Hi all. I was bored so I created the following spreadsheet: https://docs.google.com/spreadsheet...ei9iMjSFwupyYWjfOgzbbK-EBM/edit#gid=911477072(adsbygoogle = window.adsbygoogle || []).push({});

I'm currently having some trouble with this. I want to find the values ofexpendituresfor each year such that thehappiness present valueis maximized (explained below).

Basically, change all the values of the orange cells to maximize the green cell. (Note: Your wealth cannot go below zero.) I cannot find a consistent way to do this.

Assumptions I've made:

1. Happiness is a direct function of expenditure.

2. The same expenditure will have a lower impact on happiness as you age

3. Increasing expenditures will have diminishing returns on happiness.

Using assumptions 2 and 3, I've created a function to modulate that, shown in Tables 1 and 2.

4. Happiness now is worth more than the identical value in the future.

Thus, the present value of happiness value can found by discounting the future "streams" of happiness given a happiness discount rate. (Exactly identical to finding present value in finance.)This is the value I want to maximize.

5. You start with a wealth of 100 units. You consume X units immediately at the beginning of the year and make a 7% return on investment. Meaning, if you consume 4 units, you'll have 102.72 unit the next year [(100-4)*1.07].

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How it works:

So basically, your happiness for the current year can be found by inputing your expenditure for that year into the diminishing return function, followed by the age function.

Example.)

Diminishing return function:

Expenditures/Base expenditures = X

Happiness(X)=(0.7232*LN(X) + 0.9265)/0.93

So if your base expenditure is $4 and you spend $8, you'll have a happiness of 1.54 units

X = 8/4 = 2

Happiness(2)=(0.7232*LN(2) + 0.9265)/0.93

or simply look at Table 1

Next, this value is multiplied with the happiness multi (age function), so if you're 41 years old, you multiply that with 0.90 (Table 2)

Thanks for reading all that! Any guidance on how I can solve this will be much appreciated.

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# B Maximize happiness

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