Utility Function in a Recession?
I am currently doing a dissertation and my results show that although people are in the same financial situation or better they are actually paying off debts and saving rather than consuming.
What I am wanting to know is with regards to the utility function. If people are not choosing to increase their utility but actually reduce it even though their financial situation has not changed will this have an effect on how the utility function should look which is:
U=XY
Should it be adapted to look more like U=(XY)-C
C =The credit that is being paid back.
I am a novice at the mathematical science bit as you can see but thought that I might have stumbled on some thing good to discuss further.
Can you help explain things
Comments
Current problem is about changed expectations of future income and rapid devaluation of accumulated wealth (which was partially illusion due to "bubble" issues) - thus current and planned consumption pattern adjustment occurs.
Rational individuals are trying to maximize utility function - this part mostly relates to intertemporal economics. Utility here is discounted summation of utility in each period:
∑U = (U°)/(1+i)°+U¹/(1+i)¹ +U²/(1+i)²+U³/(1+i)³+... +Uⁿ/(1+i)ⁿ
(Powers at utility means sequence but not power of).
For instance assume for simplicity person lives two years and interest for intertemporal shift is i=2% (that is 2% factor discounting if consumption occurs this year rather than next), then total life-long utility will be:
∑U=U°+U¹/(1+2%) = U°+U¹/1.02
Or utility can take form = discounted sum of consumption (C) for each period during life there (i) is interest rate - for decisions about what to do with current income and accumulated wealth - between loans / savings, that is to borrow more and consume or consume less and save more):
U = (C°)/(1+i)°+C¹/(1+i)¹ +C²/(1+i)²+C³/(1+i)³+... +Cⁿ/(1+i)ⁿ
Current consumption is also function of expected income, expected interest rate and accumulated wealth (meaning for infinite horizon person/family can't spent more or less than it earns during life).
Wealth at the end of each period is W¹=(1+i)W°-δW°+I-C
(1+i) - interest earned on wealth
δ - depreciation/devaluation factor of wealth
I - income earned during period
C - consumption during period
Also price level dynamics makes some differences in transition between nominal/real types of wealth/income/consumption.
Of course not any individual acts completely rationally (or many persons act partially rationally and partially not very, but decisions often are made intuitively) and there are many volatile factors.
It's more probabilistic/stochastic model rather than strictly pre-determined because many factors are hardly predictable.
There are a lot of different mathematically good-looking concepts and many theories of economics about this issue.
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