Elasticities

  • To maximize total revenue, we want elasticity to be unitary
    • Without demand function, we have to predict the optimal price via elasticities
  • Elasticity: $e_p = \frac{\Delta Q}{\Delta P} \cdot \frac{p_0}{q_0} = \frac{\partial logQ}{\partial logP}$
    • Keep guessing until |ep| = 1
    • If |ep| > 1, decrease price; if |ep| < 1, increase price
  • Heterogeneity: Different (groups of) consumers have different demand curves and different optimal prices
    • Can use either uniform pricing (less profit) or price discrimination (more profit)
    • The elasticities of demand can affect your pricing strategy
      • Less elastic = more room to play with; more elastic = less room to play with
  • Goal of firm is to maximize producer surplus (equal to profit if there is no fixed cost)
    • Depends on demand (unknown) and supply curve (cost)
    • This class will not focus on fixed costs; the total cost will be made up of variable costs
      • $MC = \frac{\partial TC}{\partial Q}$
  • Demand can be elastic for two reasons
    • Product has low valuation: price increases, people stop buying
    • Competitive market, many substitutes
    • To alleviate elasticity elasticity and increase market power, firms use product differentiation
      • Vertical differentiation: Changes in quality
      • Horizontal differentiation: Changes in superficial features
  • In the long run, goods become more elastic because it’s easier to substitute in the long run
  • Can calculate demand function from elasticities (assuming D has a constant slope)
    • $e_p = \frac{\Delta Q}{\Delta P} \cdot \frac{P}{Q} = \text{Slope} \cdot \frac{P}{Q}$
    • Plug this slope into Q = mP + b
    • Can only do this if the firm is a price maker; can change price and affect demand
      • Implies high market power
    • Quirk: When demand is straight line, you can double the slope (of P = mQ + b) to get marginal revenue
  • Midpoint elasticity: $e_p^{mid} = \frac{\Delta Q}{q_1 - q_0} \cdot \frac{p_1 - p_0}{\Delta P}$

Income Elasticity

  • Income elasticity: $\frac{\% \Delta Q_d}{\% \Delta I} = \frac{\partial log Q_d}{\partial log I}$
    • Income is positive for normal goods and negative for inferior goods
      • Normal goods: coffee, games
      • Inferior goods: canned soup, instant ramen
    • Quasi-linear preferences have an income elasticity of 0
      • Includes necessities like salt or toothpaste
    • Normal goods include luxury goods (e > 1) and Veblens goods (upwards sloping demand curve)
      • Veblens goods include status-indicating goods, such as jewelry and designer brands
    • Inferior goods include Giffen goods (upwards sloping demand curve)
      • Giffen goods are driven by poverty; income effect dominates the substitution effect

Cross Price Elasticity

  • Cross price elasticity: $\frac{\partial log Q_A}{\partial log P_B}$
    • If e = 0, goods are unrelated, as $\Delta Q_A = 0$, so $P_B$ doesn’t affect it
    • If e > 0, A and B are substitutes; when the price of B goes up, the quantity demanded of A goes up because it is cheaper
    • If e < 0, A and B are complements; when the price of B goes up, the quantity demanded of A goes down because it’s consumed in conjunction with B

Market Power

  • Factors that affect market power
    • Number of firms
      • Consumers have more options (substitutes)
      • Demand becomes more elastic
    • Consumer preference; value of market
      • Low value implies willingness-to-pay is low
  • Shifts to demand caused by above factors
    • Number of firms
      • Lower consumer base implies an inward shift, and more substitutes implies a higher elasticity
    • Invaluable market
      • Low willingness-to-pay implies high elasticity
  • Linking market power to elasticity
    • Market power: ability to set P above MC
    • Learner index: $LE = \frac{P - MC}{P}$
    • Range of Learner index: 0 <= LE <= 1
      • LE = 0: Perfect competition
      • LE > 0: Firms have some market power
      • LE = 1: Monopoly or dominant firm
  • Higher market power (P - MC) means lower elasticity of demand

Price Discrimination

  • Two types of consumer base
    • Homogenous: All consumers are the same or are indistinguishable
    • Heterogenous: Consumers differ by income, preferences, etc.
  • If homogenous, use a uniform pricing strategy
  • If heterogenous, have to ask if resale can be prevented? If it can, price discriminate
  • Different types of price discrimination: 1st, 2nd, or 3rd
    • 1st: Offer different prices to individual consumers
    • 2nd: Product versioning; offer different prices for different versions of products
    • 3rd: Offer different prices to different groups
    • 1st is always preferred
  • Welfare is measured by the sum of consumer surplus and profit
  • Two part pricing strategy: Charging an entrance fee (fixed) and a user fee (variable based on preferences)
  • Bundling pricing: Offering items in a bundle
    • Pure bundling: Must buy all items of a bundle
    • Mixed bundling: Can buy whole bundle or single items at a higher cost

Advertising and Marketing

  • Benefits of advertising
    • Can increase willingness-to-pay which increases the slope, easier to raise prices
    • Can increase consumer base which means demand shifts outwards
    • Create awareness
    • Reduce search costs by giving hard information
    • Differentiate product(s)
    • Brand loyalty; can lead to higher market power
  • Advertising: Increasing awareness about a product
    • Informative advertising: Based on objectivity
    • Persuasive advertising: Based on subjectivity
  • Marketing: Initiating conversations about a product for brand loyalty
    • Inbound Marketing: Consumers come to you to discuss your product
    • Outbound Marketing: You go to consumers to discuss your product
  • ROAS: Return on ad spend, calculated as revenue produced by ads divided by amount spent on ads
  • Two types of information in ads
    • Hard information: Direct details about a product; price, qualities, etc
    • Soft information: Indirect details about a product; signalling

Formulas

  • Total Revenue
    • $TR = P(Q)Q \rightarrow MR = \frac{\partial TR}{\partial Q} = \frac{\partial P}{\partial Q} Q + P = P[\frac{\partial P}{\partial Q} \cdot \frac{Q}{P} + 1] = P[\frac{1}{e_p} + 1]$
  • Marginal Cost
    • Revenue maximized when MR = MC
    • $MC = P[\frac{1}{e_p} + 1] \rightarrow \frac{MC}{P} = \frac{1}{e_p} + 1 \rightarrow \frac{P - MC}{P} = - \frac{1}{e_p} \rightarrow LE = - \frac{1}{e_p}$
  • Percent change in demand
    • Factors: Price, income, preferences, price of related goods, expectations
    • $Q^d = f(P, I, P^R) \rightarrow dQ^d = \frac{\partial f}{\partial P} dP + \frac{\partial f}{\partial I} dI + \frac{\partial f}{\partial P^R} dP^R$
    • Implies $\% \Delta Q^d = e_P \% \Delta P + e_I \% \Delta I + e_{AB} \% \Delta P^R$