Unity 2: Consumer’s Theory
Utility Maximization: 3 steps
1. Assumptions about preferences
1.1. Completeness: when you compare, you have a favorite. One cannot be indifferent or not sure about a certain bundle of goods.
1.3. Non-satiation (more is always better)
// Properties of indifference curves
An indifference curve is a curve showing all combinations of consumption along which an individual is indifferent. Higher indifference curves are better (non-satiation); they are always downward sloping; they cannot cross and there is one indifference curve per bundle.
2. Utility functions: it’s the mathematical representation of preferences.
2.1. Marginal Utility: how your utility changes with each additional unit of the good, or the derivative of the utility function, that means that each additional thing, diminishes your utility (it diminishes because it is worth less to you and it is positive because of non-satiation).
2.2. Marginal Rate of Substitution: it’s the rate at which you are willing to trade-off the Y-axis for the X-axis. MRS = -MUm(x)↓ / MUp(y)↑
3. Budget constraints (ignore savings, budget = income)
3.1. Concept of Opportunity Cost: value of the foregone alternative
3.2. Constrained choice: what’s the highest utility you can achieve given the budget constraints? Intuitively: what’s the most you can have given the constraints that are placed on you? Graphically: what’s the furthest out indifference curve you can achieve?
3.3. Marginal Rate of Substitution: ratio of the marginal utilities. It’s the negative of the marginal utility of movies over the marginal utility of pizza (-x / y). It’s the rate at which you’re willing to substitute between movies and pizza, which is a function of your marginal utilities. If your marginal utility for movies is very high, then you need a lot of pizzas. If your marginal utility of movies is very low, you’d be happy to give up a movie even for a small fraction of pizza.
MRS = – x / y = budget constraint slope = MRT = -Pm /Pp
Benefits = Costs (maximization)
MUmovies / Pmovies = MUpizzas / Ppizzas