Horizontal

Question 1

Characteristics of Horizontal differentiation?

Answer 1

• Product is differentiated based on things other than quality
• Uniform distribution of consumers
• linear scale between preferences (location example)

Scale:
0 -> L
(Positions measured from 0)
Firm A position = a
Firm B position = L-b
Consumer position = x
Price A = Pa
Price B = Pb
T = Cost of travel

Either:
- Linear Consumer Utility
- Quadratic Consumer Utility

Question 2

What are the two stages of Horizontal Diff.? What are their characteristics?

Answer 2

• Location choice (fixed price)
• Price choice (given (fixed) location)

Question 3

What is the Linear Utility function?

Answer 3

For A: [Ua] - Pa -T|x-a|
For B: [Ub]-Pb-T|x-(L-b)|

Question 4

Under Linear Utility: What is the Location Choice outcome?

Answer 4

-(Downsian electoral Competition) Both firms move to each other’s location… to steal the others’ Demand, increase profits

• larger a -> larger Da -> larger Profit(a)

-No minimal Differentation

Question 5

Under Linear Utility: What is the Price Choice outcome? Under what conditions does it not work?

Answer 5

• Lower Pa -> larger Da ->
  Larger Profit(a)
• the higher T is the -> more concentrated D -> more flexibility the firms have in charging higher prices :. Larger Profits

Conditions not working…

Pb-Pa < - T(L-a-b) - (indiff. cons -> 0) All D -> B

Pb-Pa > T(L-a-b) - (indiff. cons -> 1) All D -> A

Ie. If differences in price is too large or the distances between firms is too small

Question 6

What are the problems with Linear Utility in a 2 stage game?

Answer 6

• There is no Subgame Nash Equilibrium…
• Stage 2 is not initialled because firms do not differentiate in location choice

Proved by:
dProfit(A)/da >0… Meaning that as ‘a’ rises profits rise

Question 7

What is the Quadratic Utility Function?

Answer 7

[Ua] -Pa -T(x-a)^2
[Ub] -Pb -T(x-(L-b))^2

Question 8

Under Quad Util: What is the Location Choice outcome?

Answer 8

• As a rises, so do profits(A)
  A -> 0
  B -> L

Maximum product differentiation occurs

Proved by…
dProfits(A)/d(a) < 0 :. As a falls profits rise

Question 9

Under Quad. Until: What is the Price Choice outcome?

Answer 9

• Similar to linear however there is no (threshold) restriction on price difference
• as prices fall profits rise(prices matter less e.g a wont steal entire deman from b if they have a smaller price)
• further A and B are the less price competition matters and vise versa