EFFECTS OF THE SINGLE EUROPEAN MARKET ON WELFARE OF THE PARTICIPATING COUNTRIES (theoretical approach)

Transcription

1 EFFECTS OF THE SINGLE EUROEAN MARKET ON ELFARE OF THE ARTICIATING COUNTRIES theoretil pproh O ELHD&DU\:DUVDZ6FKRRORIFRRLFV:DUVDZRODG Agnieszk Rusinowsk, rsw Shool of Eonomis, rsw, olnd In this note we show how retion of united mrket uses welfre surplus even if the mrket stys imperfet ompetitive. e disuss simple prtil euilirium model with monopoly initilly supplying two ntionl mrkets susripts,. e differentite these mrkets y different hrteristis of their demnd funtions, though we ssume tht the demnd funtions in oth ountries re liner: with,,, >. e ssume tht > whih mens tht the demnd in mrket is generlly less elsti thn the one in mrket the line is steeper thn the. e ssume lso tht > whih mens tht onsumers in ountry re generlly redy to ept higher prie thn onsumers in ountry prohiition prie for ountry is higher thn for ountry. Tehnology of prodution is desried in the following wy. There is onstnt mrginl ost MC = > whih is the only ost to over. e ignore the onstnt ost of prodution e.g. investment ost euse it doesn t influene the optimistion result sunk ost. By ssumption > this is tehnil ondition neessry for positive untity of goods supplied to oth mrkets. Hene, the profit funtion of prie differentiting monopoly hs form of sum of revenues on oth mrkets sutrted osts of prodution: First order ondition llows us to lulte the profit mximising untities supplied to oth mrkets: w Ÿ w w Ÿ w

2 From the eutions nd nd the ssumptions onerning,,, we n t see whether the optiml untity supplied to mrket is igger thn the one sold in mrket. e hve in the numertors of oth frtions desriing the optiml untities: >, ut lso in the denomintors: >. As >, oth mrkets re supplied. The overll untity produed is eul to *: The pries in oth mrkets re eul to respetively: 5 6 As y ssumption i i =, nd re positive, oth pries re positive. Beuse we ssume tht >, * is igger thn *. The mximl profit is eul to: 7 * * * The mximl profit lulted in the eution 7 is surely positive s it is sum of two positive frtions. e define soil welfre of ountry s sum of monopoly profit nd onsumers surplus. e ssume tht the hnges in the nlysed mrkets don t influene other mrkets in oth ountries the prtil euilirium model, eteris prius ondition. In oth ountries the onsumer surpluses re eul to respetively: š

3 9 š e illustrte oth onsumers surpluses in grph.

4 Fig. : Consumer surplus in the segmented mrkets of ountries nd ountry * * ountry * * Soure: own onept. The ggregted onsumers surplus of oth ountries is sum of the onsumers surpluses in oth mrkets expressions in eutions nd 9:

5 5 š š Therefore, the overll welfre in oth ountries with ntionl mrket segmenttion is the sum of onsumer surpluses formul nd monopoly profit eution 7. š š In this setting the most importnt result of the retion of single mrket is liuidtion of rriers to ritrge etween oth ntionl mrkets. e show it s possiility to ggregte oth ntionl demnd funtions nd get n unified demnd funtion : Ÿ Ÿ Aggregting demnd llows us to settle unified prie in oth mrkets = :. e reverse the demnd funtion from eution to lulte mximl profit of the monopoly: Now we define profit of the monopoly s:

6 6 The eution summrised the most importnt result of the introdution of single mrket in our setting. A uniue euilirium prie is set in oth mrkets in oth nlysed ountries. For simpliity we ssume zero trnstion osts of supplying oth mrkets in se of segmented mrkets we mde this unspoken ssumption, too. Suh sitution my our in se of supplying mrkets of neighouring ountries. Before lulting the mximl profit we put the reversed demnd funtion from the eution into the profit funtion of the nlysed monopoly eution : 5 Then we use first order ondition for profit mximistion: w w nd lulte the profit mximising untity supplied to the ommon mrket nd the euilirium prie : 6, 7 Importntly, the unified prie set in oth mrkets lies etween differentited pries under segmented mrkets:.

7 7 Note lso tht it holds: nd. If we dditionlly ssume tht, then we get: 9. Eution 9 is neessry ondition for monopoly to supply oth ntionl mrkets fter introduing single mrket regultion nd s onseuene unified prie in oth mrkets. The mximl monopoly profit in the unified mrket is eul to: * [ * in formul is oviously positive, euse > >, whih mens tht > nd >. In numertor of the frtion oth prts of the sum exeed the sutrted prt. Now we n lulte new onsumer surplus in oth ountries under unified euilirium prie. e present this result lso grphilly in grph. e first lulte in grph. e use demnd funtion in ountry with the prie eul to :. The euilirium untity is igger thn :

8 . Fig. : Consumers surpluses in the single mrket + Soure: own onept. Before we lulte the soil welfre of oth ountries under the single mrket euilirium without prie differentition we hve to lulte the onsumer surplus s sum of the res A, B nd C in grph : A As y ssumption >, the re A in formul is positive.

9 9 C B [ e n prove tht sum of res B nd C lulted in the formul is positive. e trnsform the eution s follows: whih is eul to: In eution the denomintor is positive, s nd re the positive prmeters of the demnd funtions. All elements in the first set of rkets nd in the first multiplition in the

10 seond set of rkets re positive ssumed reltion etween prmeters, nd. The lst multiplition in the seond set of rkets is positive euse: + =, where is igger thn due to ssumption. It mens tht lso the lst prt of the multiplition in the numertor is positive nd the totl frtion in the formul is positive. Adding up the res lulted in formuls nd we get the onsumers surplus in oth ountries: 5 [ C B A [ [ [ [ The soil welfre of oth ountries under single mrket euilirium without prie differentition n e lulted s sum of the monopoly profit * formul nd the onsumers surplus A + B + C grph ; formul 5: 6 [ [ * C B A [ The lst step of our nlysis is omputtion of the levels of welfre under the initil segmenttion of oth ntionl mrkets lulted in the formul nd under the rules of the single mrket D in the formul 6. Let us strt with trnsforming the formul s follows:

11 6 [ [ [ e hve finlly: [ The soil welfre under the single mrket rules from the formul 6 is eul to: [ [ e n trnsform it s n expression eul to the initil soil welfre under prie differentition nd some dditionl positive element. e proeed s follows: nd hene, 7

12 The expression dded to the initil soil welfre is ertinly positive, euse is positive y ssumption out hrteristis of oth mrkets nd tht the sum in the seond set of rkets ontins only positive expressions. Also + in denomintor re the positive prmeters of the demnd funtions. In eution 7 we hve proved tht retion of united mrket results in welfre surplus even if oth mrkets re still supplied y the monopoly. e re wre tht our simple model doesn t tke into ount mny importnt spets of introduing the Single Europen Mrket. e put our ttention only to the influene of prie unifition on the interntionl level here represented y two eonomies onstituting united mrket. e ignored e.g. possile results of uniting mrkets for the ompetition it is possile tht more thn one produer will e supplying oth mrkets. e lso ssumed zero trnstion osts nd other trnstion osts. One reson is tht some of them re existent or negligile in oth situtions: with nd without single mrket. Another reson is tht in onseuene of uniting the mrkets some trnstion osts re eliminted e.g. dministrtive osts of supplying foreign mrket. The esiest wy to uild it into our model is to ssume deresing mrginl ost fter the mrket unifition. It would mke inrese in welfre even igger. e lso didn t lulte the eonomi onseuenes of uniting mrkets from the point of view of every ountry seprtely espeilly interesting n e results for the produer ountry. e hope tht our setting shows n interesting spet of the omplex phenomen of unifition of the Europen mrket. It n e lso helpful in nlysing more generl se of ntionl eonomies iming t unifition of their mrkets.