The Elasticity of Demand

• Firm maximizes profit by selecting a point where slope of the isoprofit curve (MRS) is equal to the slope of the demand curve (MRT)
• Note that the isoprofit curve is the firms indifference curve.
• The firms decision to increase or decrease price depends on how steep the demand curve is
  • in other words, how steep is the demand curve or how much would the consumer demand change due to the change in price.
• The price elasicity of demand \(\epsilon = -\frac{\% \; change \;in \;quantity \;demand}{\% \;change \;in \;price}\)
  • \(\epsilon\) is the Greek symbol denoting elasticity
  • the negative sign in the formula is so that we get a positive \(\epsilon\). Note that \(\frac{\% \; change \;in \;quantity \;demand}{\% \;change \;in \;price}\) is negative
• \(\varepsilon = -\frac{-5}{10}=0.5\)

The Elasticity of Demand and Slope

• The elasticity of the demand is related to the slope of the demand curve. If the demand curve is flat then a small change in price will cause a larger proportion change in quantity demanded.

Figure 1. Shows demand curve

• Figure 1 shows a demand curve with slope \(-80\)

• \[\begin{align*} \text{slope of the demand curve} &= -\frac{\Delta P}{\Delta Q} \\ &= -80 \end{align*}\]

• Since, \(\Delta P=-\$80\) when \(\Delta Q=1\), \[\begin{align*} \%\text{ change in }Q &= 100(\frac{\Delta Q}{Q}) = 100(\frac{1}{20}) = 5\% \\ \%\text{ change in }P &= 100(\frac{\Delta P}{P}) = 100(\frac{-80}{6400}) = -1.25\% \end{align*}\]

• So, \[\begin{align*} \varepsilon &= -\frac{5}{-1.25} \\ &= 4 \end{align*}\]

• Similarly, one can calcuate \(\epsilon\) at several points in Figure 1.

  • at \(Q=20\) and \(P=\$6400\), \(\epsilon = \frac{5}{-1.25}=4\).

• Demand is elastic if the elasticity is greater than 1, inelastic if it less than 1 and unit elastic if its equal to 1

Question1 Choose the correct answer(s)

• A shop sells 20 hats per week at $10 each. When it increases the price to $12, the number of hats sold falls to 15 per week. Which of the following statements are correct?

  • choice 1. When the price increases from $10 to $12, demand increases by 25%.
  • choice 2. A 20% increase in the price causes a 25% fall in demand.
  • choice 3. The demand for hats is inelastic.
  • choice 4. The elasticity of demand is approximately 1.25.

Elasticity of Demand and firm’s decision

• Remember that the car manufacturer’s profit is maximized when \(Q=32\).
• The firm would not choose a point \(D\) as this falls at the inelastic portion of the demand curve and the firm can always increase profit by increasing price (as the marginal revenue is positive at the elastic potion)
  • In other words, the firm would never produce at the inelastic portion of the demand curve.
  • A firm would choose a point where \(\epsilon>1\).

Figure 2. A Firm Facing Elastic Demand

Figure 3. A Firm Facing Less Elastic Demand

• Note that the point F is where MC = price. It is the point where the profit margin is zero and we’ll also use this as a benchmark point.
• Note that in Figure 2, when the demand is relatively more elastic, the profit maximization point (E) is not too far away from point F.
• But in Figure 3, when the demand is inelastic, point E is far away from point F, compared to Figure 2.
• What this means is if the demand is relatively inelastic, the firm can enjoy higher price, and thus higher profit margin.
  • this is because, even if the firm increases its price, the quantity demanded will reduce by only a little.

Question 2.

• Based on this figure, which of the following statements are correct?

Figure 4.

- choice 1. At E, demand curve D₁ is less elastic than D₂.
- choice 2. The elasticity is the same at A and C.
- choice 3. At E, both demand curves have the same elasticity.
- choice 4. The elasticity is higher at E than at B.

• Answer:
  • At E, the price and quantity are the same on both demand curves, but D₁ is steeper, so it is less elastic than D₂.
  • The slope is the same at E and B. But at E the price is higher and quantity is lower, so the elasticity is higher.

Market Faliure

• The deadweight loss as shown in Figure 3 shows the extent of the market failure.
• Market failure occurs when markets allocate resources in an inefficient way.
  • For example, in Figure 3, price could have been set at point F, where the profit margin is zero. But setting the price at a high margin deters people who otherwise would’ve bought the product for a cheaper price.
• Note that the size of the deadweight loss depends on the elasticity of demand.
  • If the demand is inelastic the deadweight loss is larger compared to an elastic demand. For example the deadweight loss in Figure 3 is larger that the deadweight loss in Figure 2.
  • But what determines the elasticity of demand?

Competition or substitutes a Determinant of Elasticity

• The elasticity of demand depends on how much of competition there is in the market.
• If there exist huge competition, it means that there are a lot of substitutes
  • If a consumer can choose between several car providers, a consumer can move from a company (say Ford) to Honda if Ford increases the price.

Price-setting, competition, and market power

• A manufacturer of a very specialized car will have quite a bit of market power.
• Think about Tesla in this case. Tesla is highly specialized and different from other cars in the market
  • has less competition and will have less elastic demand
• Can make monopoly rents
• A firm will be in a strong position if competition is less (low substitutes).
• If there are no competitors in the market, then there will be a single seller in the market.
  • In this case, this single seller will act as a monopoly
  • The monopolist will face a demand curve that is relatively more elastic. Here, a firm will set a price that is greater than the marginal cost of production.

Question 3.

• Suppose that in a small town a multinational retailer is planning to build a new superstore. Which of the following arguments could be correct?

  • choice a. The local protestors argue that the close substitutability of some of the goods sold between the new retailer and existing ones means that the new retailer faces inelastic demand for those goods, giving it excessive market power.
  • choice b. The new retailer argues that the close substitutability of some of the goods implies a high elasticity of demand, leading to healthy competition and lower prices for consumers.
  • choice c. The local protestors argue that once the local retailers are driven out, there will be no competition, giving the multinational retailer more market power and driving up prices.
  • choice d. The new retailer argues that most of the goods sold by local retailers are sufficiently differentiated from its own goods that their elasticity of demand will be high enough to protect the local retailers’ profits.