Product Differentiation

Question 1

Are Cartels more or less likely to occur with homogenous products?

Answer 1

According to OFT 2005, they are more likely to occur if products are homogenous

Question 2

What are the assumptions for the endogenous model of product differentiation?

Answer 2

1. There are only 2 firms, A&B, that compete in prices
2. Normalise marginal costs c = 0 and fixed costs F = 0
3. Locations are exogenous and there is maximum differentiation θa = 0 and θb = 1
4. All consumers purchase in equilibrium
   - note: this is Bertrand’s Model of Oligopoly

Question 3

What is Bertrand’s Paradox?

Answer 3

One extra firm in the market is enough to go from a situation of monopoly to a situation of perfect competition

Question 4

What is the utility of a consumer who purchases from firm i with a price p(i)?

Answer 4

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

Question 5

What is the profit of firm i with price p(i)?

Answer 5

πi = p(i)q(i)(pi,qi)

Question 6

How do we draw a graph to show utility of a consumer purchasing from firm A or B based on where they are located?

Answer 6

Question 7

When will a consumer at θ prefer firm A to B?

Answer 7

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

Question 8

What is the marginal consumer?

Answer 8

The location where a consumer is indifferent between A & B

Question 9

Where is the marginal consumer located?

Answer 9

θ[p(A),p(B)] = 1/2 + [p(B)-p(A)]/2k

Question 10

What happens to the utility of a consumer purchasing from firm A as the price of A falls?

Answer 10

The marginal consumer moves further away from A, meaning more customers are going to A

Question 11

What is the inequality for firm A to supply all customers?

Answer 11

1/2 + [p(B)-p(A)]/2k >= 1, or p(A) <= p(B) - k

Question 12

What is the inequality for firm A to lose all customers?

Answer 12

1/2 + [p(B)-p(A)]/2k <= 0, or p(A) >= k + p(B)

Question 13

What is firm A’s demand if prices are sufficiently close?

Answer 13

q(A)[p(A),p(B)] = 1/2 + [p(B)-p(A)]/2k

Question 14

What is firm B’s demand if prices are sufficiently close?

Answer 14

q(B)[p(A),p(B)] = 1/2 + [p(A)-p(B)]/2k

Question 15

What is the price elasticity of demand for firm i?

Answer 15

δq(i)/δp(i) = -1/2k < 0

Question 16

What is the cross price elasticity of demand for firm i with respect to firm j?

Answer 16

Question 17

What are the necessary conditions for Nash Equilibrium in prices?

Answer 17

Question 18

What is the demand for firm A given p_B and differentiation k?

Answer 18

Question 19

What is the Best Response Function price for i when j sets price, p_j?

Answer 19

Question 20

How do we draw the BRFs for both firms?

Answer 20

Question 21

How does product differentiation affect price?

Answer 21

As product differentiation increases, a firm’s demand is less responsive to a change in its rivals’ price and therefore will charge higher

Question 22

How are k and the nash equilibrium price related?

Answer 22

They are the same

Question 23

What is the firms best response function?

Answer 23

p(i) = [k+p(j)]/2

Question 24

What is the nash equilibrium price if k = 0?

Answer 24

The marginal cost (this is the Bertrand Paradox)

Question 25

What is consumer utility under monopoly?

Answer 25

V - k(θ)² - p(m)

Question 26

What is the value p(m)?

Answer 26

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

Question 27

How do we model the monopoly price on the BRF price graph?

Answer 27

Question 28

How does a consumers utility change under monopolist prices versus Nash prices?

Answer 28

Question 29

Are unilateral effects more or less likely when products are differentiated?

Answer 29

“Where products are differentiated, for example by branding or quality, unilateral effects are more likely where the merging firms’ products compete closely.”

Question 30

How do we solve the principle of minimum differentiation?

Answer 30

d’Aspremont et al find that when prices are endogenous firms want maximum differentiation by positioning themselves as far away as possible