2- Product Differentiation

Question 1

What are the 2 main forms of Product Differentiation?

Answer 1

Vertical & Horizontal

Question 2

Describe Horizontal differentiation

Answer 2

Consumers don’t agree which product is better (e.g. colour taste) so would not buy the same product given equal prices

Question 3

Describe Vertical differentiation

Answer 3

Consumers agree which product is better based on objective quality (e.g. horsepower) so would buy the same product given equal prices

Question 4

In the General Hotelling game, what are the 2 opposing effects at play?

Answer 4

-Demand (business stealing) effect
-Strategic (price) effect

Question 5

Describe the Demand (business stealing) effect

Answer 5

The more similar to your rival, the more market share you capture

Question 6

Describe the Strategic (price) effect

Answer 6

The more similar to your rival, the less differentiated your product, intensifying price competition

Question 7

What is the base equation for the indifferent consumer in the Last (price) stage of General Hotelling game?

Answer 7

pᵢ + tx = pᵢ₋₁ + t(1/n - x)

Question 8

How do you derive the Symmetric equilibrium in the Last (price) stage of General Hotelling game?

Answer 8

1.Find the indifferent consumer (x) for both sides of i
2.Sum for Demand and insert to profit function (pᵢ-c)D
3.Differentiate profit wrt pᵢ using product rule
4.Impose symmetry on p and solve for it

Question 9

How do you derive equilibrium number of firms (nᶜ) in a symmetric equilibrium?

Answer 9

Substitute equilibrium price (p) and demand (q) into standard profit function (=0) and solve for n

Question 10

How do you derive equilibrium price (pᶜ) in a symmetric equilibrium?

Answer 10

Substitute equilibrium number of firms nᶜ into standard profit function and solve for p

Question 11

How do you calculate total transportation costs (T) in equilibrium

Answer 11

-Integrate x for both sides of the firm between 0 and x (symmetry imposed)
-Multiply by transportation costs (t) and equilibrium number of firms (nᶜ)

Question 12

How do you determine whether there are too many firms in equilibrium?

Answer 12

If n*<nᶜ there is brand over-proliferation and there are too many firms

Question 13

How do you find the socially optimal number of firms (n*)?

Answer 13

-Minimise the sum of entry costs (nF) and Total transportation costs (T) wrt n
-Solve for n

Question 14

How do you find the indifferent consumer between 2 products from a utility function (θ^)?

Answer 14

Equate the utility function for both qualities, and solve for taste parameter θ^

Question 15

How do you find the indifferent consumer between buying a product or none at all (θ₀)?

Answer 15

Equate the low quality utility to zero, and solve for taste parameter θ₀

Question 16

How do you find equilibrium firm demand in vertical product differentiation (high quality)?

Answer 16

Upper bound of constraint (income/taste) - consumer indifferent between 2 products (θ^)

Question 17

How do you find equilibrium firm demand in vertical product differentiation (low quality)?

Answer 17

Consumer indifferent between 2 products (θ^) - consumer indifferent between buying (θ₀)

Question 18

How do you find equilibrium prices in vertical product differentiation?

Answer 18

-Setup profit function π=pD
-Differentiate π wrt p, and solve for it
-Solve equation system for p*

Question 19

How can you show the range of consumers who do not buy any product?

Answer 19

θ<θ₀

Question 20

How do you find quality level if firms can decide it before price in vertical differentiation?

Answer 20

-Differentiate high quality profit wrt q₁, >0 means it will choose highest quality possible
-Sub into q₂ profit maximum