On dynamic standards for energy efficiency in differentiated duopoly. Peter Michaelis, Thomas Ziesemer

Transcription

1 On dynamic standards fr energy efficiency in differentiated duly Peter Michaelis, Thmas Ziesemer Beitrag Nr. 35, Nvember 015

2 On dynamic standards fr energy efficiency in differentiated duly Peter Michaelis* and Thmas Ziesemer** Abstract. We cnsider a tw-erids-mdel f differentiated duly. Firms rduce an energy cnsuming husehld durable differentiated by its energy efficiency. Cnsumers differ by the weight they aly t their future energy csts when deciding which rduct t buy. In line with the Jaanese T Runner Prgram, the regulatr intrduces a minimum efficiency standard in erid t= which is fixed accrding t the efficiency f the rduct sulied by the high efficiency firm in t=1. We shw that in t=1 bth firms suly lwer efficiency rducts and the high efficiency firm gains in market share and rfits. In t= these effects are reversed. Calculated ver bth erids, ttal energy cnsumtin des nt change. Althugh there is n eclgical effect, ttal welfare increases because rice cmetitin becmes tighter and the cst savings accruing t the cnsumers exceed the firms lsses in rfits. Keywrds: energy efficiency standards, rduct differentiatin, duly, regulatin JEL Classificatin: 3, Q48, Q58 * Crresnding authr: Peter Michaelis, University f Augsburg, Deartment f Ecnmics, Universitaetsstrasse 16, D Augsburg, Germany. eter.michaelis@wiwi.uni-augsburg.de. Phne: +49(0) Fax: +49(0) ** Thmas Ziesemer, University f Augsburg, Deartment f Ecnmics, Universitaetsstrasse 16, D Augsburg, Germany. thmas.ziesemer@wiwi.uni-augsburg.de.

3 1 1. Intrductin Cncerns abut envirnmental degradatin due t climate change and dwindling reserves f fssil fuels generated an nging debate abut efficient and effective ways t save energy. In additin t utting a rice tag n emissins frm burning fssil fuels and rmting renewable energies, enhancing energy end-use efficiency f durables is a majr licy gal in e.g. the Eurean Unin (EU 006, EU 009), several states in the USA (EPA 006) and Jaan (METI 010). Besides building cdes, efficiency standards cncerning the secific energy cnsumtin 1 f husehld durables are widely used. There are (at least) three reasns leading t the resumtin that the secific energy cnsumtin f such durables is t high frm the viewint f the scial timum (fr a mre thrughut discussin f this tic see, e.g., Schier and Hawk 1991): 1) Energy rices may be t lw cmared t the scial timum due t negative externalities. ) Cnsumers may be subject t infrmatin asymmetries cncerning the secific energy cnsumtin f the durables. 3) Cnsumers may behave myic when deciding which aliance t urchase. This might lead t unduly high discunt rates r even full neglect f the energy csts accruing ver the useful life f a durable. Of curse, the first tw reasns d nt necessarily require the intrductin f standards fr energy efficiency since external csts can be catured by an emissin tax and infrmatin asymmetries may be crrected with the hel f labeling bligatins. 3 Hwever, myic behavir by cnsumers might nt be adequately met with thse licies. Cnsequently, energy efficiency standards are an arriate instrument in the licy maker s tlbx fr enhancing energy end-use efficiency. An advancement f this licy arach are dynamic energy efficiency standards which incrrate the actual levels f the durables energy efficiency. Such dynamic standards tighten the mandatry efficiency level ver time based n a benchmarking arach by determining a feasible r the mst efficient aliance in each line f rduct er erid. Next the regulatr sets this efficiency level fr all rducers. 1 3 The term secific energy cnsumtin refers t the energy cnsumtin er unit f service. Fr examle, frm urchasing atterns fr a standard and an energy-efficient refrigeratr, Meier and Whittier have estimated the fllwing distributin f imlied cnsumer discunt rates: Rughly /5 f the cnsumers behaved as if they had real discunt rates abve 60 %, 1/5 between 35 and 60 %, and /5 less than 35 % (Meier and Whittier, 1983,. 957). Cncerning the imact f ec-labelling n cnsumer behaviur see, e.g., Sammer and Wüstenhagen (006).

4 An examle fr such dynamic standards is the Eurean Ecdesign Directive (EU 005, EU 009). Althugh it ffers the ssibility f vluntary agreements by industry it als enables mandatry energy efficiency targets accmanied by rduct labeling bligatins. These targets are revised in regular intervals and may therefre be subject t cntinuus tightening. Hwever, a mre rminent examle fr dynamic energy efficiency standards is the Jaanese T Runner Prgram which started in 1998 with 9 rducts and by 01 cvers 3 rducts (Osamu 01). The cre f the T Runner Prgram is that it bliges rducers t establish the currently highest efficiency level fr the resective durable by a certain target year. Althugh this licy arach is cnsidered t have erfrmed well, 4 a dynamic standard fr energy efficiency gives rise t strategic decisin making. Esecially a rducer f high efficiency durables can influence the future standard by his efficiency chice tday. This incentive might therefre affect envirnment and energy related licy gals cunterrductively, if the high efficiency rducer chses t understate his actual caabilities. Examles frm rducts regulated by the Jaanese T Runner Prgram like flurescent lighting and liquid crystalline shw that the efficiency targets were met much earlier than required by the rgram (Osamu 01). This bservatin surts the resumtin that dynamic standards fr energy efficiency may rmt rducers t refrain frm imlementing the actual tential fr efficiency imrvements. T the best f ur knwledge, the ecnmic incentives caused by dynamic standards fr energy efficiency as described abve have nt been cnsidered in the literature s far. Hwever, ur wrk is clsely related t the literature n the effects f a minimum quality standard (MQS) because energy efficiency can be interreted as a secial tye f quality. The resective literature traces back t the seminal aers f Leland (1979) and Shahir (1983) wh demnstrate that an MQS can increase welfare in the case f asymmetric infrmatin abut rduct quality when firms have n market wer. Rnnen (1991) was the first t analyze the welfare effects f an MQS using a standard set u f vertically differentiated duly. In his mdel, the demand side is given by a cntinuum f cnsumers wh are differentiated by the value that they lace n quality. The suly side is described by tw identical firms each ffering ne single quality, where csts nly cnsist f quality deendent fixed csts. Assuming quality cmetitin n the first and Bertrand cmetitin n the secnd stage, Rnnen shws that intrducing an arriately chsen MQS can increase welfare even in the absence f infrmatin asymmetries. The reasn is that the sitive effect n cnsumers surlus, which 4 See Nrdqvist (006) and Osamu (01). Mrever, the Jaanese T Runner Prgramme has been celebrated by litical scientists t be the mst advanced and shisticated arach t eclgical mdernisatin (Jänicke, 006,. 17).

5 3 is caused by limiting rduct differentiatin and intensifying rice cmetitin, dminates the negative effect n the firms rfits. Subsequently, the arach f Rnnen (1991) has been mdified and extended in several ways. Fr examle, Crames and Hllander (1995) intrduce unit csts that increase in quality and Valetti (000) cnsiders the case f Curnt instead f Bertrand cmetitin in the secnd stage f the game. Bth aers shw that Rnnen s timistic results cncerning the welfare effects f an MQS can nt always be sustained and deend n the set u f the mdel. Mrever, since the mid nineties, the issues dealt with in the literature n minimum quality standards have becme increasingly diversified. Fr examle, Häckner (1994), Ecchia and Lambertini (1997) as well as Nael and Oldehaver (011) analyze the imact f minimum quality standards n the incentives fr cllusin; Lehmann-Grube (1997) and Kuhn (006) assess the advantages and disadvantages t be the high r the lw quality firm, resectively; Maxwell (1998), Puller (006) and Garella (006) evaluate the effects n the incentive t innvate; Bm (1995) and Lutz and Baliamune-Lutz (003) cnsider the rle f minimum quality standards in internatinal trade mdels; Lee and Phuyal (013) study strategic entry deterrence by an incumbent under a MQS regime; and Cellini and Lamantia (013) analyze the jint effects f minimum quality standards and rice regulatins within a dynamic framewrk. In cntrast t the mre recent literature cited abve we are nt cncerned with advanced tics like, e.g., cllusin r the incentive t innvate. Instead, ur wrk is in the sirit f the earlier cntributins t the literature as we exlre the mre fundamental questin whether r nt a dynamic standard accrding t the Jaanese T Runner Prgram is an arriate instrument at all when the regulatr aims at increasing energy efficiency r ttal welfare. The remainder f ur aer is rganized as fllws. In Sectin, we intrduce the mdel and in Sectin 3, we calculate the unregulated equilibrium as ur reference case. In Sectin 4, we derive the regulated equilibrium and in Sectin 5, we cmare ur results cncerning energy cnsumtin and welfare btained fr the regulated case with thse fr the unregulated ne. Finally, in Sectin 6, we summarize ur main cnclusins and identify sme tics fr future research.. The Mdel We emly a mdified dynamic versin f the mdel n MQS in differentiated duly resented by Crames and Hllander (1995). The time hrizn cmrises tw erids t=1,, where the length f each erid equals the useful life f the durables under cnsideratin. There are tw firms j=h,l each rducing a single variant differentiated by the energy cn-

6 4 sumtin ε >0 which is calculated ver the durables cmlete useful life. 5 In line with the literature and withut lss in generality we assume ε >ε, 6 i.e., the rle f each firm as high- r lw-efficiency rducer, resectively, is cnsidered as given. The rice f variant j in erid t is dented by. The demand side is given by a unit mass f cnsumers indexed by i, each buying exactly ne unit er erid (this assumtin will be discussed in Sectin 6). When deciding which variant t buy, the cnsumers cmare the sum f urchase rice and erceived energy csts. The latter are given by i w, where w indicates the energy rice and α i, which is distributed unifrmly n the interval [a,b] with 0 a 1 and b 1a, is the individual weight assigned t energy csts by cnsumer i. Interreting the different values f i is straightfrward: A cnsumer with i 1 can be characterized as myic since he underestimates future energy csts, whereas a cnsumer with i 1 can be characterized as green since he accunts nt nly fr ttal energy csts but als fr envirnmental damage csts caused by energy cnsumtin. Slving the equatin w w fr α i yields the sitin f the indifferent cnsumer in erid t: ˆ [ ]/[w( )]. As mentined abve, ur arach is clsely related t the literature n minimum quality standards. Hwever, quality is a sitive characteristic, whereas energy cnsumtin is a negative ne. In rder t ensure cmarability f ur results with the literature n MQS, we transfrm energy cnsumtin ε int the sitive characteristic energy efficiency e using max the definitin e e 0. 7 With this transfrmatin, the sitin f the indifferent cnsumer can be re-written as: ˆ t. (1) w[e e ] Cnsequently, in erid t, all cnsumers with ˆ chse variant L, whereas all cnsumers with firm L and i t i t t i ˆ chse variant H. The resulting market shares in erid t are s ˆ a fr s a 1ˆ fr firm H. Mrever, frm e e max and ε > ε we btain t e < e, i.e., L is the lw efficiency sulier and H is the high efficiency sulier. Bth firms share the same technlgy, and rductin csts er unit are assumed t be indeendent f i t This way f mdelling energy cnsumtin imlies that all cnsumers aly the same rate f utilizatin (fr examle, fur washes er week in the case f a washing machine). The case ε =ε can be ruled ut a riri because Bertrand cmetitin wuld eliminate all rfits. The term e max is an arbitrarily chsen but sufficiently large cnstant which cancels ut in all f ur calculatins.

7 5 quantity but increasing in energy efficiency. 8 In line with several ther studies n MQS in differentiated duly (e.g., Mtta 1993, Ecchia and Lambertini 1997, Nael and Oldehaver 011) we use a quadratic unit cst functin c(e ) e with 0. In bth erids, firms cmete in tw stages: In stage ne, firms chse the level f energy efficieny e, 9 and in stage tw they simultaneusly chse rices. Finally, the regulatin cnstitutes the link between the tw erids: In erid t=1 there is n regulatin, whereas in erid t= a minimum standard cncerning energy efficiency dented by e is intrduced. In line with the Jaanese T Runner Prgram we assume that e is fixed accrding t the energy efficiency chsen by the high efficiency firm in erid t=1: e e H 1. Cnsequently, in erid t= the firms have t cmly with the restrictin e j e. The slutin cncet we emly is subgame erfect equilibrium, i.e., we slve the mdel backwards. 3. Unregulated Equilibrium 10 Withut regulatin, there is n link between the tw erids, and the equilibria in bth erids will be identical. Hence, it suffices t calculate the equilibrium fr a reresentative erid t. 11 In the rice game in the secnd stage, energy efficiency e is already fixed, and the firms rfits are given by s[ e ]. Inserting s ˆ t a as well as s a 1 ˆ t and accunting fr (1) leads t: wa(e e ) (, ) [ e ], w(e e ) (a) w(1 a)(e e ) (, ) [ e ]. w(e e )] (b) 8 9 Our assumtin f variable csts increasing in energy efficiency imlies that a higher degree f efficiency requires mre exensive inuts like, e.g., skilled labur and raw materials. An alternative way f mdelling wuld be t assume fixed csts increasing in energy efficiency; in this case the main burden f efficiency imrvements is caused by R&D activities (see Mtta 1993). Hwever, in ur mdel we fcus n imrvements in energy efficiency stemming frm incremental innvatins which usually entail increases in variable csts. In the reference case withut regulatin in Sectin 3 firms simultaneusly decide n efficiency as usual in mst mdels n MQS. In cntrast, under the dynamic standard in Sectin 4 firm H attains the rle f a leader in the efficiency game. 10 Fr the unregulated (i.e., static) case, aart frm differences in ntatin and the use f a quadratic instead f a general cst functin, the frmal structure f ur mdel is almst cmletely identical with Crames and Hllander (1995,.73-75). 11 In rincile, due t the static nature f the unregulated case, the time index t culd be suressed in this Sectin. Hwever, since we need sme f the fllwing equatins als in the dynamic analysis in Sectin 4, we refrain frm suressing t.

8 6 Frm the first rder cnditins 0 we btain the resective reactin functins / which can be slved fr the timal rices deending n e : (e (e,e,e 1 ) [w(1 a)(e e ) (e e )] 3, (3a) 1 ) [w( a)(e e ) (e e )] 3. (3b) Inserting (3a) and (3b) int (a) and (b) yields the reduced rfit functins t be used in the efficiency game in the first stage: (e e )[w(1 a) (e e )] (e,e), (4a) 9w (e e )[w( a) (e e )] (e,e). (4b) 9w The first rder cnditins e,e )/ e 0 lead t the fllwing reactin functins: 1 ( w(a 1) e e (e), (5a) 3 w( a) e e (e ). (5b) 3 Slving these reactin functins results in the timal levels f the durables energy efficiency: 13 (w /8) (4a 1) and (w /8) (4a 5). 14 The imlicatins f this result are e e bvius: Everything else equal the energy efficiency is the higher, 1) the higher the energy rice w is, ) the lwer the cst arameter γ is, and 3) the higher the average weight that cnsumers assign t energy csts is (given by a+1/). Hwever, since negative values fr energy efficiency are ruled ut, 15 e and e reresent the equilibrium nly under the assumtin a 0. 5 which guarantees an interir slutin. In cntrast, fr a 0. 5 ur mdel leads t a crner slutin where firm L always chses ~ e 0 and firm H chses ~ e (w /3) ( a ) accrding t (5b). 1 Fr bth firms there exists a secnd slutin t ( e,e ) / e 0 which, hwever, is irrelevant because it leads t zer rfits. 13 In the fllwing, we indicate the unregulated equilibrium by the suerscrit and the regulated equilibrium in Sectin 4 by the suerscrit *. 14 Inserting e and e int the secnd derivatives ( e,e ) / e rfs that the secnd rder cnditins are satisfied. Mrever, in the Aendix we shw that leafrgging can be ruled ut. 15 Due t the quadratic unit cst functin, cst wuld be decreasing in energy efficiency fr e <0 which makes n sense. Fr a similar argument relating t negative quality levels and quadratic unit cst functins see Cremer and Thisse (1994,.616).

9 7 In the fllwing we cncentrate n the mre interesting case f an interir slutin, with a 0.5. Inserting e int (3a) and (3b) yields the crresnding rices in equilibrium: (w / 64) [5 8a(a 1)] and (w / 64) [49 8a(a 5)]. In the next ste, inserting e and int (1) yields the sitin f the indifferent cnsumer, a 0. 5, and the accmanying market shares are s s 1/. Finally, inserting e int (4a) and (4b) yields the rfits in equilibrium: 3. w / 16 Cncerning the latter result, it might seem aradxical that increasing energy rices lead t increasing rfits f firms that rduce energy cnsuming durables. Hwever, within the framewrk f ur mdel, the ecnmic exlanatin is straight frward: A higher energy rice accelerates the imrtance f differences in energy efficiency frm the viewint f cnsumers. This effect relaxes rice cmetitin between the firms and increases rfits (see, e.g., Shaked and Suttn, 198). 16 ˆ t 4. Regulated Equilibrium In the fllwing, we slve the mdel backwards starting with erid t=. In the rice game in the secnd stage, energy efficiencies e j are already given. Cnsequently there is n difference cmared t the unregulated case analyzed abve and we can emly the reduced rfit functins (4a) and (4b) fr t=: (eh el )[w(1 a) (eh el )] L(eL,eH ), (6a) 9w (eh el )[w( a) (eh el )] H(eL,eH ). (6b) 9w Hwever, in the efficiency game in stage ne, the firms have t cmly with the standard e j e e L. Since the latter is a binding restrictin fr the lw efficiency rducer, we btain e e. Cnsequently, intrducing the dynamic standard is equivalent t granting firm H quality leadershi. Inserting e e int firm H s reactin functin (5b) fr t= yields: L w( a) e eh. (7) 3 Hence, firm H s timal chice f energy efficiency in erid t= slely deends n the efficiency chsen in t=1. Next, frm inserting e e as well as (7) int the reduced rfit L functins (6a) and (6b) we btain equilibrium rfits in erid t= as a functin f firm H s decisin in t=1: 16 Of curse, the abve result cncerning rfits als deends n the assumtin f inelastic demand, i.e., each cnsumer buys exactly ne unit er erid irresective f the energy rices given. See Sectin 6 fr a discussin f this assumtin.

10 8 [w( a) e ][w(a 5) 4e ] L (e ), (8a) 43w 4[w( a) e ] H (e ). (8b) 43w 3 It is easy t shw that e )/ e 0. Cnsequently, firm H faces a trade-ff: The higher H( the efficiency chsen in erid t=1, the lwer will be the rfit in t=. The ecnmic reasn is straightfrward: Increasing e leads t a mre severe efficiency standard in t= thereby lwering the sce fr rduct differentiatin and intensifying rice cmetitin. We nw turn t the firms decisins in erid t=1. The reduced rfit functins fr this erid are given by (4a) and (4b) fr t=1: (e e)[w(1 a) (e e)] (e,e ), (9a) 9w (e e)[w( a) (e e)] (e,e ). (9b) 9w With their decisin in erid t=1, bth firms aim at maximizing ttal rfits which are given by j j1 j ( e,e ) : (e,e ) (e ). Discunting is neglected fr simlicity. The first rder cnditins e,e )/ e 0 lead t the fllwing reactin functins: j ( j1 w(a 1) e el 1(e ), (10a) 3 w( a) 3e eh 1(e). (10b) 5 Fr the lw efficiency firm we btain the same reactin functin as in the unregulated case analyzed in Sectin 3 because firm L is nt able t influence the secnd erid utcme via the chice f e (see als equatin 8a). In cntrast, due t the effect f e n the standard fixed in erid t=, the reactin functin f the high efficiency firm is steeer cmared t the unregulated case. Slving the reactin functins yields the durables energy efficiency in the regulated equilibrium in t=1 fr the case f an interir slutin with a 0.5: e (w / 4) (a 1) and e (w / 4 ) (a 1 ). 17 In cntrast, fr a<0.5 we btain a crner slutin with ~ e 0 and ~ e (w / 5) ( a ). 17 Inserting e and e int the secnd derivatives j ( e,e ) / e j1 rfs that the secnd rder cnditins are satisfied. Mrever, in the Aendix we shw that leafrgging can be ruled ut fr bth firms and bth erids if leafrgging is assciated with sitive but arbitrarily small csts (which seems t be retty reasnable).

11 9 In the fllwing, we again cncentrate n the mre interesting case f an interir slutin and assume a>0.5. Frm inserting e j1 int (3a) and (3b) fr t=1 we btain the equilibrium rices (w / 48) [11 1a(a 1)] and (w / 48) [19 1a(a 1 )]. Mrever, inserting 1 j e and j1 int (1) yields the sitin f the indifferent cnsumer, (1/ 3) a, which leads t market shares f s 1/ 3 und s / 3. Finally, frm inserting e j1 int [9a] and [9b] we btain the accmanying rfits ˆ 1 L 1 / 18 and w / 9 w H 1. We nw turn t erid t=. Inserting e int e L eh 1 as well as int (7) yields the energy e L efficiency f the durables sulied: (w / 4) (a 1) and (w / 4) (a 3 ). Mrever, fllwing ur arach fr the first erid we btain equilibrium rices j f (w / 48) [19 1a(a 1)] and (w / 48) [35 1a(a 3 )], the sitin f the L indifferent cnsumer at (/ 3) a, market shares f / 3 and 1/ 3, and rfits f ˆ L w / 9 and / Cmarisn f Results H e H H w. Table 1 cmares the results f Sectin 4 with thse calculated fr the unregulated equilibrium in Sectin 3. As can easily be verified, in erid t=1 energy efficiency and rices f bth rduct variants are lwer cmared t the unregulated case. Mrever, firm H gains in market share and rfits, whereas firm L lses. In erid t=, these results are reversed: energy efficiency and rices f bth rduct variants are higher cmared t the unregulated case, firm L gains and firm H lses. The ecnmic reasns leading t the changes in energy efficiency described abve are bvius: In the first erid, firm H reduces energy efficiency because f the detrimental effect n its secnd erid rfits caused by the standard rvked due t e e H 1. This decrease in e induces firm L als t reduce energy efficiency since bth levels f efficiency are strategic cmlements. In the secnd erid, firm L is frced t increase energy efficiency e L s L s H due t the standard alied, and this in turn induces firm H als t increase e H. The changes in market shares and rfits caused by the standard can als readily be exlained: In erid t=1 firm H gains due t its leadershi. In erid t= firm L gains because setting a standard has the same effect as granting firm L the ability t cmmit t a higher level f efficiency (see als Crames and Hllander, 1995,. 76).

12 10 Unregulated Equilibrium Regulated Equilibrium Regulated Equilibrium Perids t=1, Perid t=1 Perid t= Energy efficiency e e w(4a 1) 8 e w(a 1) e 4 e L w(a 1) e 4 L e w(4a 5) 8 e w(a 1) e 4 e H w(a 3) e 4 H w [5 8a(a 1)] 64 w [11 1a(a 1)] 48 L w [19 1a(a 1)] 48 L Prices w (49 8a(a 5)] 64 w (19 1a(a 1)] 48 H w (35 1a(a 3)] 48 H Market shares s s 1/ s 1/ 3 s s L / 3 s L s 1/ s / 3 s s H 1/ 3 s L Prfits π w 16 3 w 18 L w 9 L w 16 3 w 9 H w 18 H Table 1: Cmarisn f results (interir slutin).

13 11 In the fllwing, we are interested in the ttal effects calculated ver bth erids. Let us dente the average degree f the durables energy efficiency weighted by erids and market shares as ê, i.e.: 1 ê (s e s e ). (11) t1 Alying the results summarized in Table 1, we btain (w / 4) (a 1) fr the unregulated case and the same fr the regulated case: ê ê (w / 4) (a 1) ê. Due t the linear relatinshi between energy efficiency and energy cnsumtin (see Sectin ), this imlies that calculated ver bth erids ttal energy cnsumtin caused by the durables sld in the market des nt change. Cnsequently, within the framewrk f ur mdel, a dynamic standard fr energy efficiency accrding t the Jaanese T Runner Prgram has n eclgical effect at all. Mrever, aggregated ver bth erids, firm L as well as firm H are wrse ff under the standard because the degree f rduct differentiatin decreases in each erid and rice cmetitin becmes tighter. 18 Prfits aggregated ver bth erids are in the unregulated case and L H w / 8 3 L H 5w / 18 j in the regulated case, resectively. Hence, frm an verall ersective f welfare, the ttal lsses in firms rfits are j j. ( ) 7w / 36 Gru G 1 Gru G Gru G 3 Gru G 4 Psitin 0.3 a 0.3 a i 0.5 a 0.5 a i 0.6 a 0.6 a i i Unregulated (t=1,) Variant L Variant L Variant H Variant H Regulated (t=1) Variant L Variant H Variant H Variant H Regulated (t=) Variant L Variant L Variant L Variant H Cst Difference ΔC k ( 13 8a)w 3 ( 71 7a)w 96 ( 7a 1)w 96 ( 8a 5)w 3 Table : Cnsumers buying decisins. Next, we cnsider hw cnsumers are affected. As shwn in Table, cnsumers can be divided int fur different grus G k (k=1:4) accrding t their buying decisin. The interre- 18 Frm the results in Table 1 it is easy t calculate that the degree f rduct differentiatin amunts t e e 3w / 4 in the unregulated case and t e e w / in the regulated case.

14 1 tatin is straightfrward: Fr examle, cnsumers belnging t G, wh are characterised by the sitin 0.3 a i 0.5 a, always chse variant L in the unregulated case whereas in the regulated case they chse variant H in erid t=1 and variant L in erid t=. Nw, let us dente the actual mnetary csts caused by the urchase and the use f a durable f variant j in erid t by w. 19 Frm this we can calculate ttal cst summed u ver bth erids fr a reresentative cnsumer f each gru dented by cncerning a cnsumer in gru G we btain fr the unregulated case chses variant L in bth erids, whereas the regulated case imlies C C k. Fr examle, since she L C since she chses variant H in erid t=1 and variant L in t=. In the last ste, we calculate the difference in cst between the regulated and the unregulated regime: C k C k C k. The results f this calculatin are shwn in the last rw f Table. A sitive difference C k 0 indicates that the cnsumer under cnsideratin is better ff in the regulated case because his actual csts are smaller cmared t the unregulated case. A negative difference C k 0 indicates the site. As shwn in the last rw f Table, cnsumers belnging t G 1 and G, that aly a weight belw average t energy csts when deciding which durable t buy, will win r lse in terms f their actual cst burden deending n the magnitude f the arameter a. In cntrast, cnsumers belnging t G 3 and G 4 that aly a weight abve average will always be better f in the regulated case. 0 Finally, we cnsider the net effect n welfare aggregated ver bth erids. Since ttal energy cnsumtin des nt change, it suffices t cmare the firms ttal changes in rfits,, with cnsumers ttal changes in actual csts, dented by C. The latter can be btained by weighting Ck with the different grus shares n the ttal unit mass f cnsumers: (1/ 3) (C C ) (1/ 6) (C C ). Alying the results in the last rw f Table leads t C C 89w / 88. Cmaring with 7w / 36 reveals C such that cnsumers cst savings exceed the firms lsses in rfits and ttal welfare increases. Cnsequently, dynamic standards fr energy efficiency accrding t the Jaanese T Runner Prgram d nt necessarily cntribute t energy savings but nevertheless they can be viewed as a ssible measure t increase ttal welfare. 19 Nte that frm an verall welfare ersective, actual accruing energy csts wε are relevant and nt energy csts individually erceived at the stage f buying decisin, α i wε. 0 Remember that we have assumed a>0.5 in rder t guarantee an interir slutin.

15 13 6. Summary and Cnclusins We analyzed a simle mdel f dynamic energy efficiency standards in a differentiated duly with tw firms rducing a durable which varies in its level f energy efficiency. Demand is assumed t be inelastic and cnsumers weigh energy csts individually in the sense that myic cnsumers underestimate future energy csts and green cnsumers additinally accunt fr envirnmental damages caused by energy cnsumtin. We fund that cmared t the unregulated scenari the high efficiency firm has an incentive t set a lwer level f energy efficiency in the first erid in rder t relax the standard t be intrduced in the secnd erid. This induces its cmetitr als t reduce the energy efficiency f the durable because bth levels f efficiency are strategic cmlements. In the secnd erid, the standard alied cnstitutes a binding restrictin fr the lw efficiency firm and the energy efficiency f the durables sulied by bth firms increases cmared t the scenari withut regulatin. Hwever, in ttal, energy cnsumtin calculated ver bth erids des nt change. Cnsequently, under the assumtins f ur mdel, dynamic standards fr energy efficiency have n eclgical effect at all. Cncerning the ecnmic effects f such standards we fund that the degree f rduct differentiatin decreases in bth erids and rice cmetitin becmes tighter. As a cnsequence, the firms rfits calculated ver bth erids are als decreasing. Hwever, cnsumers are better f in terms f their cst burden (urchase rice lus actual energy csts) and ttal welfare increases because the cnsumers cst savings exceed the firms lsses in rfit. Hence, within the framewrk f ur mdel, dynamic energy efficiency standards d nt cntribute t energy savings but they weaken the negative imacts f imerfect cmetitin n cnsumers surlus and welfare. Of curse, a ssible shrtcming f ur analysis is the assumtin f inelastic demand, i.e., each cnsumer buys exactly ne unit er erid irresective f the urchase rice and energy csts given. T what extend this assumtin is realistic deends n the secific durable under cnsideratin. Cncerning durables that are essential in the sense that they are abslutely necessary fr a vast majrity f cnsumers (like, e.g., refrigeratrs r heating aliances), the assumtin f inelastic demand seems t be justifiable n the whle. In cntrast, fr nn-essential durables (like, e.g., freezer chests r mbile air cnditinings) it wuld be mre realistic t assume an elastic demand such that increasing csts cause cnsumers with a cmaratively high weight factr i t refrain frm buying at all. In this case, it is nt guaranteed that cnsumers surlus will increase due t the regulatin f energy efficiency. Cnsequently, it cannt be ruled ut that ttal welfare will decrease (althugh everything else equal

16 14 a smaller number f durables sld in the market as well imlies less energy cnsumtin and thereby decreasing envirnmental csts). Hwever, the analytical cmlicatins assciated with incrrating the ssibility f an uncvered market wuld g well beynd the sce f ur aer and are therefre left t future research.

17 15 Aendix We start with leafrgging in the unregulated case calculated in Sectin 3. In rder t rule ut leafrgging by firm H we have t shw, that chsing an efficiency level with e <e des nt ay fr firm H if firm L adheres t its initial sitin (w /8) (4a 1). Fr e <e the reduced rfit functin f firm H is given by: (e e )[w(1 a) (e e )] (e,e ). (A.1) 9w Inserting (w /8) (4a 1) int (A.1) yields the leafrgging-rfits f firm H slely as a e functin f its decisin n e : [w(4a 1) 8e ][w(4a 7) 8e ] ˆ (e ). (A.) 4608w Frm the first rder cnditin ˆ (e )/ e 0 we btain the timal leafrgging-strategy f firm H in the unregulated case: (w / 8) (4a 3). Inserting ê int (A.) yields the accmanying leafrgging-rfit ê ˆ e w / 144. Cmaring this with the equilibrium-rfit calculated in Sectin 3, 3w / 16, reveals ˆ. Cnsequently, leafrgging des nt ay fr firm H. 1 Due t symmetry, calculating alng the same lines fr leafrgging by firm L yields ut. ˆ w /144 3w / 16. Hence, leafrgging by firm L can als be ruled We nw turn t the regulated case calculated in Sectin 4 where leafrgging has t be cnsidered fr bth erids exlicitly. With leafrgging by firm H in the first erid we btain the reduced rfit functin e,e ) by inserting the time index t=1 int (A.1). In the next ste ( we relace e by firm L s initial sitin (w / 4) (a 1) which leads t: e [w(a 1) 4e ][w(a 3) 4e] ˆ H 1(e ). (A.3) 576w ˆ The first rder cnditin (e )/ e 0 yields the timal leafrgging-strategy f firm H ê in erid t=1: (w /1) (6a 5). Inserting int (A.3) leads t the accmanying leafrgging-rfit ˆ 9 H 1 w / 486 w /. Hence, leafrgging by firm H in erid t=1 can be ruled ut. Mrever, leafrgging by H in erid t= can als be ruled ut because the standard e j e is already binding fr firm L such that eh el is nt ssible. 1 The case f a crner slutin fr a<3/4 des nt need t be analyzed in detail since it is bvius that if leafrgging des nt ay fr firm H in the case f an interir slutin it wuld ut firm H in an wrse sitin in case f a crner slutin. This is due t firm H s lss in flexibility in a crner slutin.the same argument hlds fr leafrgging leading t crner slutins in the regulated case t be cnsidered belw.

18 16 Next, we cnsider leafrgging by firm L. In erid t=1, firm L s reduced rfit functin fr the case e >e is given by: (e e )[w( a) (e e)] (e,e ). (A.4) 9w Relacing e by firm H s initial sitin (w / 4) (a 1) yields the leafrgging-rfits f firm L deending n its decisin n e : e [4e w(a 1)][w(7 a) 4e] ˆ L 1(e). (A.5) 576w Frm the first rder cnditin (e )/ e 0 we btain the timal leafrgging-strategy ê ˆ f firm L in erid t=1 with (w / 4) (a 3). Inserting this result int (A.5) yields the rfit ˆ w / 486. Cnsequently, in erid t=1 firm L wuld earn the same rfit with leafrgging as well as withut it. Hwever, this calculatin des nt accunt fr ssible csts assciated with leafrgging by firm L: If a firm hithert knwn as a chea lw efficiency rducer tries t enetrate the high efficiency segment f the market, it will mst likely be frced t change its marketing strategies and distributin channels. Hence, it seems reasnable t assume that leafrgging by Firm L will lead t additinal fixed csts. Althugh we are nt able t quantify these csts, frm it L 1 ˆ is bvius that even assuming an arbitrarily small amunt f additinal csts suffices t rule leafrgging by firm L in erid t=1. Finally, we cnsider leafrgging by firm L in erid t=. Fr this case, the reduced rfit functin e,e ) can easily be btained by changing the time index in (A.4) frm t=1 t L( L H t=. Next, relacing e H by (w / 4) (a 3) yields: e H [4eL w(a 3)][w(5 a) 4eL ] ˆ L (el ). (A.6) 576w The first rder cnditin ˆ L(eL )/ el 0 yields ê L (w /1) (6a 11). Inserting ê L int (A.6) leads t ˆ w / 486 w / 9. Cnsequently, leafrgging by firm L in L erid t= can als be ruled ut. L

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