Final vs. Intermediate Price Regulation in the presence of
Demand-Enhancing Investments
Olga Rozanova∗
March, 2015
Abstract
The work compares intermediate and final price regulations in a vertically related markets when
upstream firm is engaged into the demand-enhancing activity. I show that if target price is below the
price without regulation and if for a given wholesale price equilibrium final consumer price is rising in
investments the intermediate price regulation is always preferred to the final price regulation from the
consumers’ perspective under two-part tariff contracts between the parties. The sufficient condition
under which intermediate price regulation is better (compared to the final price regulation) from the
welfare point of view is also provided. However,in case of linear price contracts between upstream and
downstream firms the opposite result holds: final price regulation allows achieving higher consumer
surplus than intermediate price regulation.In case when upstream firm invests in cost reduction rather
than demand enhancement the two regulation schemes are identical. Also the paper demonstrates
that intermediate price regulation allows achieving lower final consumer prices without harming the
investments level. This gives intermediate price regulation an advantage over a classical price-cap
regulation (i.e. final consumer price regulation).
JEL classification: L51, L50, L98
Key words: Price-cap regulation; final price regulation; intermediate price regulation; demandenhancing investments
∗
Toulouse School of Economics, Manufacture des Tabacs 21, Alle de Brienne 31015, Toulouse Cedex 6 FRANCE;
E-mail address: [email protected].
1
1
Introduction
Many industries are subject to the price controls. The examples range from food industries (e.g.
Venezuela, Argentina) to pharmaceutical markets and energy markets (e.g. final consumer prices in
the electricity market are usually regulated also sometimes the petroleum products (e.g. gasoline)
prices are regulated). There are also cases of intermediate price regulation. Access price regulation in
a railway market is one of the illustrations.
So the two regulating schemes (i.e. final price regulation and intermediate price regulation) coexist in the reality. The aim of the current work is to understand what type of price regulation is
preferred from the consumer surplus and social welfare perspectives. The analysis in the present work
shows that the answer is ambiguous and depends on many factors such as the type of investments
(demand-enhancing vs. cost-reducing), the type of the contract between the upstream and downstream
enterprizes, the characteristics of the demand function.
One of the key results of the work is that if the government wants to keep the price below its level
without regulation then under two-part tariff contracts between upstream and downstream producers
and in the presence of upstream demand-enhancing investments regulation of the intermediate price
is preferred to the final price regulation from the point of view of the consumers. This result holds
under natural assumption that for a given intermediate price equilibrium final price rises in demandenhancing investments.
Moreover, the present work contributes to the discussion on the desirability of price regulation.
Is it good to regulate the prices? On the one hand, the lower price level allows consumers to be
better-off. However, the generally held view is that lower price results in lower incentives to invest in
quality improvement of the good since decreased price means lower marginal revenue from each unit
invested. Lower price accompanied by decrease in quality provided may turn out to be harmful for
the consumers.
White(1972), Spence(1975), Sheshinski(1976), Weisman (2003) demonstrate a harmful effect of
price controls on equilibrium investments into quality of the product. Sappington (2005) tells the
following about the effect of price-cap regulation on the quality of the product chosen: ”[..]a monopoly
supplier of a single product will always supply less than welfare-maximizing quality when the firm is
required to sell its product at a fixed price. This is the case because a price ceiling prevents the
firm from capturing any of the incremental consumers’ surplus that the higher service quality would
engender.”
2
There are empirical evidence that justify the negative effect of price-cap regulation on the investments in quality. For example, Booz and Hamilton (1999) demonstrated that introduction of the
price-cap regulation lead to the decrease in quality of Railtrack (a holder of the railway network in
UK). Another example is given by Zyzak (2010): price-cap implementation in Ukrainian gasoline
market in 2004 resulted in a quality deterioration of the gasoline.
So, it is well documented that price-cap regulation has negative effects on the incentives to invest
in quality improvement. Due to this the desirability of this kind of regulation is questionable.
The contribution of the current work is that it proposes a price regulation scheme that allows
achieving lower final consumer prices (compared to the ones without regulation) without harming the
investments in quality (or any other demand-enhancement). It is demonstrated that price-cap on the
intermediate price (rather than final price) may lead to this result in case when there are two-part
tariff contracts between the parties.
The article is structured as follows: Section 2 presents the model. Sections 3,4 solve the model
for the cases of final price and intermediate price regulations. Section 5 compares the regulation
schemes. Section 6 makes robustness check of the results. Section 7 considers the case of cost-reducing
investment. After the conclusion follows.
2
Model
Here we assume that there is one producer that sells its good via the retailer. The demand function for
the good is D(p, I), where p is the final consumer price and I is the level of demand-enhancing investments. The subscripts are used to denote partial derivatives with respect to prices and investments.
For example, DpI =
dD2
dpdI .
We make the following assumptions concerning the demand function:
Assumption 1: Demand is decreasing and concave in the price Dp < 0; Dpp ≤ 0.
Assumption 2: Demand is increasing in investments at a decreasing rate DI >; DII < 0.
Let the production costs of the manufacturer are constant and equal to c. The demand investment
costs are Φ(I).
Assumption 3: The investment costs are increasing and convex in I: ΦI > 0; ΦII > 0 Assume
that there is a two-part tariff contract between manufacturer and retailer: T = wD(p, I) + F , where
3
T is the total tariff paid by the retailer to the manufacturer, w is the wholesale price and F is the
fixed part of the tariff.
The payoff of the manufacturer is: Π = (w − c)D(p, I) − Φ(I) + F
The payoff of the retailer is: R = (p − w)D(p, I) − F .
Assumption 4: ΠII · Rpp − RpI · ΠIp > 0.
The timing is the following: at the first stage of the game the government chooses the type of the
regulation (intermediate or final price regulation). If the government regulates intermediate price (i.e.
w) then at the second stage of the game the manufacturer chooses the investments level; and at the
third stage it sets the fixed part of the tariff (i.e. F ). At the fourth stage of the game the retailer
chooses the final consumer price (i.e. p).
If, however, the regulator sets the final consumer price (instead of intermediate per unit price)
then at the second stage of the game the manufacturer chooses I; and at the third (and last) stage of
the game the manufacturer chooses the terms of the contract with retailer (i.e. w, F ).
Assume that the purpose of the regulator is to guarantee the particular price in the market.
3
Solution of the game under final price regulation
Assume that the final price is regulated at the level p = pr . Backward induction is used to find the
subgame-perfect Nash equilibrium in the game.
At the third stage of the game the manufacturer maximizes its profit subject to the retailer’s
participation constraint:
maxw,F,I Π = (w − c)D(pr , I) − Φ(I) + F s.t.R ≥ 0
(1)
Please note, that since upstream producer is a monopolist the solution does not depend on whether
the investments and contract terms are set by the upstream firm sequentially or simultaneously. That
is why in the maximization problem above the manufacturer chooses simultaneously the thee variables
in spite of the each variable one after another.
For any level of w the profit-maximizing level of F for the manufacturer is
F = (pr − w)D(pr , I)
4
(2)
Substituting (2) into (1) gives
max Π = (pr − c)D(pr , I) − Φ(I)
w,I
(3)
The (3) does not depend on w. So any level of w can be set. The equilibrium investments are
found from the following condition:
ΠI = (pr − c)DI − ΦI = 0
(4)
Let us denote the Nash equilibrium investment level found from (4) by I f .
4
Solution of the game under intermediate price regulation
Assume now that intermediate price is regulated instead of final price. The wholesale price is set at the
level w = wr . Again we use the backward induction to find the subgame-perfect Nash equilibrium in
the game. In case of intermediate price regulation we start from the retailer’s maximization problem
(since price is set by the retailer in contrast to the previous case, where it was set by the regulating
body).
Profit-maximization problem of the retailer is:
maxp R = (p − wr )D(p, I) − F
(5)
The first-order condition to (5) is:
dR
= D(p, I) + (p − wr )Dp = 0
dp
(6)
From (6) we get price as a function of wr , I: p = p(wr , I).
The manufacturer maximizes its profit subject to the retailer’s participation constraint and taking
into account how the final price chosen by the retailer depends on the demand-enhancing investments
I:
maxF,I Π = (wr − c)D(p, I) − Φ(I) + F s.t.R ≥ 0; p = p(wr , I)
(7)
For any level of w the profit-maximizing level of F for the manufacturer is
F = (p − wr )D(p, I)
(8)
max Π = (p − c)D(p, I) − Φ(I)
(9)
Substituting (8) into (7) gives
I
5
The equilibrium investments are found from the following condition:
ΠI = (p − c)DI − ΦI + (wr − c)Dp ·
dp
=0
dI
(10)
Let us denote the Nash equilibrium investment level found from (10) by I i .
From the system of conditions out of which the equilibrium price and investments are determined
(i.e. from (6) and (10)) we find:

Dp ΠII Rpp − (RpI )2
dpe


 dw = R · Π R − R Π
pp
II pp
pI Ip
e

Π
−
R
dI
Ip
pI


= −Dp ·
dw
ΠII Rpp − RpI ΠIp
Under very mild conditions
dpe
dw
(11)
is positive, that is equilibrium price is rising in wholesale price.
Lemma 1:
If sign(ΠII Rpp − (RpI )2 ) = sign(ΠII Rpp − RpI ΠIp ) then
dpe
dw
> 0.
The proof of Lemma 1 follows directly from (11).
Lemma 2:
Without regulation the manufacturer sets w = c.
Proof: The manufacturer’s FOC for finding w is: Πw = (w − c)Dp ·
dpe
dw
= 0. Therefore w = c.
Q.E.D.
Based on lemmas 1 and 2 we may formulate lemma 3.
Lemma 3:
To achieve the level of final price below the one without regulation the wholesale price should be
set below c; and wholesale price above c allows to achieve the level of final consumer price above the
one without regulation. Formally p(wr ) < p(c) if wr < c, and p(wr ) > c if wr > c.
5
Comparison of final and intermediate price regulation
Proposition 1: Provided that there is two-part tariff contract between manufacturer and retailer
and that intermediate and final price regulations guarantee the same level of final consumer price
6
i)intermediate price regulation (final price regulation) results in a higher investments and consumer
surplus compared to final (intermediate) price regulation if
dpe
dI
> 0 and target price (pt ) is below
(above) the one without regulation, i.e. pt < p(c)(pt > p(c)).
ii) final price regulation (intermediate price regulation) results in a higher investments and consumer surplus compared to intermediate (final) price regulation if
dpe
dI
< 0 and target price (pt ) is
below (above) the one without regulation, i.e. pt < p(c)(pt > p(c)).
iii) intermediate price regulation is totally identical to final price regulation in terms of investments
and agents’ surpluses if
dpe
dI
= 0.
Proof:
Under final price regulation the investments are found from the condition (4): (pr − c)DI − ΦI = 0.
Under intermediate price regulation the investments are found from (10): (p − c)DI − ΦI + (wr − c)Dp ·
dp
dI
= 0.
Assume that both types of regulation guarantee the same final price (i.e. p = pr = pt ). If I f is the
solution to (pr − c)DI − ΦI = 0 then [(p − c)DI − ΦI + (wr − c)Dp ·
i) Assume
dp
dI ]|I=I f
dp
dI
dp
dI ]|I=I f
= [(wr − c)Dp ·
dp
dI ]|I=I f
> 0. If pt < p(c) then wr < c (this follows from lemma 3). Therefore [(wr − c)Dp ·
> 0. Assuming globally concave profit of the manufacturer we conclude that I i > I f .
If, however, pt > p(c) then wr > c; and [(wr − c)Dp ·
dp
dI ]|I=I f
< 0. Therefore I i < I f .
Consumer surplus is decreasing in price and increasing in investments. Given that the two regulation schemes guarantee the same price level, consumers are better-off with the scheme that results
in a higher investments. That is, consumers prefer intermediate price regulation if pt < p(c) and final
price regulation if pt > p(c). This proves point i) of proposition 1.
ii) Assume
dp
dI ]|I=I f
dpe
dI
< 0. If pt < p(c) then wr < c (this follows from lemma 3). Therefore [(wr − c)Dp ·
< 0. Assuming globally concave profit of the manufacturer we conclude that I i < I f .
If, however, pt > p(c) then wr > c; and [(wr − c)Dp ·
dp
dI ]|I=I f
> 0. Therefore I i > I f .
Given that the two regulation schemes guarantee the same price level, consumers are better-off
with the scheme that results in a higher investments. That is, consumers prefer final price regulation
if pt < p(c) and intermediate price regulation if pt > p(c). This proves point ii) of proposition 1.
iii) Assume
dpe
dI
= 0.
In this case [(wr − c)Dp ·
dp
dI ]|I=I f
= 0, therefore I f = I i and CS f = CS i . Q.E.D.
7
A direct corollary of proposition 1 is that consumers are better-off under intermediate price regulation whenever it allows achieving higher investments (compared to the final price regulation).
Corollary 1:
When government’s objective is consumer surplus (CS) maximization, target price is below the
one without regulation and
dp
dI
> 0, then CS under intermediate price regulation exceeds the one under
final price regulation.
Proof:
Assume that under p regulation price equals pf . Due to proposition 1 under wholesale price
regulation (w) pf could be reached with higher investments (i.e. I i > I f ). If consumer price under
intermediate price regulation is not equal to the one under final price regulation (i.e. pi 6= pf ) it means
that pi allows achieving higher CS than pf . Q.E.D.
Now let us assume that the objective function of the government is welfare maximization. Proposition 2 identifies a sufficient condition under which intermediate price regulation guarantees higher
welfare than final price regulation.
Proposition 2:
Assume that government’s objective is welfare maximization (W ), target price is below the price
without regulation and
dp
dI
> 0.
Then sufficient condition for W being higher under w regulation being higher or equal than W
under p regulation is: DpI ≤ 0
Proof:
Welfare-maximizing level of I is found from : (p − c)DI − ΦI + uI + pDI = 0. Denote the level of
investments found from this condition as I SW . Under w regulation, I is found from: (p − c)DI − ΦI +
dp
(w − c)Dp dI
= 0.
dp
Due to the condition DpI ≤ 0 it is easy to see that pDI ≥ (w −c)Dp dI
since p− |w −c|α > p− |w −c| =
p − c + w > 0, where α =
Dp
2Dp +Dpp (p−w)
∈ (0, 1). Therefore, for any given p I SW > I i > I f . The latter
inequality follows from proposition 1. From here the result of proposition 2 follows. Q.E.D.
The most common and natural case is when
dp
dI
> 0. In this case (according to proposition 1)whole-
sale price regulation results in higher investments and consumer surplus than final price regulation if
8
target price is below the one without regulation. The intuition for this result is the following: under
final price regulation (i.e. when the final price is set at some level exogenously) the final price is not
sensitive to the choice of manufacturer. In other words the manufacturer can’t affect the final price
via choice of intermediate price or investments. On the contrary, in case of intermediate price regulation the manufacturer can affect the final price via choice of investments. In case when the regulator
would like to achieve the price level below the one without regulation, the wholesale price is set at the
level which is lower the one that is optimal for the upstream firm (i.e. wr < c). The upstream firm
then tries to increase the final price via higher investments. So, under wholesale price regulation the
upstream firm has more incentives to invest compared to final price regulation if pt < p(c).
So, decrease in wholesale price on the one hand reduces the final price, but on the other hand
stimulates investments (once again upstream firm uses investments as an instrument to raise final
price, when the other instrument (i.e. wholesale price) is unavailable due to the regulation). So, for
each given final price, fall in the wholesale price leads to higher investments upstream. However we
can’t state that fall in the wholesale price always rises investments since the change in wholesale price
affects final price. Smaller final price (other things being equal) reduces investments since the return
from each unit invested falls down. Thus, change in w induces two effects on investments that move
in opposite directions. The aggregate effect is ambiguous. But there is a possibility that regulation of
the wholesale price below upstream firm’s profit-maximizing level (i.e. at wr < c) will result in lower
final price without the harm to the investments (compared to the case without regulation). Formally
it is possible to achieve pt = p(wr ) < p(c) and I(wr ) ≥ I(w = c).
Proposition 3 formulates a necessary and sufficient condition for the above result to hold for the
additively separable (in terms of price and investments) demand function, i.e. DpI = DIp = 0 for all
the price and investments levels.
Proposition 3:
For any additively separable (in terms of price and investments) demand function wholesale price
regulation below marginal costs (i.e. wr < c) results in lower price without reduction in investments
compared to the one without regulation if and only if (Dpp )2 ≤ Dp Dppp .
Proof:
If demand function is additively separable RpI = DI and ΠIp = DI +(wr −c)·(−DI )·
From (11) we get:
Dp DI (w − c)
(Dpp )2 − Dp Dppp
dI e
=
·
dw
(ΠII Rpp − RpI ΠIp )
(2Dp + Dpp )2
9
(Dpp )2 −Dp Dppp
.
(2Dp +Dpp )2
For wr < c
dI e
dw
≤ 0 if and only if (Dpp )2 − Dp Dppp ≤ 0.
Once again ΠIp = DI (1 − (wr − c) ·
Therefore due to assumption 4
dpe
dw
(Dpp )2 −Dp Dppp
)
(2Dp +Dpp )2
< DI when wr < c and (Dpp )2 − Dp Dppp < 0.
> 0.
Thus, setting w at the level below c allows to reduce price (compared to the one without regulation)
and not harm the investments level. Q.E.D.
The examples of the demand functions that satisfy the condition (Dpp )2 − Dp Dppp ≤ 0 include
linear in price demand function (i.e. D(p, I) = A − kp + f (I), where f (I) is an arbitrary increasing in
I function) and the demand function of the form D(p, I) = A + exp(−ap) + exp(−bp) + f (I), a, b > 0.
5.1
Illustration. Linear in price demand
Assume that the demand function is of the form D(p, I) = A−kp+f (I). In this case
0. Also we find that ΠIp = RpI = DI . Using (11) we conclude that
dI e
dw
dp
dI
I
= − 2DpD+D
>
pp
= 0. That is in case of a linear
demand function the two effects identified above (i.e. fall in price that tends to reduce investments and
fall in wholesale price that tends to increase investments) cancel each other so that the equilibrium
investments stay unchanged when the wholesale price changes 1 . In other words, in case of intermediate
price regulation (i.e. wholesale price regulation) the equilibrium
2
investments is the same whatever
the level of wholesale price, while final consumer price depends positively on the wholesale price. Thus,
intermediate price regulation (i.e. wr < c) allows to achieve lower final price compared to the one
without regulation without reducing the demand-enhancing investments of the upstream firm.
This outcome is impossible to achieve under final price regulation (if
dp
dI
> 0). Provided this
positive relationship between equilibrium price and investments price reduction below the level p(c)
is necessary accompanied by the fall in the investments of the upstream firm.
So, proposition 2 suggests the price regulation scheme that does not harms investments of the
upstream firm. Instead of final price regulation we suggest to make sure that there are two-part tariff
contracts between upstream and downstream firms and to regulate variable part of this contract (i.e.
wholesale price).
Note that in general fall in price does not guarantee increase in welfare (total surplus) since it is
associated with the change in investments and as we know from Spence (1976) the monopolist can
1
2
Provided that internal solution exists.
Quasi-equilibrium or constrained equilibrium investments since wholesale price is set exogenously and not decided
by the market.
10
overprovide or underprovide the investments compared to the socially optimal ones. In case when price
fall is accompanied by increase (or no change) in investments consumers are better-off (compared to
the situation before these changes)3 . However, the case when investments don’t change while price is
falling (like in the situation of linear demand function) allows to state that welfare is rising from such
a regulation.
6
Nash bargaining solution
Here we assume that instead of take-it-or-leave- it offer from the upstream producer to the downstream
firm there is a Nash bargaining process between the companies. At the stage when the companies
decide on the terms of the two-part tariff contract they maximize the Nash product. Bargaining power
of the upstream firm is denoted by β while the bargaining power of the downstream producer is 1 − β.
The timing is the following: Firstly, the upstream firm chooses the level of demand-enhancing
investments. Secondly, the firms maximize Nash product by choosing w, F (in case of w is not
regulated) and by choosing F (if w is regulated). Lastly, the downstream firm sets final consumer
price (if it is not regulated).
Note that at the stage when upstream and downstream firms decide on the terms of the contract
the costs of investments don’t enter upstream firm profit since at this stage spending on investments
is already sunk.
Formally, at the stage when the parties decide on F (the fixed fee of the two-part tariff contract)
they maximize the following:
maxF ((w − c)D(p, I) + F )β ((p − w)D(p, I) − F )(1−β)
(12)
From here we get fixed fee for each levels of w, p, I:
F ∗ = β(p − w)D(p, I) − (1 − β)(w − c)D(p, I).
At the first stage of the game the upstream firm chooses investments:
maxI Π = (w − c)D(p, I) + F − Φ(I)s.t.F = F ∗
3
(13)
A necessary and sufficient condition for this to happen for the additively-separable demand function is formulated
in proposition 2
11
Plugging F ∗ in to (13) we get the following maximization problem:
maxI Π = β(p − c)D(p, I) − Φ(I)
(14)
In case of final price regulation the investments are found from the following first-order condition:
ΠI = β(pr − c)DI − ΦI = 0
(15)
In case of intermediate price regulation (i.e. regulation of w) the investments are found from the
following condition:
ΠI = β(pr − c)DI − ΦI + β(w − c)Dp ·
dp
=0
dI
(16)
Comparison of (15) and (16) allows to conclude that proposition 1 is robust to the switch from
the take-it-or-leave it offer to the Nash Bargaining solution between the parties.
Proposition 4: Assuming that both types of regulation guarantee the same final consumer price
i) Intermediate price regulation results in higher (lower) investments than final price regulation
for the case of positive
dpe
dI
and when target price is below (above) than the one without regulation.
ii)Intermediate price regulation results in lower (higher) investments than final price regulation for
the case of negative
iii) If
dpe
dI
dpe
dI
and when target price is below (above) than the one without regulation.
= 0 both regulation schemes are absolutely identical.
The proof of proposition 3 is the same as the one to proposition 1.
In it easy to check that in case of linear in price demand function equilibrium investments don’t
depend on w (as in previous section). Therefore intermediate price regulation allows to lower price
level while keeping investments unchanged (compared to the absence of regulation case).
So, we see that the results of the previous section are qualitatively the same in case of Nash
bargaining between the firms.
7
Cost-reducing investments
Here we assume that instead of demand-enhancing investments the upstream monopolist sets the level
of marginal cost reducing investments. We show that the result of the previous section vanishes and
is unapplicable to this case.
The profits of upstream and downstream firms are respectively:
12
Π = (w − c + I)D(p) − Φ(I) + F,
R = (p − w)D(p) − F
Assuming two-part tariff contract between the firms and that upstream monopolist makes takeit-or-leave-it offer to the downstream company, the fixed fee is F = (p − w)D(p). The first-order
condition for finding investments under final price regulation is:
D(p) − ΦI = 0
(17)
The first-order condition for finding investments under intermediate price regulation is:
D(p) − ΦI + (wr − c + I)Dp
dp
=0
dI
(18)
Note that when the upstream firm invests in cost reduction rather than demand enhancement,
change in investments affects prices indirectly (via wholesale price). In case of final price regulation
price is by definition is not affected by the choice of the upstream firm, and therefore in this case
dp
dI
= 0. In case of wholesale price regulation, wholesale price is fixed exogenously and, therefore, is
not affected by I. Therefore in case of intermediate price regulation
dp
dI
= 0. In other words (18) and
(17) become absolutely identical provided that both regulation schemes guarantee the same consumer
price level. So, in this case the two regulation approaches are the same in terms of investments and
surpluses (assuming that they result in the same consumer final price).
In case of Nash bargaining solution between upstream and downstream firms the fixed fee is equal
to F = β(p − w)D(p) + (1 − β)((w − c + I)D(p)), where β is a bargaining power of the upstream
producer.
Upstream firm’s profit is: Π = β(p − c + I)D(p) − Φ(I).
Due to the same reasons discussed for the case of take-it or leave-it offer the first order conditions
for finding investments are the same for both regulation schemes (if they guarantee the same consumer
price) and it is the following:
βD(p) − ΦI = 0
(19)
Thus, the two regulation schemes are identical. Moreover we may conclude that if the target
price is below the one without regulation then both regulation schemes unavoidably result in a fall in
13
investments below the one without regulation (and vice versa). This is because
dI
dp
of take-it or leave it offer from the upstream producer to the downstream one (and
D
= − ΠIIp > in case
dI
dp
D
= −β ΠIIp > in
case of the Nash bargaining solution).
Proposition 4 summarizes the results of this section.
Proposition 5:
In case when upstream producer invests in cost reduction instead of demand-enhancement the two
regulation schemes (i.e. intermediate price regulation and final price regulation) are identical (provided
that they result in the same final consumer price). If target price is below (above) unregulated one such
a regulation results in decreased (increased) cost-reducing investments (compared to the investments
without regulation).
8
Linear price contract
Here we assume that instead of two-part tariff contracts there is a linear price contract between
upstream and downstream firms.
It is straightforward that in case of
dp
dI
> 0 the result of proposition 1 is reversed.
Proposition 7: Provided that there is linear price contract between manufacturer and retailer
and that intermediate and final price regulations guarantee the same level of final consumer price
intermediate price regulation results in a higher investments and consumer surplus compared to final
price regulation if
dpe
dI
> 0 and target price (pt ) is below the one without regulation, i.e. pt < p(c).
The proof immediately follows from comparing the first-order conditions for finding investments
under intermediate and final price regulations and from taking into account the fact that w must
exceed c for the participation constraint of upstream producer to be satisfied.
9
Conclusion
The paper compares the final price and intermediate price regulations for the case when the upstream
producer invests in demand-enhancement. The work identifies the conditions under which one or
another regulation scheme is preferred in terms of the level of investments and consumer surplus.
These conditions include the characteristics of the demand function, the type of investments, the type
of the contract between upstream and downstream firms.
14
The central result of the paper is that it is possible to achieve lower final price (compared to the
one without regulation) without harming the investments level. In order to achieve it there should be
two-part tariff contracts between upstream and downstream producers and intermediate (instead of
final) price should be regulated. The paper provides a sufficient condition for this result to hold.
The proposed regulation scheme is important since it contradicts the conventional wisdom that
there is a trade-off between final price and demand-enhancing investments.
As for the further work I’m going to study the difference between final and intermediate price
regulations in the context where there is competition between upstream (and downstream) firms. The
other direction of future research includes the cases when downstream firm (instead of upstream one)
makes the investment.
References:
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Currier, K., 2007. ”A Practical Approach to Quality-Adjusted Price-Cap Regulation”. Telecommunication Policy, Vol. 31, pp. 493-501.
Kriehn,C., 2004.”Quality Regulation without Regulating Quality”, Working paper.
Sappington, D., 2003. ”The effect of incentive regulation on retail telephone service quality in
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Weisman, D.L., 2005. ”Price Regulation and Quality”. Information Economics and Policy, Vol.
17(2),pp. 165-174.
White, L.J., 1972. ”Quality Variation when Prices are Regulated”. Bell Journal of Economics and
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