H2: Product differentiation
Q: If differentiation reduces price competition, is more differentiation always better?
A: No! It depends on the costs and benefits of differentiation
=> If you can produce more efficiently than rivals, price competition is good
=> Costs of differentiation might increase quicker (quadratic) than benefits (linear)
=> Being different will not necessarily result in many customers
Horizontal product differentiation
=> Consumers disagree on ranking of products (pepsi vs cola)
- Similar packaging, size, quality
- Consumers choice depends on i) price ii) how closely a product matches their
preferences
- Objective: find simplest model that conveys the essence of horizontal product
differentiation (visually)
- Harold Hotelling’s 1929 model of horizontal product differentiation
- Uni-dimensional differentiation: Products only differ on 1 dimension
(hot vs cold, tight vs loose fit…)
- Unit-demand: Each consumer is buying only 1 of the options
- Watch example: make histogram to see where consumers are based on a
survey: Consumers are distributed on the line according to preferences
=> We assume here that the distribution is uniform to make math simple
- Location on the line can be thought of as product differentiation in the
broadest sense of the word (e.g. the same product being offered at different
locations or times) => see examples sl15
Adding prices to the hotelling line
- Trade-off between preferences and prices: if the price difference is high
enough, consumers might buy a product that is not their preferred
- The reservation value r is the value a consumer assigns to their favorite
product type => max price or WTP (Willingness to pay)
- Also look at “travel cost”, how far are they willing to go for their favourite
variety => High “τ” means strong consumers preferences
=> Travel cost = d*τ (d = distance, τ = measurement for how strong
consumers preferences are, How quickly WTP declines as we move to less
preferred products)
- Example: if a consumer is located at l = 0,5 and the product is located at l = 1,
the most that consumer would be willing to pay for the good is r - 0,5τ
Assumptions in model
- Firms have constant marginal cost c
- Assume: r-c-τ>0: Implies: if p=c, even consumer at l=0 would buy good at l=1
1
, - N Consumers are spread out equally over the line with length 1
(l∊[0,1])
Graphs Hotelling line sl17 ev
- Firm 1 is located at l=0,5 => consumer2 at x2 will pay at most r - (x2-0,5)τ
- Consumer1, located at the left of firm 1, will pay at most r - (0.5-x 1)τ
- General: consumer at x, firm at li => WTP is r - |x - l1|τ
- Sl18: Plot WTP function f(x) = p1 + |x - 0,5|τ
=> all x between xL and xR buy at price p1 => see where p1 + |x - 0,5|τ = r
- xL: r - (0,5 - xL)τ = p1 => xL = 0,5 - (r - p1)/τ => xL = li - (r - p1)/τ
- xR: r - (xR - 0,5)τ = p1 => xR = 0,5 + (r - p1)/τ => xR = li + (r - p1)/τ
- More customers if: p1 decreases, τ decreases or if r increases
Duopoly with fixed locations (sl20)
- Two firms located at 0 and 1
- On right of x: consumers will go to firm 2, even though it is more expensive
- If p1 increases in price: x goes more to the left
- Consumers are uniformly distributed between l=0 en l=1
- Blue line: p1 + xτ = total cost of consumer at location x buying from firm 1
- Green line: p2 + (1-x)τ = total cost of a consumer at x buying from firm 2
=> in ^x the consumer is indifferent = The marginal customer
- If p1 changes, the marginal bury goes more to the left
=> If your price is lower than your rival, consumers who prefer their products
will still buy yours if they are located close enough
- Area under the curve is the total demand
Marginal consumer
- Indifferent consumer: x = (p2 - p1 + τ)/2τ (see calculation sl22)
- Firm 1’s (firm 2’s) demand is equal to the share of consumer to the left (right)
of x times the total mass of consumers N
- If uniformly distributed: q1 = Nx = N[(p2 - p1 + τ)/2τ]
- Firm 2: q1 = N(1 - x) = N[(p1 - p2 + τ)/2τ]
- We assume here that locations are given, and based on them the firms
choose their prices => Differentiation increases profit so you would not like to
be in the exact location, but going to the right is good
- Captive customers/market: If you go to the right, the customers on the left of
you will go to you so you have more customers => get closer to firm 2
2
Q: If differentiation reduces price competition, is more differentiation always better?
A: No! It depends on the costs and benefits of differentiation
=> If you can produce more efficiently than rivals, price competition is good
=> Costs of differentiation might increase quicker (quadratic) than benefits (linear)
=> Being different will not necessarily result in many customers
Horizontal product differentiation
=> Consumers disagree on ranking of products (pepsi vs cola)
- Similar packaging, size, quality
- Consumers choice depends on i) price ii) how closely a product matches their
preferences
- Objective: find simplest model that conveys the essence of horizontal product
differentiation (visually)
- Harold Hotelling’s 1929 model of horizontal product differentiation
- Uni-dimensional differentiation: Products only differ on 1 dimension
(hot vs cold, tight vs loose fit…)
- Unit-demand: Each consumer is buying only 1 of the options
- Watch example: make histogram to see where consumers are based on a
survey: Consumers are distributed on the line according to preferences
=> We assume here that the distribution is uniform to make math simple
- Location on the line can be thought of as product differentiation in the
broadest sense of the word (e.g. the same product being offered at different
locations or times) => see examples sl15
Adding prices to the hotelling line
- Trade-off between preferences and prices: if the price difference is high
enough, consumers might buy a product that is not their preferred
- The reservation value r is the value a consumer assigns to their favorite
product type => max price or WTP (Willingness to pay)
- Also look at “travel cost”, how far are they willing to go for their favourite
variety => High “τ” means strong consumers preferences
=> Travel cost = d*τ (d = distance, τ = measurement for how strong
consumers preferences are, How quickly WTP declines as we move to less
preferred products)
- Example: if a consumer is located at l = 0,5 and the product is located at l = 1,
the most that consumer would be willing to pay for the good is r - 0,5τ
Assumptions in model
- Firms have constant marginal cost c
- Assume: r-c-τ>0: Implies: if p=c, even consumer at l=0 would buy good at l=1
1
, - N Consumers are spread out equally over the line with length 1
(l∊[0,1])
Graphs Hotelling line sl17 ev
- Firm 1 is located at l=0,5 => consumer2 at x2 will pay at most r - (x2-0,5)τ
- Consumer1, located at the left of firm 1, will pay at most r - (0.5-x 1)τ
- General: consumer at x, firm at li => WTP is r - |x - l1|τ
- Sl18: Plot WTP function f(x) = p1 + |x - 0,5|τ
=> all x between xL and xR buy at price p1 => see where p1 + |x - 0,5|τ = r
- xL: r - (0,5 - xL)τ = p1 => xL = 0,5 - (r - p1)/τ => xL = li - (r - p1)/τ
- xR: r - (xR - 0,5)τ = p1 => xR = 0,5 + (r - p1)/τ => xR = li + (r - p1)/τ
- More customers if: p1 decreases, τ decreases or if r increases
Duopoly with fixed locations (sl20)
- Two firms located at 0 and 1
- On right of x: consumers will go to firm 2, even though it is more expensive
- If p1 increases in price: x goes more to the left
- Consumers are uniformly distributed between l=0 en l=1
- Blue line: p1 + xτ = total cost of consumer at location x buying from firm 1
- Green line: p2 + (1-x)τ = total cost of a consumer at x buying from firm 2
=> in ^x the consumer is indifferent = The marginal customer
- If p1 changes, the marginal bury goes more to the left
=> If your price is lower than your rival, consumers who prefer their products
will still buy yours if they are located close enough
- Area under the curve is the total demand
Marginal consumer
- Indifferent consumer: x = (p2 - p1 + τ)/2τ (see calculation sl22)
- Firm 1’s (firm 2’s) demand is equal to the share of consumer to the left (right)
of x times the total mass of consumers N
- If uniformly distributed: q1 = Nx = N[(p2 - p1 + τ)/2τ]
- Firm 2: q1 = N(1 - x) = N[(p1 - p2 + τ)/2τ]
- We assume here that locations are given, and based on them the firms
choose their prices => Differentiation increases profit so you would not like to
be in the exact location, but going to the right is good
- Captive customers/market: If you go to the right, the customers on the left of
you will go to you so you have more customers => get closer to firm 2
2
