James’s Page | Actuary / ConsumerChoice

Theory of consumer choice

Everything here is taken from the consumer point of view

Total utility and marginal utility
- Marginal utility (MU) is the additional utility gained from consuming one additional unit of good
- Total utility (TU) is the sum (integral) of all marginal utilities gained from each of the unit of good consumed
- Graph of TU is like an upside down parabola. Graph of MU (the derivative of TU) is a decreasing line crossing from positive to negative y values. This corresponds to law of diminishing marginal utility: the MU declines as more of the good is consumed.
- Water-Diamond Paradox: Water is essential but costs less than diamond, which is not essential. Difference is that supply of water far excees diamond. So we consume water at a much lower price/marginal utility than diamond, but the total utility (area under demand curve) for water is still bigger than diamond.
Utility maximization: equalizing marginal utility per dollar

Basic idea of the equimarginal principle: maximization occurs when the return on the last dollar spent is the same in all areas. That is,

{$$ \frac{\text{Marginal Benefit of A}}{\text{Price of A}} = \frac{\text{Marginal Benefit of B}}{\text{Price of B}} $$}