Econ 5700

Lecture 11: Monopolistic Competition I Econ 5700 SP20

Prof. Adam Dearing

The Ohio State University

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Agenda

1. PS3 Due Today

2. Monopolistic Competition

2.1 Homogeneous Products

3. Later today: PS4 posted

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Overview

I We’re going to add entry to an oligopoly model

I Until now, the number of firms was exogenous I Given to you in advance

I Today, number of firms will be endogenous I Determined by the model

I Key: we’ll need to add some fixed costs

I We’ll also need to change how we think about welfare

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Monopolistic Competition

I Monopolistic competition: requires two key features 1. Each firm faces a downward-sloping residual demand curve

2. Free entry/exit

I (Nash) Equilibrium under monopolistic competition will feature:

1. p > MC

2. Zero profits

I We’ll need fixed costs to accomplish this I Otherwise, only get zero profits with p = MC when MC is

constant

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Monopolistic Competition

I Monopolistic competition can feature homogenous products or differentiated products

I Today: homogenous products

I Next time: differentiated products

I The two will have very different welfare implications

I Homogeneous products case is easier

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Monopolistic Competition: Equilibrium

I How do we determine the equilibrium? Think of this as having two stages

I Stage 1: firms enter

I Stage 2: market outcome is realized

I Depends on outcome of stage 1

I We can use backwards induction!

I Start with stage 2

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Homogeneous Products with Cournot Competition

I Today: Homogenous products, Cournot competition

I Stage 1: firms enter (n firms)

I Stage 2: n firms engage in Cournot competition I We’ll be given p(Q), ci(qi)

I i is a firm index: i = 1, 2, . . . , n

I Want to find: equilibrium price (p⇤), quantity (Q⇤), and number of firms (n⇤)

I Start by finding p(n) and Q(n) . . . this is the stage 2 outcome

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Example

I p(Q) = 50 � 1 20 Q

I ci(qi) = 10qi + 80 I What is the (Nash) equilibrium? I Useful equality:

Q = qi + Q�i

where Q�i = q1 + q2 + · · · + qi�1 + qi+1 + · · · + qn

I Q�i is the aggregate production of firm i’s rivals I Firm i best responds to this I Simplifies solving the model

I Math will be a bit harder, especially when we solve stage 1 . . .

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( men , FC = So )

With n firms ,

find eqim

Pr E . . . Should depend ON N

( een = Nyhavn )

. firm is BR for :

-

PLA ) a so - Is Q

and D= q ; t A - i

p = so - Iole : t Q - i )

P - - so - Iou - Is Q - i

IT , =p . qi - log ; - SD

=L so - Loq. - foot ;) Ei - log . - SD

Maxine Went

. 9 ;

: D= so - fog ; - Tsai - ID

To Ei -

- 40 - foot

q=4oo-I

. Find Nash aim- .

. Nhe : firms have

identical

costs

. Assure : IN ee 'm =

q=q£ . . . -

- 9h

=q

→

canal

best nessorse requires

g. = 400 - IQ . i

→

q . . = 400 - I A . i

q = too - I in - it q

2 q = Soo - I n - I 9

2 q t I n - r ) q

= S OD

( 2 t n - l ) q = So D

( ht I ) q = SO D

q=sh ← in a Kai OUT PVT

Q = n q

a=soon ← FEET

p = so - Is Q = so - In ( soo . ¥ . )

p=so-4an firm Pro r its

-

"

Tl i = Pq ; - b q ; - SO

= p . q - lo q - S D

Te;=fo-ysH%-iot÷y

Example

I What about number of firms?

I I won’t ask you to solve it explicitly . . . it’s a tough problem!

I I might ask something like this:

I Is n = 7 the equilibrium number of firms? If not, should there be more or fewer firms in equilibrium?

I [Work through this.]

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Pwg n=7 into Profits

or go the Long way around

q=h = If

a P = so - yo

. ! , = so - to . Is

= To - 35

Te , = P

. q - loq - SO

= 15400 ) - 101100 ) - SO

= 500 - SD

a÷ - n ±

( eoin : n - - 9)

Graphical Representation

I ATCi = 10 + 80qi ! economies of scale

I [Draw the graph of eq’m]

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Firm i

§

.

Finn i in egm -

'

residual denard

Discussion

I We see that ATCi is tangent to (inverse) residual demand

I p = ATC so zero profits

I Key: not possible for firm to earn positive profit, given other rivals’ behavior

I What’s the effect of changing FC?

I If FC ", then n⇤ #

I Why? Firms must earn higher variable profits to make up for fixed costs

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Welfare

I There are two issues with welfare here

1. p > MC

2. Economies of scale imply “excessive” entry

I Recall: total welfare = (benefits to consumers) - (costs to firms)

I Until now, we’ve had zero fixed costs when doing welfare calculations

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=

Welfare: Solutions

I First-best solution: restrict to 1 firm and force it to set p = MC

I Problem: firm now has negative profits!

I Must subsidize its FC’s!

I Second problem: this is very heavy-handed

I Second-best solution: limit the number of firms

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Welfare: Second-Best Solution

I There’s a tradeoff to decreasing n:

I Good: lower (total) fixed costs paid

I Bad: less competition means price increases

I There’s a “sweet spot” that balances these two effects

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Limiting Entry

I Itemize we won’t worry about finding the “sweet spot”

I But we should think about how the govt. can limit entry

I A couple ways to do this:

1. Set a maximum number of firms

2. Tax on entry

I Option 2 is “better”: it generates tax revenue

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mom

Entry tax

I From firm standpoint, a tax on entry increases the FC

I This is different than a tax on production

I Tax on production increases MC

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