Product Differentiation Flashcards
Are Cartels more or less likely to occur with homogenous products?
According to OFT 2005, they are more likely to occur if products are homogenous
What are the assumptions for the endogenous model of product differentiation?
- There are only 2 firms, A&B, that compete in prices
- Normalise marginal costs c = 0 and fixed costs F = 0
- Locations are exogenous and there is maximum differentiation θa = 0 and θb = 1
- All consumers purchase in equilibrium
- note: this is Bertrand’s Model of Oligopoly
What is Bertrand’s Paradox?
One extra firm in the market is enough to go from a situation of monopoly to a situation of perfect competition
What is the utility of a consumer who purchases from firm i with a price p(i)?
U(θ,p(i)) = V - kD² - p(i)
kD² that a consumer is more likely to buy from a firm closer to it as its disutility from travel is quadratic
What is the profit of firm i with price p(i)?
πi = p(i)q(i)(pi,qi)
How do we draw a graph to show utility of a consumer purchasing from firm A or B based on where they are located?
When will a consumer at θ prefer firm A to B?
When U(θ,p(A)) > U(θ,p(B))
i.e.
V - TD(A) - p(A) > V - TD(B) - p(B)
->TD(B) + p(B) > TD(A) + p(B)
known as delivered prices
What is the marginal consumer?
The location where a consumer is indifferent between A & B
Where is the marginal consumer located?
θ[p(A),p(B)] = 1/2 + [p(B)-p(A)]/2k
What happens to the utility of a consumer purchasing from firm A as the price of A falls?
The marginal consumer moves further away from A, meaning more customers are going to A
What is the inequality for firm A to supply all customers?
1/2 + [p(B)-p(A)]/2k >= 1, or p(A) <= p(B) - k
What is the inequality for firm A to lose all customers?
1/2 + [p(B)-p(A)]/2k <= 0, or p(A) >= k + p(B)
What is firm A’s demand if prices are sufficiently close?
q(A)[p(A),p(B)] = 1/2 + [p(B)-p(A)]/2k
What is firm B’s demand if prices are sufficiently close?
q(B)[p(A),p(B)] = 1/2 + [p(A)-p(B)]/2k
What is the price elasticity of demand for firm i?
δq(i)/δp(i) = -1/2k < 0
What is the cross price elasticity of demand for firm i with respect to firm j?
What are the necessary conditions for Nash Equilibrium in prices?
What is the demand for firm A given pB and differentiation k?
What is the Best Response Function price for i when j sets price, pj?
How do we draw the BRFs for both firms?
How does product differentiation affect price?
As product differentiation increases, a firm’s demand is less responsive to a change in its rivals’ price and therefore will charge higher
How are k and the nash equilibrium price related?
They are the same
What is the firms best response function?
p(i) = [k+p(j)]/2
What is the nash equilibrium price if k = 0?
The marginal cost (this is the Bertrand Paradox)
What is consumer utility under monopoly?
V - k(θ)² - p(m)
What is the value p(m)?
p(m) = V - kθ²
In a monopoly, the stores will be placed at 0 and 1, so θ = 1/2
p(m) = V - k/4
How do we model the monopoly price on the BRF price graph?
How does a consumers utility change under monopolist prices versus Nash prices?
Are unilateral effects more or less likely when products are differentiated?
“Where products are differentiated, for example by branding or quality, unilateral effects are more likely where the merging firms’ products compete closely.”
How do we solve the principle of minimum differentiation?
d’Aspremont et al find that when prices are endogenous firms want maximum differentiation by positioning themselves as far away as possible
