Lecture 6

MIT OCW 14.01SC L6 - Deriving Demand Curves

MIT OCW 14.01SC - Lec 6 (Youtube)

Food Stamps
- Indifference curves and budget line for Two individuals X & Y for food vs other goods
- Total income $1000 (poor people)
- Look at the Original budget line
  - X cares a lot about other goods while Y cares much more about food.
- Imagine govt wants to give these people $500.
  - Two ways
    - Give cash
      - Shifts budget constraint out
      - X would choose to move from X1 to X2
      - X would spend most of it on other goods and only a bit more on food. (possibly even 0?)
      - Y would spend most of it on food and a bit on other goods.
    - Give food stamps
      - Shifts budget constraint to the right (but does not include the dotted portion of the line).
      - Opportunity set is now a trapezium.
      - Y would still go to Y2, but X now must go to X3. (Corner solution.)
  - Revealed preference: X now makes a choice they'd have turned down before. Therefore it is revealed that they're worse off.
  - Why give food stamps?
    - $35B on food stamps in the US (Anyone below $25,000 income).
    - But Why?
    - Imagine 'other goods' was not labelled 'other goods' but 'Cocaine'.
    - 'Paternalism': We don't trust people with the cash.
  - How do we measure how much good/bad are food stamps doing?
    - One idea: measure if they're buying food beyond the food stamps.
    - Another idea: run an A/B experiment by giving people cash vs food stamps.
    - Emperical result: 15% people are like X / people spend 15% more on food when given food stamps.
Where do demand curve come from?
- Drawing demand curve given different prices of a good and the same budget:
- In this particular example, price change in movies did not change demand for pizzas. This is called No cross-price elasticity.
- This will not be true in general.
Demand curve shifting
- For example because we got richer
- We can draw different demand curves given different budget constraints.
- Engel Curve: Demand for movies changing due to changing income (at the same price of movie)
  - Engels worked with Marx
  - This is Engel, not Engels, different guy (lol)
- Income Elasticity of Demand - important concept
  - Percentage change in quantity over percentage change in income
  - gamma = (dQ / Q) / (dy / y)
  - gamma > 0 for MOST goods - normal goods
  - gamma < 0 - inferior goods
    - E.g. canned food or potatoes
  - within normal goods
    - gamma < 1 - Necessities
    - gamma > 1 - Luxuries
    - harder to determine (as compared to normal vs inferior) as it could depend on person
Where does (price) elasticity (of demand) come from?
- Demand = MAX(Utility function) (given income, price of good)
- Demand = (% of good A) * (how much total goods I can buy?)
- (*) Derivative of Demand wrt Price = (how does % of good A change) + (how does total amt of goods I can buy change with price)
  - (*) How does % of good A change? first order derivative (wrt money I have) is already 0 at eqm! But not wrt prices! If prices change => M.R.Transformation changes => I will have to move to another point to make it equal to marginal rate of substitution.
  - (*) How does money I have affect demand? Simple -> should just be linear factor of (% of good A)
- (*) Q_a = Y/P_a * alpha(Y/P_a)
- (*) dQ/dP = -Y/P^2 * alpha - Y/P^2 * alpha'(Y/P)
- Two main factors:
  - Substitution Effect
    - Change in quantity demanded, when price increases, holding utility constant
    - [(∂Q/Q)/(∂P/P)]_{U const}
    - Shift away from good as good gets expensive
    - The Substitution effect is Always negative!
    - If price goes up, steeper budget curve, if we are on the same indifference curve (U const) then we must move to the left.
  - Income Effect
    - Change in quantity demanded, with change in income, holding prices constant
    - [(∂Q/Q)/(∂Y/Y)]_{P const}
    - Sign of Income Effect depends on whether good is normal or inferior good!
      - Can lead to Giffen Goods (next time) (subset of inferior goods) where demand increases with price!