Let's define the words we'll be using first with the help of merriam-webster, removing the first obsolete entries of course.
Wealth:
2
Abundance of valuable material possessions or resources
3
Abundant supply
: profusion
4
a
: all property that has a money value or an exchangeable value
b
: all material objects that have economic utility;
especially : the stock of useful goods having economic value in existence at any one time <national
wealth>
Happiness:
2
a
: a state of well-being and contentment
: joy
b
: a pleasurable or satisfying experience
So, the question is, what relation is possible between wealth and happiness.
A. Wealth is necessary for happiness.
B. Wealth makes achieving happiness easier.
C. Wealth makes achieving happiness harder.
D. No wealth is necessary for happiness.
E. Wealth does not allow happiness.
F. Wealth has no relation to happiness.
Let's approach the problem first from the direction of Maslow's hierarchy of needs.
According to Maslow, the human mind focuses on one level of the pyramid before turning to the other, progressing from bottom to top. This means that in order for a person to feel completely well, both consciously and subconsciously, they have to climb each step of the pyramid.
For the relation of wealth, if you count money as the vector of wealth, it can be easily seen that the closer someone is to the bottom of the pyramid, the more some money can help. You can sate your physiological needs with money in almost every cases, especially if we're talking about around first world citizens. Buying food for money is more than possible, as well as securing shelter for the night or clothes to wear against the cold.
Even if you don't count money however, bear in mind that wealth implies possessions or possible possessions. A tribe where everybody's happy could be happy because of the abundant food they have and afterwards all steps of the pyramid fulfilled. In a communistic society without personal wealth, it is the community's wealth that is related to the individual's happiness.
Safety, while can be easily reinforced by wealth, is never guaranteed, especially when it comes to one's personal fears and paranoia. Love and belonging may come easier with money, but they aren't commodities to be bough. Esteem is something earned almost all the time, it cannot be bought.
Self-actualisation is much easier with money, that's for sure, it's far easier to live your dream life if you are financially secure, or if you have all the credit you need.
Going out from these, two steps from the Maslow pyramid cannot be bought for money, two steps are in the grey zone and one step is almost purely money. Taken that this one step is the base of the whole pyramid, I think it's proven that some amount of wealth is necessary for a person's well-being, and going out of the pyramid, this wealth is the amount of wealth needed to sustain basic physiological needs.
So now we see that a person's possible well-being does in fact have some relation to wealth, the only question is what the function of well-being looks like if we draw it, with X being wealth measured and Y being possible happiness to achieve.
Absolute happiness is impossible to achieve.
This is because one never knows when they are absolutely happy, absolute happiness is the highest possible happiness, and without knowing one has reached it one can never consider themselves to be absolutely happy, therefore missing one tiny detail of happiness. This in mind, absolute happiness is a goal set out in front of us, one we thrive towards but will never reach.
With the answer to the question of relation between happiness and wealth established as 'wealth, even if minimally, to be a necessity', we now have to consider whether more wealth than what's necessary to sate physiological needs would bring more happiness to a person. As stated before, the second step of the pyramid is in the grey-zone. Safety includes financial safety, the feeling of being secure and being convinced that you won't lose your wealth necessary to sustain physiological needs. With this in mind, of course this is easier with more wealth.
In another strain of logic, happiness is better if it lasts longer. In order for happiness to last longer, one needs more time spent happily. In order to have more time spent happily, one needs less time spent stressed or in sorrow. Without the restrains of a wage-dependent life, on is free to decide what to do with their time.
The more wealth a person has, the less time they must allocate to earning money, or if they enjoy earning money the more freedom they have in regards to their work rules and restraints. Even if one enjoys their workplace, earning less means more profit for the company meaning better wages for others meaning happiness for others around the person, while donating one's earnings to charity also brings happiness.
All of these in mind, let's answer OP's question, the exact relation between happiness and wealth, in a function where X represents wealth and Y represents happiness originating from wealth.
1. Wealth is necessary for physiological well-being
2. Duplicating your wealth when living in poverty brings far more happiness and satisfaction when it comes to the impact on one's life than duplicating your wealth when living in luxury.
Therefore, the plotted relation between wealth and happiness will have the form of a quadratic function.
1. The amount of wealth is extremely influential in the first brick of the pyramid of human needs
2. The amount of wealth is less-important in later parts.
Therefore, the plotted relation between wealth and happiness will be a concave function.
1. Zero-wealth brings financial strain and therefore stress, the opposite of well-being and happiness
2. There is a limit to the stress that one person can take before breaking and giving up.
Therefore, the plotted relation between wealth and happiness will cross the X axis and start, and the function will have a limit in negative-wealth where more debt does not make a change.
1. The relation between wealth and happiness is subjective, meaning that the amount of wealth that satisfies someone on a certain level cannot be determined, the point of finance-related stress cannot be determined.
Therefore, the function will have multiple variables that decide about where it crosses the X and Y axes as well as the limit.
All of these in mind, the relation between wealth and happiness, according to Medvekoma, is something like
y = -0.9^(x+S-D) + D , where:
S stands for the amount of negative wealth (debt) one can psychologically endure, proportional to the average person's (0.9, 1.2 etc).
D stands for wealth-related demands that contribute towards happiness, D >= 0, proportional to the average person's (0.5, 3.2, etc).
Numbers meant to be closely around 0, didn't really experiment much, point is the layout of the function. I presumed the average person would go unhappy as soon as they no longer have wealth but debt. A wealth of 5 on the X axis could be understood as middle-class level wealth.
This function will draw-out the wealth-related happiness of an individual. There I did it. A function as an answer, but mathematically, a function is the best way to show a relation.