Environmental Regulation and Industry DynamicsContribution of the paper Establishes a relation...

Environmental Regulation and Industry Dynamics

Aditi Sengupta

Southern Methodist University

30th January, 2010

Aditi Sengupta (SMU) Environmental Regulation and Industry Dynamics 30th January, 2010 1 / 24

Question

What is the relationship between environmental regulation andindustry dynamics?

How does the increasing stringency of exogenously givenenvironmental regulation a¤ect:

size distribution,capital formation in �rms,inter-�rm heterogeneity,entry-exit, andshake-out (�early� exit ) of �rms?

Question

size distribution,

capital formation in �rms,inter-�rm heterogeneity,entry-exit, andshake-out (�early� exit ) of �rms?

Question

size distribution,capital formation in �rms,

inter-�rm heterogeneity,entry-exit, andshake-out (�early� exit ) of �rms?

Question

size distribution,capital formation in �rms,inter-�rm heterogeneity,

entry-exit, andshake-out (�early� exit ) of �rms?

Question

size distribution,capital formation in �rms,inter-�rm heterogeneity,entry-exit, and

shake-out (�early� exit ) of �rms?

Question

Contribution of the paper

Establishes a relation between environmental regulation and industrydynamics via investment in compliance technology.

More speci�cally, the e¤ect of the increasing stringency ofenvironmental regulation on industry dynamics i.e., size distribution,investment behavior, heterogeneity, and shake-out of �rms.

Shows that �rms that exit earlier on the industry equilibrium pathhave higher cost of compliance and are smaller in size.

Finds su¢ cient conditions under which on the equilibrium path withmore stringent regulation:

the industry experiences higher shake-out, andthe active �rms have lower cost of compliance.

the industry experiences higher shake-out, and

the active �rms have lower cost of compliance.

Explains

the empirical regularities of industry dynamics,the (mixed) empirical evidence on the e¤ect of environmentalregulation on shake-out.

In our model shake-out occurs as a part of socially e¢ cientcompetitive behavior of dynamic equilibrium path of an industry. Itdoes not imply any anticompetitive role of environmental regulation.

Explains

the empirical regularities of industry dynamics,

the (mixed) empirical evidence on the e¤ect of environmentalregulation on shake-out.

Explains

Structure of the model

T (1 < T < ∞) period deterministic dynamic model.

Homogenous good industry with exogenously given level ofenvironmental regulation (α).Continuum of identical price taking potential entrants, each ofmeasure zero.

Free entry and exit.

Stationary market demand D(p).

T (1 < T < ∞) period deterministic dynamic model.Homogenous good industry with exogenously given level ofenvironmental regulation (α).

Continuum of identical price taking potential entrants, each ofmeasure zero.

T (1 < T < ∞) period deterministic dynamic model.Homogenous good industry with exogenously given level ofenvironmental regulation (α).Continuum of identical price taking potential entrants, each ofmeasure zero.

Production Cost

Continuously di¤erentiable production cost c(q) where c : R+ ! R+

Upward sloping marginal cost with �xed cost

c (0) > 0, c0> 0, c

U-shaped average cost curve.

Production Cost

Continuously di¤erentiable production cost c(q) where c : R+ ! R+Upward sloping marginal cost with �xed cost

c (0) > 0, c0> 0, c

Production Cost

Continuously di¤erentiable production cost c(q) where c : R+ ! R+Upward sloping marginal cost with �xed cost

c (0) > 0, c0> 0, c

Investment

γ (x): cost of investment where x � 0 is the investment made by a�rm.

γ : R+ ! R+ is continuously di¤erentiable, strictly increasing convexfunction.

γ (0) = 0,γ0> 0 and γ" � 0.

y 2 R+ : the stock of capital of a �rm.If a �rm enters in period τ, then for t > τ,

yt = xτ + xτ+1 + ......+ xt , yτ = 0.

No externality across the �rms arising from cost reducing investment.

Investment

γ (0) = 0,γ0> 0 and γ" � 0.

y 2 R+ : the stock of capital of a �rm.

If a �rm enters in period τ, then for t > τ,

yt = xτ + xτ+1 + ......+ xt , yτ = 0.

Investment

γ (0) = 0,γ0> 0 and γ" � 0.

yt = xτ + xτ+1 + ......+ xt , yτ = 0.

Investment

γ (0) = 0,γ0> 0 and γ" � 0.

yt = xτ + xτ+1 + ......+ xt , yτ = 0.

Environmental Regulation

α 2 R+ : the exogenous level of regulation imposed on the industry inorder to control the pollution generated by these �rms.

It is assumed to be constant over a dynamic path of an industry.

α = 0 implies no regulation.

α can take di¤erent forms of pollution control measures.

Cost of Compliance

Cost of compliance with the exogenous regulation (α)

φ (q, y , α)

where φ : R3+ ! R+ is continuously di¤erentiable in all the arguments.

Assumptions:φ(q, y , 0) = 0 and φ(0, y , α) = 0

φq > 0, φy � 0 and φα > 0.

γ0(0) < �δφy (q, 0, α) 8q > 0, α > 0 where δ 2 (0, 1)φqq > 0, φqy � 0, φqα > 0, φyy > 0 and φyα � 0.

Maximization problem

Given α and p = (p1, ....pT ) , a typical �rm i maximizes discounted sum ofpro�t

τ(i )

∑t=τ(i )

δt�τ(i ) [ptqt (i)� c (qt (i))� φ (qt (i) , yt (i) , α)� γ (xt (i))]

with respect to the period of entry τ (i), period of exit τ (i) ,output qt (i) ,and investment xt (i).

De�nition of Industry Equilibrium

Given the exogenous level of regulation α > 0, an industry equilibriumconsists of period of entry, period of exit, output and investment pro�le of�rms and price vector p such that

market clears in every period,

the output-investment for each active �rm maximizes its netdiscounted sum of pro�ts over its lifetime,

irrespective of the period of entry and exit, all that enter the industryearn exactly zero net intertemporal pro�t over their lifetime in theindustry,

no �rm can make strictly positive intertemporal pro�t irrespective ofits period of entry

There exists an industry equilibrium, and it is (restricted) sociallyoptimal (maximizes discounted sum of consumer and producer surplusin the industry over time).

Main ResultsCharacteristics of dynamic equilibrium path

For a given level of regulation (α), on any industry equilibrium path

prices are non-increasing over time,

no entry occurs after the initial period,

some �rms exit before others (shake-out), and

�rms that exit earlier have lower accumulated investment, highercompliance cost, and smaller in size.

Why does shake-out of �rms occur on the industryequilibrium path?Social planner�s perspective

Introduction of regulation=) steep marginal cost curve =) large numberof �rms to # the total cost of the industry.

Strictly positive investment =) �atter e¤ective marginal cost overtime.=) # number of �rms in the industry.

Numerical example 1Three period model

D(p) = 100� p, c(q) = 10+ eq , γ(x) = 0.5x2

φ (q, y , α) = α.e(q, y) = αeq�λy

δ = 0.5 is the discount factor

λ � 0 is the e¢ ciency of accumulated capital in compliance costreduction.

α = 0.03 is the exogenous unit pollution tax rate.

Example 1: results

Table 1: Dynamic equilibriumt pt D(pt ) nt =

D (pt )qt

nt�nt�1nt�1

1 8.7637 91.2362 42.6125 �2 8.7569 91.2430 42.5474 �0.00153 8.7432 91.2567 42.5366 �0.0002

Example 1: results

Table 2: Firm that exits at the end of period 2t qt xt πt

1 2.1410 0.1141 �0.00652 2.1434 0 0.0130

Table 3: Firm that exits at the end of period 3t qt xt πt

1 2.1410 0.1588 �0.01262 2.1445 0.0990 0.01803 2.1454 0 0.0142

Comparative dynamicsExample 2

D(p) = p�1.5, c(q) = 1+ q2, γ(x) = 0.5x2

φ (q, y , α) = αe(q, y), e(q, y) = q1.5(1� y)5

ResultsExample 2

Table 4

t α q x1 p D (p) n = D (p)q

nt�nt�1nt�1

1 0.03 0.9925 0.0585 2.0299 0.3457 0.34832 0.03 0.9961 0 2.0256 0.3468 0.3481 �0.00041 0.05 0.9876 0.0865 2.0498 0.3407 0.34492 0.05 0.9958 0 2.0392 0.3433 0.3448 �0.00051 0.07 0.9828 0.1094 2.0696 0.3358 0.34172 0.07 0.9962 0 2.0519 0.3404 0.3416 �0.00011 0.10 0.9827 0.1358 2.0588 0.3313 0.33712 0.10 0.9827 0 2.0588 0.3313 0.3371 0

Main ResultsComparative dynamics

Consider two period model.

Additional assumption: for any given level of regulation, on industryequilibrium path some �rms exit after period 1.

Comparative dynamics

Su¢ cient conditions under which on the equilibrium path with morestringent regulation active �rms invest more i.e., have lower cost ofcompliance.

Why would a �rm not invest more on the higher regulation path?

With high regulation the compliance cost is high, and thus �rms wantto invest more to reduce that cost.But there is a disincentive e¤ect: If regulation is quite high then thereturn from investment may not be that pro�table.Two extreme cases: Prohibitive regulation (regulation too high) andNo regulation =) zero investment.

With high regulation the compliance cost is high, and thus �rms wantto invest more to reduce that cost.

But there is a disincentive e¤ect: If regulation is quite high then thereturn from investment may not be that pro�table.Two extreme cases: Prohibitive regulation (regulation too high) andNo regulation =) zero investment.

With high regulation the compliance cost is high, and thus �rms wantto invest more to reduce that cost.But there is a disincentive e¤ect: If regulation is quite high then thereturn from investment may not be that pro�table.

Two extreme cases: Prohibitive regulation (regulation too high) andNo regulation =) zero investment.

Su¢ cient conditions under which the industry experiences highershake-out.

Conditions under which on a dynamic path with higher regulation thenumber of �rms is higher in period 1 and lower in period 2.

Su¢ cient conditions under which the industry experiences highershake-out.Conditions under which on a dynamic path with higher regulation thenumber of �rms is higher in period 1 and lower in period 2.

Average cost under

weak regulation

Marginal cost under

weak regulation

Marginal cost under

stringent regulation

Average cost under

stringent regulation

Demand curve

Higher number of firms in period 1 under stringent regulation

Price under

stringent

regulation

Price under weak

regulation

Number of firms = Total industry output (Q) /

minimum efficient scale (q)

q1 Q1q2 Q2

Q1/q1 > Q2/q2

Comparative dynamicsHigher number of �rms in period 1

The price in period 1 is exactly equal to minimum average cost of anew entrant.

Each �rm produces at its minimum e¢ cient scale earning exactly zerocurrent pro�t (gross of investment).

Therefore, the number of �rms in period 1 is higher on the morestringent regulation path i¤ the minimum e¢ cient scale is moresensitive to regulation than the total industry demand (possible whenthe demand curve is su¢ ciently inelastic).

Comparative dynamicsThree e¤ects of higher regulation on the number of �rms

E¤ect 1: (Given investment) higher level of regulation =) " costof the industry =) " the equilibrium price and # total industryoutput sold =) # the number of �rms in period 2. (Direct e¤ect)

E¤ect 2: (Given investment) higher level of regulation =) " theaverage cost and the e¤ective marginal cost =) alter the optimalscale =) a¤ect the number of �rms depending on the direction andextent of changes in optimal scale. (Direct e¤ect)E¤ect 3: " in regulation may " investment =) " in the optimalscale =) # the number of �rms. (Indirect e¤ect)

E¤ect 1: (Given investment) higher level of regulation =) " costof the industry =) " the equilibrium price and # total industryoutput sold =) # the number of �rms in period 2. (Direct e¤ect)E¤ect 2: (Given investment) higher level of regulation =) " theaverage cost and the e¤ective marginal cost =) alter the optimalscale =) a¤ect the number of �rms depending on the direction andextent of changes in optimal scale. (Direct e¤ect)

E¤ect 3: " in regulation may " investment =) " in the optimalscale =) # the number of �rms. (Indirect e¤ect)

E¤ect 1: (Given investment) higher level of regulation =) " costof the industry =) " the equilibrium price and # total industryoutput sold =) # the number of �rms in period 2. (Direct e¤ect)E¤ect 2: (Given investment) higher level of regulation =) " theaverage cost and the e¤ective marginal cost =) alter the optimalscale =) a¤ect the number of �rms depending on the direction andextent of changes in optimal scale. (Direct e¤ect)E¤ect 3: " in regulation may " investment =) " in the optimalscale =) # the number of �rms. (Indirect e¤ect)

Conclusion

The e¤ect of the increasing stringency of environmental regulation onindustry dynamics i.e., size distribution, investment behavior,heterogeneity and shake-out of �rms.

the industry experiences higher shake-out (; anti-competitive role)the active �rms invest more to reduce future stream of compliance cost.

Explains the empirical regularities of industry dynamics. and the(mixed) empirical evidence on the e¤ect of environmental regulationon shake-out.

Conclusion

the industry experiences higher shake-out (; anti-competitive role)

the active �rms invest more to reduce future stream of compliance cost.

Conclusion

Environmental Regulation and Industry DynamicsContribution of the paper Establishes a relation...

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