Budget Chapter

Real World Applications: Food Stamp Program (Continued)

  • Building from last time, suppose that you can now trade a food stamp for 50 cents
    • Assume that food stamps can only be sold, not purchased, by households
    • The budget constraint increases at the top while the majority of the budget constraint remains the same
      • This is because a household would never sell food stamps most of the time; you lose 50 cents of value, and if you cut back on spending, you would cut back on dollar spending, not food stamp spending
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Relative Prices

  • Numeraire: Unit of account
    • Changing the numeraire does not change neither the budget constraint nor the budget set, as all relative prices remain the same
    • Interestingly, we can use the price of a good as a numeraire
      • For example, good 1 would be worth 1 unit of good 1, and good 2 + consumer income would be evaluated similarly

Shape of Budget Constraints

  • A linear budget constraint means that the exchange rate (or opportunity cost) remains constant, but oftentimes, that is not the case
    • Consider the food stamps example; the graph of the budget constraint had changing slopes because the exchange rate varied
    • In general, if prices are constant, the budget constraint will be a straight line (AKA a budget line)
  • Quantitative discounts and quantity penalties will often affect the price of a good depending on how much ones buys
    • “Buying in bulk” is an example of a quantitative discount, while government restrictions on buying too much of a good would be an example of a quantity penalty
    • Assuming that one good’s price (on y axis) is constant and the other’s price (on x axis) fluctuates:
      • A quantitative penalty would cause the graph to be concave dow; i.e. the more you buy, the worse the relative price gets (represented in black)
      • A quantitative discount would cause the graph to be concave up; i.e. the more you buy, the better the relative price gets (represented in red)
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Preferences Chapter

  • Budget is one aspect of a consumer’s choice; preferences allow the consumer to choose a consumption bundle from the bundle set
  • This chapter assumes that all consumers act rationally
    • Decisionmakers always choose their most preferred alternative from their set of available alternatives
    • This isn’t inherently realistic; bound regressionality states that decisionmakers can only spend so much time + energy making choices, meaning that they’re not always going to make the right decision

Preference Relation

  • Comparing two different consumption bundles, x and y: Weak Preference: x is weakly preferred to y: x⪰yStrict Preference: x is strictly preferred to y: x≻y. i.e. x⪰y,x⋠yIndifference: x and y are equally preferred: x∼y. i.e. x⪰y,x⪯y\text{Weak Preference: x is weakly preferred to y: } x \succeq y \\ \text{Strict Preference: x is strictly preferred to y: } x \succ y \text{. i.e. } x \succeq y, x \npreceq y \\ \text{Indifference: x and y are equally preferred: } x \sim y \text{. i.e. } x \succeq y, x \preceq y \\ \\

  • These relations are only ordinal; that is, they state only the order in which bundles are preferred, but not by how much more
  • Note that weak preference implies that x could EITHER be strictly preferred or equally preferred to y