a general equilibrium analysis of regulation and income distribution

ELSEVIER European Journal of Political Economy

Vol. 10 (1994) 625-638

EuropeanJournalof

POLITICAL ECONOMY

A general equilibrium analysis of regulation and income distribution

Ravi Batra, Hamid Beladi * a Department of Economics, Southern Methodist Uniuersity, Dallas, TX 75275, USA

b Department of Economics and Finance, University of Dayton, Dayton, OH 45469, USA

Accepted for publication September 1993

Abstract

In this paper we have utilized a two-sector, two-factor general equilibrium model of production to analyze the implications of the fair-rate of return regulation for resource allocation as well as real factor rewards. Our main conclusion is that regulation in one sector has an effect on factor rewards and resource allocation in the entire economy.

Keywords: Regulation; Factor rewards; Monopoly

JEL classification: L51

1. Introduction

The pioneering contribution of Averch-Johnson (A-J) (1962) has led to the development of a rich literature concerning the input-output decision-making by a monopoly firm facing a constraint on its rate of return on capital. However, in spite of the great interest generated by the A-J results, the implications of the regulatory constraint have been explored only in terms of partial equilibrium frameworks, although in view of the large size of the regulated sector in the U.S. and several European countries such as West Germany (Muller and Vogelsang, 1979), the United Kingdom (Peacock, 1981) and Belgium (Baron and De Bondt, 19791, the implications of the regulatory constraint ought to be explored in terms

* Corresponding author. We are grateful to a referee for constructive comments and suggestions.

0176-2680/94/$07.00 0 1994 El sevier Science R.V. All rights reserved SSDI 0176-2680(94)00023-D

626 R. Batra, H. Beladi/European Journal ofPolitical Economy 10 (1994) 625-638

regulation on regulated as well as unregulated sectors in the economy are taken into account.

The purpose of this study is to provide a theoretical framework for a general- equilibrium analysis of the effects of the rate of return regulation in the regulated industries. The study relies heavily on the properties of the well-known two-sector, two-factor, constant-returns-to-scale general equilibrium model of production which has found eloquent expression in the works of Heckscher, Ohlin, Samuel- son, Harberger, and Jones among many others.

We assume that the economy can be divided into two distinct sectors, one regulated and the other unregulated, each employing two factors of production, capital and labor. The regulated sector consists of public utilities which are responsible for supplying (locally and/or over long distances) water, electricity, gas, telephone and transit services, as well as those industries which provide interregional transport such as railroads, oil pipelines, motor carriers, water carriers and airlines. The firms in the regulated sector are many and diverse, but they share certain characteristics and an institutional environment dominated by regulation. In these industries, the monopoly firm faces a constraint on profits in the sense that its rate of return from assets cannot exceed a certain ‘fair’ rate of return as determined by the regulatory commission.

The unregulated sector includes the rest of the economy. This sector consists of industries facing varying degrees of unregulated corporate sector as well agriculture, real estate and services. ’

2. Assumptions and the basic model

competition. Here we may include the as the non-corporate industries such as

Unless otherwise specified, the following assumptions will be used throughout the analysis:

1. There are two sectors in the economy, X,, the regulated and X, the unregulated sector. The production function in each sector is linearly homogeneous and concave and is given by,

xi=Fi(Ki,Li) =L,f,(k,) (i=1,2) (1)

where K = capital, L = Labor and k = (K/L) and the subscript i denotes the sector. 2. There is perfect competition in factor markets, factors are fully mobile between the two sectors and factor price flexibility ensures the full employment of inelastic factor supplies.

1 It may be pointed out here that the division of the economy into a regulated and unregulated sector

poses no problems. This is because the regulated and the unregulated sectors are clearly defined.

R. Batra, H. Beladi/ European Journal of Political Economy 10 (1994) 625-638 627

3. Producers in the unregulated sector maximize profits and their decision making leads to the following first-order conditions in X,:

~(1 - l/e,)F,, = w2 (2)

and

P2(l- l/e2)FK2 = r2, (3)

where wi = wage rate, ri = rental capital, pi = price, ei = elasticity of demand, FLi = marginal product of labor and FKI = marginal product of capital all in the ith sector. Eqs. (2) and (3) state that the profit maximizing producers in the second sector equate the marginal revenue product of each factor with the given input price. 4. Producers in the first sector maximize profits subject to the constraint on the rate of return on capital. The so-called ‘fair’ rate of return is higher than the cost of capital, I~, but lower than the rate that would prevail in the absence of regulation. 2 Let profits in the first sector be given by

Tl =Pl(xl)xl- J%h - r1K,

where pr(X,> is the demand function facing the X, producers. Let s be the fair rate of return. The regulated firm’s problem then is to maximize rrl subject to the regulatory constraint

MXJX, -~1Jw~6~ where s > rl. 3 However, since s is less than the profit-maximizing rate of return, this constraint can be treated as an equation. The Lagrangian of the problem may be written as

H=p,(Xr)X, - WIJ% - r,K, - ~[~I(XI)XI - WIJ% - 61

where h is the lagrangian multiplier. The first-order conditions for the maximum are:

(I- h)~,(l- l/e,)% = w,(l -A),

(1 - h)p,(l - l/e,)F,, - rr = -As

(4)

I (5)

a Here we are following the literature dealing with the A-J model. In the long history of court

decisions and regulatory commission hearings, the concept of the fair-rate of return has not been

precisely defined. It is generally agreed, however, that the fair-rate of return should be high enough to

enable the company to attract new capital, operate successfully and compensate the investors for

undertaking the risks. One implication of s > r-t is that regulation does not completely eliminate monopoly profits; it simply restrits them to a level given by (S - r,)Kr.

s Following A-J and many others, we assume that depreciation of capital is zero and that the acquisition cost of capital is unity. Otherwise, depreciation would appear in the operating cost and K, would measure the depreciated value of the firm’s capital. For simplicity, these complications are ignored.


and

SK, + WrL, -prX, = 0, (6)

where pr(l - l/er) is the marginal revenue in the first sector. Baumol and Klevorick (1970) have shown that 0 < A < 1. Eqs. (4) and (5) yield

w1 =PG - l/e,)&, (7)

Yl =z+(l - l/e,)F,, + UP? (8)

where u = [s - rr] > 0 and p = [h/(1 - A)] > 0. Substituting for wr and rr in (6) and utilizing Euler’s theorem for homogeneous functions, we obtain

UP = (~rXr/eA) - u = (P1fi/cI~J - u. 4 (9)

5. One implication of the assumption of perfect factor mobility made above is that in equilibrium factors of production cost the same everywhere, that is

WI = w* = w (10)

rl = r2 = r.

6. The assumption of full employment implies that

(11)

L, +I,, =L (12)

and

L,k, + L,k, = K,

where L and K are fixed.

(13)

7. On the consumer demand side we will assume that the demand for each good is a function only of relative prices. Let the second good be considered a numeraire, so that p2 is constant at unity and p1 can be regarded as the relative price of the

first good (our results are not dependent on the choice of numeraire). With equilibrium in commodity markets, the demand for each good is equal to its supply. However, in an economy characterized by the full employment equilib-

4 Eq. (9) has been obtained as follows: Substituting w, and rr from (7) and (8) in (6), we obtain

[v(l+p)+~,(l-l/e,)F,,lK,+ p~(l-l/e~)hh- plXI=O

But since X, = L,F,, + K,F,,, this equation reduces to

u(l+p)K1-(p,X,/elK1)=O, whence we obtain Eq. (9) presented in the text. Note that in the absence of the limitation on the rate of

return, monopoly profits in the first sector would equal (pI X, /e,K,), whereas in the presence of this regulation, such profits equal vK,. In view of this, one way to represent the fact that the constraint is

inoperative or that regulation is absent is to equate /3 to zero. Note that when the constraint is

operative, p > 0.

R. Batra, H. Beladi/Europeun Journal of Political Economy 10 (1994) 625-638 629

rium, one demand equation is redundant. Hence the commodity market equilibrium may be represented by

Xl =4(PJ (14) where D, = consumer demand for the first good, with 0; = (dD,/dp,) < 0. 8. Finally, we assume that the elasticity of demand in each sector is constant. The model that we have presented here to explore the implications of regulation is a modified version of the two-sector model which Harberger (1962) developed to analyze the incidence of the corporation income tax, with the monopoly elements introduced in the corporate sector by means of a constant ‘monopoly markup’, which equals the percentage by which the price charged by the monopoly firm exceeds the marginal cost. As Harberger argues, the presence of several independ- ent firms in any sector keeps the monopoly-markup to a modest size and this mark-up is likely to be unchanged.

In our model, the constancy of this mark-up is represented by the assumption of constant elasticity of demand in each sector. 5

In assumption 4, we have briefly presented the Averch-Johnson model, assuming in effect that this model correctly describes the decision-making of the regulated firms. 6 Incidentally, the Averch-Johnson thesis that regulation stimu- lates overcapitalization has been confirmed by Spann (1974) and Courville (1974) at least for the case of electric utility industry.

3. Development of the general solutions

Among the equations presented in the previous section, five are of immediate concern, Two deal with factor-market equilibrium, two with full employment and one with the commodity-market equilibrium. First, the factor-market equilibrium conditions can be obtained from (2) (3) and (7) to (11). Thus

and

(15)

’ The general case is one where the elasticity of demand in each sector is a function of the relative prices as well as national income. The reader can confirm that when each elasticity of demand is an

increasing function of its relative price, then the rasults reported in this study remain unchanged, provided the elasticity of demand in the regulated sector is less than or equal to unity.

6 This premise is perhaps invalid, but, the A-J model is now considered to be the ‘representative’ model of the regulated firm. The reader who does not like this characterization may interpret our

analysis as one investigating the general equilibrium implications of the A-J effect.

(zz) ‘0 = (flP/QfP)

[‘~/1x141~ - z?>] + (aP/zYPYiz7+ (f7P/‘?P>(YZY + 172J17

SNUO3aq (OZ) XXICJH

(IZ) ‘(“P/z7P) = [ (‘7 - zY VI] [ (“P/“YPlZ7 + (flP/1YP)17] = (OP/‘7P)

‘(El) P=e (ZI) wo$l

(oz) ‘(“P/1dP)‘,c7= (flP/17P)LJ+ (flP/‘YP)lJ’7

la8 aM ‘0 01 IDadsal ~J!M (~1) %uleylua~a~~a

(67) ‘I = ("PWP) . (1Y/‘7tr’fJ - ‘4) + (flP/Z?P)tlZ~ -

cw~~P)[( ,‘?/“W’~ - w) - a]

Pue

(81) 0 = (RP/1dP)17Lf’” + (~P/zYP)~~zYz” + (~P/1YP)!41Y-

u!elqo aM ‘1 = ‘v’d d~~e!]!u! p?yl Bu!laqmamaJ pue ‘0 01 padsal qp~ (91) pm (51) %yle!lua~a33~a

.&IO uogeln8a.x 30 8u!ua@g e 30 suoymldur! aql %r~zdpx~e 01 slunouxe sly1 Bugeads dpc+~~s yShoq$Ie ‘ysala$u! 30 sa[qepea snoyx 103 suognIos uyqo pue fl us uo!ynpaI ~pxus e ampollu! sn Ia1 ‘uoy -ep@al 30 suogmgdm! ayy JaAomp 01 laplo UI xoge@ial lapun paf!mad Igold Qodouotu 30 ale1 ayl s! n alaH ‘(A - s) spxba qzq~ ‘R dq paluasaldal $U!E.IJS -UOD dJo]ep@a~ ay$ lapun Ougelado lo]Das auo ~I!M lapour uxnpqg~nba pxaua?! lopas-om mo aqgsap dlataldwo:, uoyas sy$ u! paluasald suopenba aA!3 aqL

8 ‘1 = Ivld SI pq ‘djrun spmba ‘_y UI anuanal px$!~eur d~p?p!ur leyj aumsse II!M aM ‘&gdmrs 30 ayes aql 103 Qamd '~~0~~03 ~eqm UI

(LI) .(Id)'a= Ij17

dq paqpxap s! ‘(I) 30 Mara u! ‘umpqg!nba laymu-dqpomuo:, aqj ‘d~pxu~

(EI) ‘X= zyz7+ Iy17

Pue

(ZI) 7=“7+‘7

:ale suog~puo~ luamLoIdma IIn ay) ‘puoDas ‘1 = Zd wq~ alay .taqmamal 0s~ ‘0 > ,‘J suopmn3 uogmpold a,wmo3

YVM ‘ ‘!yp/(!y)‘Jp E :j 91~~ [ :j’.y - ‘J] = !‘d pue :j= ‘“d ‘suoymn3 uogmpold ayl 30 diraua%omoq-.nzaug ayl 30 May u! aJayM pm (!a/~ - 1) = !I? alayM

R. Batra, H. Beladi/European Journal ofPolitical Economy 10 (1994) 625-638 631

In (18), (19) and (22) we have a system of three equations with three unknowns (dk,/du), (dk,/du) and (dp,/du). In the matrix form, this system is given by

-4fl’

[f;'Pdl - 4~Ll/kl2

J%(% +k*fi)

Let D be the determinant

Gf; %F,l

-%fi’ (f, -a,F,,)/k,

Lzf, -D’dk, - 4)

f the system (23). Then D is given by

D = -D;w,([W -a,)F,,(k, -k,)/k:f;‘] - [Wz -k&‘~~])fi’f;l

+(fi -GL/kJ[LzfAf;l +G~kzf;l(L +hfi))1 +a141

x[L,f,{f;‘-~(1 -+L/k,z} +a,L,fi’(F,, +hf;)]. (24) The immediate order of business is to determine the sign of D. It is well known

that for the existence of monopoly equilibrium, e, > 1, which means that aj = (1

- l/e,) is a positive fraction and fi > a,F,,. 9 With f: < 0, the last two terms of D are both negative. Similarly, the second expression in the first term is negative, but the sign of the first expression depends on the sign of (k, - k,), i.e., on the factor-intensities. A sufficient condition for D < 0 then is that k, > k,.

The following Lemma may now be derived:

Lemma 1. A sufficient condition for D < 0 is that the regulated sector is not capital-intensive relative to the unregulated sector.

Let us now proceed with the analysis and obtain solutions for three unknowns contained in the system (23). In solving the system we obtain

(dk,/du) = [hfi% + a,D’,p,(k, -k&f;]/%, (25)

(dk,/du) = [UdF,, +bf;) -k,f;‘(k2-kl)D’lpl]/Dp,, (26) and

(dp,/du) = [kfP,f, + a,k,f;L,(F’, + hf;)]P (27)

4. Regulation and resource allocation

A good deal of discussion in the literature related to the A-J model has focussed on the effect of the regulatory constraint on the output of the regulated firm. It has

9 This is also clear from Eq. (15) where with positive marginal productivities, a, and a2 must be positive, which is possible only if ei > 1. But if e, > 1, then clearly a, > 1. On the other hand, f, > FL,

and with a, < 0, f, is clearly greater than aIF,,.

632 R. Batra, H. Beladi / European Journal of Political Economy 10 (1994) 625-638

been argued by A-J and subsequently by Kahn (1968) that the fair rate of return regulation induces the firm to increase its output and thus move the unregulated monopolist’s output towards the socially optimal level. In this section, we will find that in terms of our general equilibrium model, the output of the regulated sector categorically rises if the unregulated sector is the relatively capital-intensive sector; furthermore if the output of the regulated sector rises, then the output of the other sector must decline. In other words, the effects of regulation in one sector are felt throughout the economy.

The implications of regulation for X, can be examined in two ways. We can directly obtain the expression for (dX,/du) or since (dX,/dp, < O), we can look at (dp,/du) from (27) and draw conclusions about (dX,/du). Either way, the results are the same. Let us proceed through the first route, because this procedure will be useful for obtaining (dX,/du) also.

Substituting for dki/du from (25) and (26) in (20, we obtain,

(dL,/du) = -dL,/dv

= -L,L,f;F,, -D’,p,(azL,k,f; +L,k,f;‘)/Dp,.

Differentiating (1) and using (25) and (281, we get

(dX,/du) =L,f;(dk,/du) +f,(d-Wdu)

=D;[G,f;(f,, +k,f;)L, +-%f,k,fj’]/D.

In a similar way, we can obtain

(28)

(29)

(dX,/du) = { -Dh[k,f;‘(F,, +hf;)Lz +G,f,k,f;]

-~PL,W”~~,}/Qv la (30)

” The procedure for getting the expression for (dX, /du) is a slightly more involved than that for obtaining (dX, /du). Differentiating (1) with respect to L’ we obtain

(dX, /du) = f,(dL, /du) + L, f;(dk, /dti)

which in view of (21) becomes

(dX, /du) = [&(& + hf;)(db /dv)+ hf,(dk, /du)]/(k, - k,). Using (2.5) and (261,

fif*-(~L*+~lf;)(~LI+~2f;)=f*f2-~f*-f;(~2-~l)~.~fi+f;(~*-~l)) =(k,-k,)[(f,-k,f;)f;-(f,-kzf;)f;l.

Now from the factor-market equilibrium conditions given be (15) and (16), with initially

a,p,=p,=l, (f,-k,f;)=a,(f,-k,f;) and (a2f;-fi)=4. Using these, we get

fif2 -_(% + ~lf~)~L1 + bfi = (4 - kI)(a2fi - fX2 = (b - kI)@C2. Using this in the expression for (dX, /du), we get Eq. (30) in the text.

R. Batra, H. Beladi/European Journal ofPolitical Economy IO (1994) 625-638 633

From (29) it is clear that with f[ < 0 and LYr < 0 the numerator is positive,

whereas in (30), the numerator is negative. Hence the sign of (dX/du) < 0 depends on the sign of D which has been argued in the previous section to be unequivocally negative if k, > k,. The following theorem may now be derived:

Theorem 1. A suficient condition for (dX,/du) < 0 and (dX,/du) > 0 is that k, > k,. In other words, a tightening of regulation leads to a rise in the output of

the regulated sector and a decline in the output of the unregulated sector, if the former is no more capital-intensive than the latter.

What is the economic explanation for Theorem l? It is well-known from the A-J analysis that the fair rate of return regulation induces the regulated firm to overcapitalize in the sense that capital is used even beyond the point where its cost equals the marginal revenue product. This is evident from (8) where rl >pl(l -

l/e,)F,,. ‘I This effect of regulation may simply be called the overcapitalization or the

substitution effect. The initial effect is that, as a result of overcapitalization, capital moves from X, to X,. Simultaneously, the rise in the demand for capital by X, producers causes a rise in the cost of capital, and, as a consequence, the sector which is the capital-intensive of the two will be hurt more in the sense that the relative price of the capital-intensive goods will rise, so that the demand and eventually the output of such goods will decline. Thus, the imposition of regulation in one sector generates two effects, one initial and one secondary. The initial impact is the overcapitalization effect and as capital moves from X, to X,, the output of X, tends to rise. The secondary effect may be called the ‘capital cost’ effect or simply the cost effect. This effect has the same repercussions for both sectors if k, = k,, or it benefits the first sector if k, > k,. Hence, if k, 2 k,, the overcapitalization and the cost effects run parallel to each other, and the implications for the two outputs are determinate.

One result that has elicited extensive response from several economists is the original A-J thesis that fair-rate of return regulation leads to a rise in the capital/labor ratio. This result has been subsequently found by Baumol and Klevorick (1974) to be incorrect. In terms of our general equilibrium model, we find that the regulatory constraint will lead to a rise in k, if k, 2 k,, the effect on the capital/labor ratio of the unregulated sector is predictable only if k, = k,, for then (dk,/du) from (26) is unambiguously positive. When k, = k,, the cost effect is zero and the overcapitalization effect is the only effect of the rate of return regulation. The following theorems are now immediate:

I’ In the absence of the rate of return constraint, the monopolist hires capital until the cost of capital

equals its marginal revenue product, i.e., r, = p,(l- l/e,)&,.


Theorem 2. If k, > k,, the rate of return regulation leads to a rise in the

capital/labor ratio of the regulated sector.

Theorem 3. If k, = k,, the regulation causes a fall in the capital/labor ratio of

the unregulated sector.

A slightly more definite result is available for the case of capital movement

from one sector to the other. Since

(dk,/du) =L,(d&/du) + k,(dl,/du)

the use of (25) and (28) enables us to obtain

(dWdu) = {-&W?i +p,D’,(&a,k?fi +-&k?fl’)}/Dp,

= - (dK,/du). (31)

Clearly with D < 0, (dK,/du) < 0 and (dk,/du) > 0. This leads to the following theorem:

Theorem 4. If k, > k,, regulation causes capital to moue from the unregulated to

the regulated sector.

A similar result, however, is not available for labor, because from (28) (dL,/du) is simply indeterminate.

5. Regulation and the distribution of income

In this section we will examine the implications of the fair rate of return regulation for the distribution of income between the wage earners and the owners of capital. Specifically, we will explore the consequences of a decline in u for the real wage rate, the real reward of capital and the real level of profit in the economy, with all variables expressed in terms of the price of the unregulated

sector. From (15) and (16)

w=a,(f2-k2f;) and r=azfi.

Differentiating these with respect to u and using (26) we obtain

(dw/du) = a,k,fJ’[&F,,(% +k2fi) -k,f;‘(k, -kI)pIDY]/DpI,

(32)

(dr/du) = -a2fl[L1%(G +k,f;) -k,f:‘(k,-k,)e,X,]/Dp,.

(33)

R. Batra, H. Beladi/European Journal of PoliticalEconomy 10 (1994) 625-638 635

Unfortunately the signs of (dw/du) and (dr/du) are indeterminate. This is because if k, > k, then D < 0 but the numerator of (32) and (33) is indeterminate. On the other hand if k, < k,, then the numerator is determinate but the denominator is not. Only if k, = k,, we can say without any further restriction that (dw/du) > 0 and (dr/du) < 0. For then D < 0 and the numerator of (32) is also negative, whereas the numerator of (33) is positive. this leads to the following theorem.

Theorem 5. Zf k, = k,, regulation leads to a rise in the real reward of capital and a decline in the real wage rate.

The reason for the indeterminacy of (dr/du) and (dw/du) and k, # k, is this. The fair rate of return regulation affects factor rewards in two ways. The initial effect stems from overcapitalization in the first sector and this, as argued before, tends to raise the real reward of capital. l2 At the same time, the real wage rate

declines, because relative to capital, labor is initially in a situation of excess supply. But then the output of the regulated sector raises when k, > k,, and the rise in the output of the first good tends to raise the demand for X1’s intensive factor relative to its unintensive factor, so that this latter effect tends to raise the wage rate and lower the reward of capital. Therefore, in the final equilibrium, capital may or may not benefit from the fair rate of return regulation. Similarly, labor may or may not be hurt.

A similar type of indeterminacy prevails when k, < k,. Also it is easy to see why the effects on w and r are predictable when k, = k,.

There still remains the question of how regulation affects total profits in the economy, which are given by

rr= m1 + 7r2 = rrr +X,/e,.

The introduction of regulation in X, must lower rrl even if K, rises. This is because regulation induces the monopolist to select input and output levels which are different from those consistent with the maximization of profits. On the contrary profits in the second sector may rise or decline depending on whether the output of X, rises or falls. If k, 2 k,, then regulation leads to a decline in the output of the unregulated sector. The following theorem is then immediate.

Theorem 6. Zf the unregulated sector is at least as capital-intensive as the regulated sector, then the fair rate of return regulation leads to a decline in monopoly profits in the economy.

I* This can also be confirmed from (33) by assuming that k, = k,, so that the cost effect is zero.

636 R. Batra, H. Beladi/European Journal of Political Economy 10 (1994) 625-638

6. Elasticity of substitution in the regulated sector

Until now we have derived our theorems by assuming that the regulated sector is no more capital-intensive relative to the unregulated sector. We will now show that if the elasticity of substitution in the regulated sector is small, some of these theorems are valid even if k, < k,. Let ai be the elasticity of substitution in the ith sector. Define wi as the ratio of the marginal product of labor and capital in the ith sector. Then, wi = (fi - kifi’)/f: so that, (dw,/dk,) = [(-hfi”>/fil> 0,

or,

(dw,/dki)( ki/‘wi) = - [ (LL”kz)/( L&i)] = l/a, > 0 (34)

where oi is the elasticity of substitution in the ith sector. In view of this relation between o-j and $‘, the first term of D from (24) can

be written as

-({[k,(l -ul)(k,-k,)f,ul]/(klf;)}+ [(k?-k1)*/~~])e,X,f;‘f~n,. Evidently as (or + 0, the first expression of this term also approaches zero and

in the limiting case of fixed proportions in the first sector, or is zero; this means that this term and hence D are negative. The following Lemma is now available.

Lemma 2. If the elasticity of substitution in the regulated sector is zero or sufficiently small, D is negative. I3

Let us now re-examine our results in the light of Lemma 2. First of all, all our theorems except Theorem 2 continues to hold when (T, = 0 or f;’ = -m, because if (or = 0, k, is fixed and regulation has no effect on it. In addition, we can derive a few more theorems.

Theorem 7. If u1 = 0, regulation causes capital and labor to mote from unregulated to the regulated sector.

The validity of this theorem can be seen clearly by factoring out f;’ from the numerator and denominator of (28) and (31) and then remembering that (TV = 0 implies that f;’ = - ~0.

Theorem 8. If u1 = 0, the change in real factor rewards is determined solely by the factor intensities. Specifically, regulation results in a rise in the real reward of

I3 The reader may be bothered by the fact that as rrl + 0, fl + --3o, so that in the limiting case, D becomes indeterminate. This, however, is not true, because f;’ can be factored out from the numerator

as well as the denominator of all the relevant equations except (25). Therefore fy will simply cancel out and we will consider the effects of the sufficiently small elasticity of substitution in any sector.

R. Batra, H. Beladi/European Journal of Political Economy 10 (1994) 625-638 637

capital and a fall in the real wage rate if the regulated sector is capital-intensiue relative to the unregulated sector, and conversely.

This theorem can be proved in the same way as Theorem 7. It can be easily seen that if f;’ = -00, then (dr/du) $0 and (dw/du) $0 if k, $ k,.

7. Concluding remarks

In the foregoing sections we have utilized the two-sector, two-factor model of production to analyze the general equilibrium implications of the fair-rate of return regulation in one sector for resource allocation as well as real factor rewards. Given that the economy can be divided into two main sectors, the regulated and the unregulated, we have derived the following results:

1. Unless the elasticity of substitution in the regulated sector is substantially large, the fair-rate of return regulation is likely to lead to a movement of capital from the unregulated to the regulated sector. This result is assured if the unregulated sector is at least as capital-intensive as the regulated sector. Furthermore, the output of the regulated sector rises at the expense of the other sector. 2. The same conditions would also lead to a rise in the capital/labor ratio of the regulated sector, although the effect on the capital/labor ratio in the other sector is indeterminate. 3. The effects of regulation on real factor rewards are in general indeterminate. However, if the capital/ labor ratios in the two-sector are the same, then regulation leads to a rise in the reward of capital and decline in the real wage rate. The same result is available if the elasticity of substitution in the regulated sector is substantially small and the regulated sector is relatively the capital-intensive sector. The effects on factor rewards are reversed if this substitution elasticity is small and the regulated sector is relatively the labor-intensive sector. 4. The conditions mentioned in conclusion 1 also lead to a decline in the monopoly profits in the economy. But an interesting result of our analysis is that the monopoly profits can rise under some circumstances.

References

Averch, H. and L.L. Johnson, 1962, Behavior of the firm under regulatory constraint, American Economic Riview 52, Dec., 1053-1069.

Baron, D.P. and R. De Bondt, 1979, Belgian price regulation and non-price competition, in: B.M.

Mitchell and P.R. Kleindorfer, eds., Regulated industries and public enterprise (Heath, Lexington,

MA). Batra, R.N., 1973, Studies in the pure theory of international trade (Macmillan, London).

Baumol, W.J. and A.K. Klevorick, 1970, Input choices and rate of return regulation: An overview of

the discussion, The Bell Journal of Economics and Management Sciences, Autumn, 162-190.

638 R. Batr, H. Beladi / European Journal of Political Economy 10 (1994) 625-638

Courville, L., 1974, Regulation and efficiency in the electric utility industry, The Bell Journal of

Economics and Management Sciences, Spring, 53-74.

Harberger, A.C., 1962, The incidence of corporation income tax, Journal of Political Economy 70,

215-240.

Kahn, A.E., 1968, The graduated fair return: Comment, American Economic Riview 58, March,

170-173.

Muller, J. and I. Vogelsang, 1979, Staatliche Regulierung (Nomos Verlag, Baden-Baden).

Peacock, A., ed., The regulation game (Basil Blackwell, Oxford).

Spann, R.M., 1974, Rate of return regulation and efficiency in production: An empirical test of

Averch-Johnson thesis, The Bell Journal of Economics and Management Sciences, Spring, 38-52.

Yu, E.S., 1981, Regional factor specificity, wage differential, and resource allocation, Regional Science

and Urban Economics 11, no. 1, 69-79.

a general equilibrium analysis of regulation and income distribution

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