Product Differentiation (Cournot With Horizontal PD, Bertrand With Horizontal PD)

Question 1

What assumption do we need to drop in order to have product differentiation

Answer 1

Homogenous goods

Question 2

How can product differentiation arise (4)

Answer 2

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!)

also different income

Question 3

So what allows for a market for product differentiation (2)

Answer 3

Different tastes
Different income levels - since with unlimited money, everyone would buy the best computer (so no room for differentiation)

Question 4

Vertical vs horizontal differentiation

Answer 4

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

Question 5

How to analyse product differentiation

Answer 5

Characteristics 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

Question 6

3 models of product differentiation we study (all duopoly)

Answer 6

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)

Question 7

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

Answer 7

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)

Question 8

Firm A’s maximisation problem

B) key result in comparison of cournot with horizontal differentiation to standard cournot

Answer 8

maxΠ𝐴 (𝑞𝐴, 𝑞𝐵) = (𝑣 − 𝑞𝐴− 𝜃𝑞𝐵− 𝑐)𝑞𝐴− 𝑓
simple, just use the inverse demand function

Solve normally (FOC then rearrange to make to get qa = (v-øqb-c)/2
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!)

Question 9

Then sub BR2 into BR1 to get optimal output (as usual for cournot)

B) Result when ø<1 compared to normal cournot

Answer 9

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.

Question 10

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: are prices higher than standard cournot? And what do prices rise with

Answer 10

B) higher prices:

Price rises as goods become more differentiated (when ø falls i.e less substitutable)

Question 11

Results of differentiation: good or bad?

Answer 11

Producers produce more than cournot standard so long as ø<1. Higher prices too.

For consumers
They get higher prices (increases as ø falls), reducing welfare

But more variety (also more output and total output)

Question 12

That was cournot with horizontal:

Now 2nd model: Price competition with horizontal differentiation

Assume products only differ in one dimension, 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

Answer 12

From travelling to good’s location,

B) disutility expressed by t per unit of distance

Question 13

Consider a consumer located at L (pg 17)

What is utility from buying from firm A or firm B

Answer 13

Firm A: v - pa - tL
Firm B: v - pb - t(1-L)

Question 14

Along this line there will be a consumer indifferent between the 2 firms. Their location is L*

How to show indifference

Answer 14

v - Pa - tL* = v - Pb - t(1-L*)

Question 15

Then solve to find L* (the location of consumer), and intuition.

B) if prices are equal, what does L*= and what does this mean

Answer 15

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

Question 16

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

Answer 16

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)

Question 17

Now find equilibrium prices by solving firm A’s max problem

Answer 17

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?

Question 18

We can show best responses Pa and Pb in diagram

Key result:

draw diagram, explain curves

Answer 18

Key result: Firms best response is to increase price if other firm increases price.

B) Y axis Pb, X axis Pa (since Bertrand)
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)

Question 19

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

Answer 19

More differentiation (less substitutability)

Pa=Pb=c+t shows with more t (differentiation), they can charge higher prices! More market power

Question 20

So far assumed fixed positioning.

Recall with equal prices, what would firms do

Answer 20

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)

Question 21

Why would they sell identical product though

Scenario 1: Assume if Lb>La>0.5 on a line

Answer 21

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

Question 22

Scenario 2: Now let La<0.5 Lb>0.5.

Also means they sell identical product. Why?

Answer 22

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

Question 23

Problem with this convergence each time for firms

Answer 23

Both at 0.5 means we have resorted back to Bertrand comp with homogenous products and 0 profits

So allowing firms to change product positioning is bad… The result of Bertrand profits only exists if positioning is fixed!

Question 24

2 effects determining choice of location

Answer 24

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)

Question 25

2 effects determine choice of quality

Answer 25

Direct effect: moving closer to rival potentially increases market share Strategic: greater differentiation (moving away) reduces competition and raises market power

Question 26

Given positioning is not fixed and firms can move. Equilibrium with linear costs B) equilibrium with quadratic costs

Answer 26

With linear costs, no nash equilibrium for any pair of locations, always incentive to move (hence why they converge back to L=0.5 and homogenous products and no profit) With quadratic costs, either locate at 0 or 1 (strategic effect stronger i.e case for differentiation) (Of course with fixed positioning, profits are possible for Bertrand!)

Question 27

So profits are available for Bertrand under what circumstances

Answer 27

Profit if fixed positioning Profit if unfixed positioning and quadratic costs! However no profit - convergence with linear costs (as shown in our model L=0.5)