June 2, 2020
Principles of Microeconomics (Course)
Preferences and Utility
- Completeness - can’t say ‘I’m not sure’. Got to have a feeling about each option
- Non-satiation - more is always better
Properties of Indifference Curves -> Preference Maps
- Prefer higher indifference curves (because of non-satiation)
- Always downward sloping (non-satiation)
- Cannot cross (transitivity and non-satiation)
- Utility function - mathematical representation of preferences
- Utility is ordinal not cardinal
- Diminishing marginal utility.
- Marginal Rate of Substitution = delta y / delta x (rate at which you’re willing to trade off between pizza and movies). Always diminishing.
- = -MUx / MUy
- Marginal utility is a negative function of quantity
- Y: income
- Y = Movies x price per movie + Pizzas x price per pizza
- Slope = -Pm / Pp = Marginal Rate of Transformation
- Opportunity cost: Value of foregone alternative
- Opportunity set: Price increases restrict your set of choices so you’re worse off. Also reduced by decreases in income.
- What’s the furthest out indifference curve you can achieve given your budget constraints?
- The point which will make you happiest is the point where the indifference curve is tangent to the budget constraint. (Slope of indifference curve = slope of budget constraint):
- Slope of indifference curve = Marginal Rate of Substitution = Ratio of the marginal utilities (-MUx/-MUy) = Marginal Rate of Transformation = -Px/Py
- Set Benefits = Cost, in particular:
- Marginal Benefit = Marginal Cost
- Marginal Utility of Movies / Price of Movies = Marginal Utility of Pizza / Price of Pizza
- And you have to spend all your budget to be optimum.
Deriving Demand Curves
- Revealed preference: if someone makes a choice that they turned down before, we know they are worse off.
- Give people $500 of food stamps: x1 has to move to x3 even though they would have preferred x2. Turns out people are about 15% ‘worse off’ than giving them cash.
- [? If we want to subsidize only food, then we would not be happy with people moving to x2. We could give them a lower amount of cash (equalling how much they spend on food) but some people spend more on food, and we would be ok to subsidise that. So if you don’t use stamps, you have to either risk people spending on stuff you don’t want to subsidise, or somehow assess who spends more on food.]
- U = sqrt(p*m) No cross-price elasticity
- Demand curves: Maximize utility at different prices given your income
- Engel curve: demand for a good at different incomes
- Income Elasticity of Demand = (dQ/Q) / (dY/Y) (usually >0, normal goods) (if <0, inferior goods e.g. canned food to fresh food) (<1 Necessities, >1 Luxuries)
- Substitution Effect
- Income Effect
- Giffen good: price increase causes you to want more of it. Income effect dominates the substitution effect.