I. Review of markets

    B. Elasticity (e)

Learning objectives: Calculate and interpret elasticity values. Use own-price elasticity of demand (e) to predict how total expenditure (TE) responds to price changes.

    Recall: Sometimes it is not enough to know the direction in which Qd or Qs changes as a result of some shock to an equilibrium.

    Sometimes we want to measure how much Qd or Qs changes--i.e., responsiveness

    Elasticity does this.

The general formula for market elasticities (e):

           %DQ
    e = ---------
           %DX

where X=something which influences Q, such as price (P)

    Example: What influences the quantity demanded of movie tickets?
        Price --> own-price elasticity of demand
        Income --=> income elasticity of demand
        Tastes (genre, MPAA rating, reviews, advertising, previews)
        Prices of related goods --> cross-price elasticity of demand
            Substitutes: Video on demand
            Complements: Popcorn

    Larger elasticity => greater responsiveness

    (1) Real world relevance: direction vs. size of change in Qd.

    (2) Percentages are the key
        Across goods: $2 change in price of Asahi vs. Mazda
        Over time: $400 change in PC prices now compared to 10 years ago

    1. How to calculate elasticity

    See handout: Elasticity formulas

    a. Arc elasticity (e_ARC)

    Measures the average elasticity between two points.

Ex: Own-price elasticity of demand:                   DQd/avgQd     eARC = |-----------------|                    DP/avgP    We use avgQ and avgP so we get the same percentage answers whether P rises or falls.     for own-price elasticity, we ignore the sign Consider D with two points:      P  Qd   a  6   4   b  4   8

    b. Point elasticity (e)

    Measures the exact elasticity at a given point.

Ex: own-price point elasticity of demand:

where, at the point (Qd,P):
    dQd/dP = "the derivative of Qd with respect to price" and
    P/Qd = the ratio of P to Qd.

    point e = |dQd/dP · P/Qd|

    Since dQd/dP is negative by law of demand, e < 0.
    By convention, we often drop the sign on own-price elasticity of demand, or talk only about its size (I do that, text doesn't).
    I don't care which you use

Example 1: Linear demand

   Geometry and calculations (Excel)

Qd = a - bP =>     dQd/dP = -b =>    (dropping the sign on b) e  = b  ·  P/Qd     constant   falls as we move down the demand curve ? What are the elasticities at the following points on the demand curve?   P Qd e 1 a/b 0 ??? 2 (1/2)(a/b) (1/2)a ??? 3 0 a ???