Product Differentiation (Cournot With Horizontal PD, Bertrand With Horizontal PD) Flashcards
What assumption do we need to drop in order to have product differentiation
Homogenous goods
How can product differentiation arise (4)
Geography e.g choosing which shop to buy from
Product quality e.g computer with fast processor vs larger hard disk
Difference tastes
Advertising/branding (create perceptions similar products are different!)
So what allows for a market for product differentiation (2)
Different tastes
Different income levels - since with unlimited money, everyone would buy the best computer (so no room for differentiation)
Vertical vs horizontal differentiation
Vertical -
Everyone can see one is better, but some buy the worse computer (as likely cheaper)
Horizontal -
can’t tell which is better, consumer makes own judgement e.g cereal, rice crispier vs cornflakes
How to analyse product differentiation
Characteristics approach
Characteristic approach
Place a value on each characteristic of the product and add them up to give a total value
E.g computers: processor speed, screen size, colour etc
3 models of product differentiation we study (all duopoly)
Cournot duopoly with horizontal product differentiation (same method as normal cournot, just with new ø)
Price competition with horizontal product differentiation (find indifferent consumer
va-pa-tL=vb-pb-t(1-L)
Price competition with vertical product differentiation (differentiate with low and high quality v, advertising to show differences (differentiation softens price comp)
Cournot with horizontal differentiation
Difference from standard cournot is now 2 prices to show differentiation.
Pa(qa,qb) = v - qa - øqb
Pb(qa,qb) = v - øqa - qb
What does ø represent?
B) when
ø=1
ø=0
ø<0
0<ø<1
Ø: degree to which products are substitutable
B)
= 1 homogenous
= 0 independent (not substitutable at all… thus each firm is a monopolist since they are only 2 firms)
<0 means complements
0< ø <1 imperfect substitutes (rmb 0 is independent, 1 is homogenous)
Firm A’s maximisation problem
B) key result in comparison to standard cournot
maxΠ𝐴 (𝑞𝐴, 𝑞𝐵) = (𝑣 − 𝑞𝐴− 𝜃𝑞𝐵− 𝑐)𝑞𝐴− 𝑓
Solve normally (FOC then rearrange to make to get qa i.e BR for A) B’s will be symmetrical.
B) each firms output is now less responsive to changes in rivals output, (makes sense as products are differentiated and less substitutable!) compared to the homogenous case
Then sub BR2 into BR1 to get optimal output (as usual for cournot)
B) Result for ø<1
Final expression qa = qb = v-c / 2+ø
B) when ø<1 ,
Each firms sells more than normal cournot. (Recall cournot q= v-c/ 3 , so as long as ø<1, they’ll produce more now!
Total output is also higher.
So output increases with differentiation (if ø<1). Sounds good for consumers… now check prices
Find price usual way by subbing the final BR into into p
B) Result:
B) higher prices: expression shows us price rises as goods become more differentiated (when ø falls i.e less substitutable)
E.g when ø is 1, P = v - 2/3(v-c)
When 0 P= v - 1/2(v-c) (higher price!)
Consumers results of differentiation: good or bad?
Mixed:
They get higher prices, reducing welfare
But more variety (also more output and total output)
Now 2nd model:
Price competition with horizontal differentiation
We assume products only differ in one dimension e.g sweetness of cornflakes, think as being located at different points on a line. Assume firm A and B locate at opposite ends
Consumers are spread evenly along the line. Gain utilities from consuming good. How do they get disutility
B) how is this expressed
From travelling to good’s location,
B) disutility expressed by t per unit of distance
Consider a consumer located at L (pg 17)
What is utility from buying from firm A or firm B
Firm A: v - pa - tL
Firm B: v - pb - t(1-L)
Along this line there will be a consumer indifferent between the 2 firms. Their location is L*
How to show indifference
v - Pa - tL* = v - Pb - t(1-L*)
Then solve to find L* (the location of consumer), and intuition.
B) if prices are equal, what does L*=
L* = 1/2 + pb-pa/2t
Everyone left of L* buys A, anyone to right buys B
B) using formula, L*=1/2 (consumer is located in the middle!) so consumers split demand and half buy from each firm
Express indifferent consumer in diagram
Diagram shows when consuming from A,
utility falls when distance from A increases. (Downwards sloping) (pg 20)
Then when consuming from B, similar effects (less utility as get further away from B) PG 21
B) What does their intersection show
Intersection is the indifferent consumer, who has same utility from consuming A or B (and left of them buy A, right of them buy B)
Now find equilibrium prices by solving firm A’s max problem
Maxπa = (pa-c)(1/2 + pb-pa/ 2t)
I.e (pa - c) times L* equation we saw earlier
Then FOC and rearrange to find best responses (in price not quantity this time) for Pa, (Pb will be symmetric)
Then sub Pb into Pa to get final Pa.
Final: Pa = Pb = c+t
(So price is MC+distance?
We can show best responses Pa and Pb in diagram
Key result:
draw diagram, explain curves
Key result: Firms best response is to increase price if other firm increases price.
B) Y axis Pb, X axis Pa
Upward sloping BRs (as firms BR is to increase price if other increases price),
So P>MC and continues to increase till intersection equilibrium where Pa=Pb=c+t)
This is first time we see P≉MC under Bertrand, and firms now make profit! A special case removing bertrand paradox!
Greater t (distance) can also be viewed as what
More differentiation (less substitutability)
Pa=Pb=c+t shows with more t (differentiation), they can charge higher prices! More market power
So far assumed fixed positioning.
Recall with equal prices, what would firms do
Recall L=1/2 + pb-pa/2t
With pa=pb L=0.5, so they would chose to sell an identical product (as already shown)
Why would they sell identical product though
Scenario 1: Assume if Lb>La>0.5 on a line
All consumers in range 0 to La+Lb/2 will buy from A, so incentive for B to move just to the left of A.
This cycle continues till both reach 0.5 (so whenever both firms are on same half of line, convergence to 0.5
Scenario 2: Now let La<0.5 Lb>0.5.
Also means they sell identical product. Why?
All consumers in range 0 to La+Lb/2 will buy from A, and the rest will buy from B.
This means whoever is closer to centre gets greater market share, so both firms move to 0.5 again
Problem with this convergence each time for firms
Both at 0.5 means Bertrand comp with homogenous products and 0 profits
So allowing firms to change product positioning is bad…
2 effects determining choice of location
Direct effect: if prices didnt change, how would profits change upon moving
Strategic effect: how does changing location affect price, and how does this affect profits
(Like moving to centre means back to bertrand no profits)
2 effects determine choice of quality
Direct effect: moving closer to rival potentially increases market share
Strategic: greater differentiation (moving away) reduces competition and raises market power
Equilibrium with linear costs
B) equilibrium with quadratic costs
With linear costs, no nash equilibrium, always incentive to move for any pair of locations
With quadratic costs, either locate at 0 or 1 (strategic effect stronger i.e case for differentiation)
