Mergers Pt 2 (modelling unilateral effects with/out efficiency gains) (awful) Flashcards
(20 cards)
4 models of mergers
Unilateral effects with no efficiency gains
Unilateral effects with efficiency gains
Double marginalisation - comparing separation equilibrium vs vertical integration
Free-riding in marketing - comparing sep vs vertical integration
Consumer surplus formula
Utility - Cost
U - R
First Unilateral effects model: with no efficiency gains
So with 3 single product firms:
If firm 1 and 2 merge, what happens in terms of products
B) what results do we get (for price, insider and outside profits and overall welfare)
Firm 1 and 2 (the merged firms) now sell 2 products, firm 3 sells 1 (we assume only 3 products)
B)
Prices increase for both, but Pi>Po (insider price>outsider price
Insider: profits increases in Bertrand (but not in Cournot)
Outsider (firm 3): profits increase since assume no efficiency gains (since no efficiency gains, instead merger exercises their market power to increase prices, alllowing outside price to rise too, increasing both profits!
Overall: welfare loss since prices have increased post-merger, CS loss, and gain in PS doesn’t fully compensate.
2nd model: Unilateral effects with efficiency gains
When we add efficiency gains - how does cost differ
B) results on CS, outsider profits, total welfare
With no efficiency gains, we assumed firms have identical unit cost c > 0, both pre and post merger.
With efficiency gains, unit cost post-merger is
ec, where e<1 (shows efficiency gains as helps cost fall) lower e means more efficiency gains
B)
CS increase
Outsider profits to fall
But total welfare could increase….
Magnitude of e: what does it determine?
Whether rival will exit the market or not.
(recall from part 1, if efficiency gains are large (e low), more likely to lower prices to gain market share (rather than maintain price) thus hard for rival to stay)
Why is efficiency gains dual-wielded for the anti-trust authority
Efficiency gains can lower prices (and more likely if gains are large), so increases CS, thus more likely merger approved
however if prices go down too much, can kill competition. (recall, AA may block merger if they believe they don’t have capacity to serve market)
Empirical observations of horizontal mergers and size of firms
Mergers are between small firms are more likely to have intent to make efficiency gains, cost-savings and thus not raise prices. Thus more likely approved
while large firms merging tend to intend to get unilateral effect i.e exercise market power for higher prices, so less likely approved
Now consider vertical relationships
Why does manufacture have incentive to control some of retailer actions i.e to vertically merge
As manufacturer profits and demand, relies on retailer to advertise adequately the product.
Vertical restraints are agreements between the 2 stages.
tightest form of restraint is vertical integration (merger)
What other examples of VR’s. (5)
quantity discount (buying from wholesaler PE.O.S)
resale price maintenance (control the retail price i,e RRP!)
quantity fixing e.g retailer must stock x amount
exclusivity clauses
Limit pricing
Recall we said vertical integration can remove externalities: (2)
Double marginalisation: remove mark-up in stages, prevents market price being too high
Free-riding in marketing: if manufacturer is producing to many retailers, retailers to free-ride on marketing, and recall how retailer affects manufacturer profits by advertising adequately; thus integration to gain control is better for them.
Double marginalisation model:
Single manufacturer & retailer (each monopolists)
Upstream (manu) charge w>c , thus
Downstream charges P>w>c
Demand q=a-p
What is the PM problem (πd) for downstream?
b) then find quantity price and profit
C) then find profit max problem πu for upstream, to find w (their price i.e downstreams cost), then find profit
(Working pg 13)
Use profit shortcut (v-p)(p-c), using the letters given;
Max πd = (a-p)(p-w)
b) FOC respect to p
p= a+w/2
q= a-w/2
C) max πu = (w-c)q
= (w-c)(a-w/2)
FOC respect to w and rearrange to find w.
Then sub w into the πu
Now have w, can find final P, final πu and πd
And PS (πd+πu)
Pg 14 top photo
So that was separate entities, i.e double marginalisation.
With vertical integration,
What is the maximisation problem
Then work out the price quantity and profit (pg 14 slide 2)
B) using this, compare PS and CS and overall welfare of vertical integration compared to 2 separate firms
Usual maximisation
Maxπd = (a-p)(p-c)
q = a-c/2
p = a+c/2
π=(a-c)²/4
B)
PS is higher as profit from merger is more
(a-c)²/4 > (a-c)²/16
as a result of no intermediary cost.
CS increases too as price from merger is less
a+c/2 < 3a+c/4
So increase in total welfare (merger keeps costs lower, so allows market price not to be too high, so good for both)
2nd externality internalised: free ride marketing.
1 upstream firm U, 2 downstream D1, D2
e: effort level (of retailer) to advertise etc
Advertising costs retailer
C = wq + μei²/2 (wq variable cost)
Perceived quality of product expression (u)
b) What do we expect e1 and e2 and p1 p2 to be in equilibrium? (compete in prices and no double marginalisation)
u = ubar + e, where e= e1+e2 (since free-ride)
ubar: inherent quality
perceived quality = inherant quality + advertising effort
B)
e1=e2=0 due to free riding (no retailer exerts effort as want to free ride)
And p1=p2=w as price competition so P=MC which is w (foc of advertising cost)! Downstream firms make no profit!
So separate entities, downstream makes no profit as compete in prices.
Do the upstream firm maximisation problem given demand q=v-w
B) then find welfare (Ws) PS, CS
Working all pg 15
Use profi shortcut (v-p)(p-c) but replace letters
since we know p=w
Max Πu = (v-w)(w-c)
FOC and rearrange to get w= v+c/ 2
Then can find answers to B from there
Now let vertical integration occur.
Now only 1 profit max problem πm (not separate πd and πu)
Now we include effort levels since free-rider problem eliminated , also need to include cost of advertising into the maximisation problem
B) then can find ei, p, q, PS, CS and Wm (welfare)
This is so long working.
C) main result
Max πm = (p-c)(v+e1+e2-p) - μe²₁/2 - μe²₂/2
since added effort levels now, also need to include cost of effort (advertising)
B) to find e1 and e2, differentiate profit with respect to price and effort separately, rearrange to find p and e respectively,
To find final e expression sub p into e
To find P then sub e into p!
C) vertical integration improves welfare compared to separate entity (under provision of marketing due to free-riding is solved)
So these examples of externality internalising (double marginalisation and free-riding marketing) have increased welfare
However, vertical merger may not always increase welfare.
Assume population to be 1
Proportion λ have high willingness to pay øh (high price)
(1-λ) have low valuation øL, but appreciate effort on behalf of seller so øL + e
What happens in separation for retailers who compete in price
B) what about the manufacturer? What are their options
Same as normal separation; they can free-ride marketing thus retailers exert no effort, thus e1=e2=e=0, and compete on prices so breakeven P=MC as compete on price.
B)
Manufacturer can set a price (w) equal to øL or øH.
Assume manufacturers set price = øL (low valuation)
I.e w=øL
What is PS, CS and Ws
Ps = (øL - c) x 1
i.e (w-c) x quantity
X by 1 as they capture the full population market which we let =1 (sell to both high and low valuation groups)
CS = λ(øh - øL)
Ws = CS+PS
Now let vertical integration occur
Maximisation problem
Maxπm = p-c - μe²₁/2 - μe²₂/2….
Now with merger, we include effort levels
Max
What do we find overall for welfare
Welfare is less with merger if λ<1/2 i.e if proportion of people with high valuation is less than half of population, since less profit to extract from them
Total welfare drops when too many low value consumers exist, since cost of effort exceeds the benefit
