[U(x)]= 18.15379770791559
C= 108610

JavaScript

2024-11-02 9.1.js

Python

2024-11-02 9.1.py

Gauche

2024-11-02 9.1.scm

Fortran

2024-11-02 9.1.f90

history

2020-11-01 create.
2020-11-02 revise.
2021-02-17 add viewport.
2021-07-18 add a Julia part2.
2024-11-02 add a JavaScript code, a Python code, a Gauche code and a Fortran code.