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Content

Introduction

1. Theoretical aspects of the equalizing regional policy

2. The position of the equalizing regional policy in regions

3. The analysis of efficiency of the equalizing regional policy

Conclusion

References

Appendix



Introduction

The new economic geography (NEG) seeks to answer the questions of how economic activity is distributed across geographical space, taking into account imperfect competition and increasing returns to scale. (Krugman, 1991; Fujita, Krugman, Venables, 1999; Combes, Mayer, Thisse, 2008, ch. 2).

The main difference between the NEG and classical economic geography is that it includes economic analysis explaining the impact of mobility of production factors, agglomeration on the market equilibrium. Nowadays one of scientific interests in the NEG is the problem of unequal resource distribution between regions. To solve this problem, Funds have been allocated for solution of this problem; there are specialized structural funds in the EU which conducting equalizing regional policy. As for the Russian practice, there is no special allocation for equalizing policy, it exists as a regional policy direction and is necessary for the social and economic development of the country.

However, equalizing regional policy may be not efficient: with the income congestion among regions and economic growth of the state there is an increase of inequal income distribution within the regions, which negatively affects the economy of the region and even the country. So the relevance of the work is that it addresses the question of need for equalization policies and the allocation of subsidies for its conduct.

Also the relevance of the work is confirmed by the big interest of scientists of the NEG. There are main works: Puga D. in the work "European regional policies in light of recent location theories". Martin P. in the article "Are European regional policies delivering? " explore the activities of European politicians to conduct an equalizing regional policy, considering transfers as instruments for carrying it out. Quah in the paper "Regional Cohesion from Local Isolated Actions: Historical Outcomes." highlights the topic of the trade-off between regional equality and aggregate economic growth. In our work we rely on the model of Pflьger M., Sьdekum J. "Integration, Agglomeration and Welfare", which, in addition to studying the problem of inequality in income distribution in the EU, pay attention to the specifics of regional policy taking into account the agglomeration.

The present work is the theoretical continuation of our previous research in the area of equal regional policy. In the course work, there was calculated the Gini index for the subjects of the Russian Federation as the existence of its relationship between the level of investments in the region was checked. Eventually it was concluded that inequality exists in Russia, but at the same time, the means for equalizing policy are not allocated in the same way as in the EU. We have chosen the Pflueger and Suedekum's model "Integration, Agglomeration and Welfare" as the main model for the final qualification work because they study the problem of equalizing policy taking into account external factors and point out the possible effective directions for this kind of policy. But this model doesn't explore the market situation in condition of prices changes because price index is determined by the CES-function. But we suppose that prices also have effect on market situation (on agglomeration (at least on the decision of workers to migrate)). So we decide to find out what effective directions of equalizing regional policy exist in case of different prices taking price index as translog-function. Therefore, the novelty of the work is to analyze the effectiveness of the regional equalization policy when taking into account the mobility of prices.

The aim of the work is to check the existence of effective directions for the regional equalization policy, which can be achieved by solution of the following objectives: regional policy efficiency equalizing

· Analysis of the Pflueger and Suedekum model "Integration, Agglomeration and Welfare";

· Solution of the Pflueger and Suedekum model for the case with translog-function;

· Analysis of the market equilibrium and welfare of the society for both cases (with constant prices (CES-function of price index formula) and changeable prices (translog-function ) and therefore, the definition of effective directions for the equalizing regional policy conduction.



1. Theoretical aspects of the equalizing regional policy

The process of convergence in income in Europe is estimated by scientists as a long process between the European regions. Sala-i-Martin concludes that for a long period (1950-1990), the average growth rates of the regions had a negative correlation with the initial income. The rate of convergence was 2%, which averaged a decrease in the income distribution inequality by 2%, therefore it took 30 years to conduct an equalizing regional policy and move away from the initial state by 50%. (Sala-i-Martin, 1996)

However, Neven and Gouyettesuggest that during the later period, beginning with the 1980s, there was a significant European integration, which was accompanied by a divergence process between the northern and southern regions in the EU. Moreover, they suggest that even long-term convergence at the regional level can mask the process of intraregional differentiation (Neven and Gouyette, 1995), which Stephan, Happich, Andreas (2005) also noticed in their works.

Among the forces that must be taken into account in the equalizing regional policy, a special place is given to the agglomeration, which promotes a divergence in income between urban and peripheral areas, attracting high-income economic activity to urban areas. Therefore, the implementation of regional policy in the EU should include at least two areas: by region and within countries.

But scientists tell about inefficiency of conducting the equalizing regional policy by pointing out the problem of significant inconsistency in the indicator of convergence in income for the regions within the EU and the regions within it. For example, Pflueger and Suedekum show that since the beginning of the conducting equalizing regional policy in the EU, the inequality of income distribution among regions has decreased by 25%, while regional inequality within states has increased by 10% (Pflueger, Suedekum, 2004). It is reflected on the graph below (Fig.1 1) (Puga, 2001) where you can see the divergence in dynamic of theGini index for country as a whole and its regions.



Fig. 1 Dynamics of income inequality distribution between regions of EU and within regions(Puga, 2001)

According to Krugman (1991), migration is one of the sources of agglomeration, which is reflected by low level of labor migration. In his opinion, the reasons for such a low rate are cultural and language barriers, as well as the presence of ties and influence in the region of residence. (Krugman, 1991)Also, according to Pflueger and Suedekum, agglomeration is induced by a drop in trade costs due to a supply-demand relationship. (Pflueger, Suedekum, 2004)

So we need to remember that police makers who are responsible for conducting equalizing regional policy should take into account specific features of two situations (when agglomeration exists and model without it).

Agglomeration without migration is characterized by the following. In the absence of interregional migration firms concentrating in the region are forced to attract workers from the agricultural sector in the same region, which increases local wages. Higher wage costs, as a rule, make the clustering of firms less reasonable. Nevertheless, the agglomeration may reach the equilibrium if there is a merger of firms, which increases the wages and reduce the cost of intermediate goods due to this synergy. The equilibrium in this case is sustainable because if the whole industry is concentrated in one region the firm considers it reasonable to move to a non-industrialized region (less developed region) and to combine imported intermediate products with cheap labor. Symmetry between regions is restored when there is a relocation of other firms, which is associated with more attractive conditions in the peripheral region. Consequently, this equilibrium will be symmetric and stable. It should be noted that at high costs, the location of firms is associated with the availability of final demand in the region, so firms are distributed among regions. At average cost levels, clusters of firms are formed. At low levels of trade costs, the firm is located where resources are cheaper, so they are also distributed by region. In this case, this type of agglomeration leads to differentiation of wages. (Puga, 2001)

In case of agglomeration where the average or high level of migration (for example, the US or Russian regions), the location of the firm is determined by the level of costs and demand that induce the agglomeration of industry. Also, the appearance of agglomeration of this type is promoted by a large share of producers in consumer spending, since there is an increase in the index of producers' prices in real wages, which allows firms located in regions with a larger share of industry to involve workers from other industries and regions of lower labor costs. Clustering of firms takes place in a region that has more favorable conditions economically, geographically and politically. The differentiation of regions into central and peripherial regions occurs under the violation of agglomeration stability because of the reduction of trade costs. (Puga, 2001)

The equilibrium market is characterized by high agglomeration for high trade costs and low agglomeration at low trade costs. Also, market equilibrium provides a socially optimal degree of agglomeration at any level of trade costs. An important consequence of this result is that, for efficiency, regional policy should facilitate the dispersion of firms only for high trade costs, but agglomeration for low trade costs. It should also be noted that the market equilibrium is characterized by a high level of agglomeration for a low level of trade freedom and low agglomeration for a high level. So there are two levels of trade freedom where political measures based on efficiency considerations. (Pflueger and Suedekum, 2004)

Reduction of transaction costs between the two regions leads to the incentive for firms to move to richer regions, where they benefit from economies of scale via selling their goods in a poor region by reducing interregional transaction costs. Thus, this type of regional policy has result in agglomeration that increases the rate of long-term growth and reduces income inequality, as the profit of the monopolistic market decreases. The policy of financing infrastructure to reduce transaction costs for goods between regions leads to greater agglomeration, but also to higher growth rates at the state level. Therefore, a dilemma arises, since policies that reduce agglomeration (transfers, financing of transport infrastructure within poor regions) can also reduce efficiency and economic growth. (Martin, 1999)

A group of the NEG scientists (Stephan A., Happich M., Geppert K.) name the following directions of state influence on regional growth: macroeconomic conditions; stateinstitutions (education, infrastructure, political institutions); national characteristics, culture and other informal institutions; the impact of the European structural policy on the country characteristic for the country. National events, state institutions, infrastructure, policies and macroeconomic conditions determine the path of growth for countries and their regions, even if there are significant regional differences in this. The main reason for this change is the fact that urban areas retain or even improve their position among countries in terms of income. (Stephan, Happich, Geppert, 2008)

The effect of transfers as tool of equalizing regional policy is considered by Martin P. in his model (Fig.2) Transfers from rich regions to poor are shown by the shift of the RR curve. The induced effect weakens the agglomeration, as increasing incomes in poor regions stimulate the movement of firms to a region that has a relatively higher purchasing power. (Martin, 1999)



Fig. 2 Transfers as instrument of conducting equalizing regional policy (Martin, 1999)

Quah's results suggest that there is a trade-off between regional equality and aggregate economic growth. According to his results, two countries, Portugal and Spain, stand out among the Cohesion group of countries (Greece, Ireland, Portugal and Spain), which have achieved high growth rates and have a relative equalization in income per capita with the rest of Europe. But they also have an inequality in the distribution of income within their borders. As for Greece and Ireland, they are characterized by another situation: with a relatively equal distribution of income within the country, there is income divergence with other EU countries and a low rate of economic growth. (Quah, 1996)

Therefore, policy makers should conduct their policies depending on the choice of the priority goal: to get growth of the national economy they should reduce inequalities between different regions within the macro-region and to let regions to get economic growth and therefore achieve the spatial justice they need to increase the equal across distribution across subjects within the borders of one region.

Thus, in the conduct of regional policy, a compromise between fairness and efficiency is inevitable and should be obtained. This issue was taken into account in times of the European expansion to the east, as the Eastern European countries have average incomes per capita, which are much lower than the income of the Cohesion countries (Greece, Ireland, Spain, Portugal). In the case of the Cohesion countries (Greece, Ireland, Spain and Portugal), as well as for the countries of Eastern Europe, the policy is almost powerless to achieve the highest rates of economic growth when conducting policies for regional disparities reduction.

2. The position of the equalizing regional policy in regions

Firstly, we should notice the difference in approach of conducting equalizing regional policy as result of difference in income distribution across these regions. The USA has a more equal distribution in income between regions, while in the EC almost a quarter of citizens live in regions eligible for assistance from the EU structural funds, the main instrument of European equalizing regional policy.

The eligibility criterion for receiving assistance in the EU is low, and if it was used similarly in the US, only two states, Mississippi and West Virginia, having a rate 2% of the total population of the country would be eligible for assistance, while in the EU countries with 25% of total population.(Puga, 2001). The reason for this may be a decrease in mobility and high trade barriers in the EU, which is a consequence of the fact that employment in the industrial sector is less concentrated in Europe, but income differences are higher than in the US. (Pflueger, Suedekum, 2004)

On the graph below (Fig.3) it is presented such rate of unequal income dispersion as Gini index. According to this graph, we could tell that the income inequalities in the EU exist and in comparison with Gini index in Russia the policy is more efficient, we also can notice that index among European countries is similar that is evidence of conducting equalizing regional policy on the state level.



Fig. 3 Gini index for EUcountries in comparison with Russian data (gks.ru)

On the base of Eurostat's data we get the graphs of the Gini index for countries of each European regions separately (Western, Eastern, South and North regions consiquently) (Appendix). The results make sense: the most of European countries has positive dynamic of the Gini index value which is explained by the good result of conducting the equalizing regional policy. Moreover, more developed regions such as Nortern and Western Europe have countries with convergence in income distribution, whereas the Eastern ans South regions have large variance of inequlity index. As for the question of whole equal income distribution, in the EU this situation is much better than in the Russian federation. In comparison with the graph of Gini index for Russian regions, plots of the EU data show more income convergence. However, it is obvious that Western and North region are in better condition than the Eastern one so we can tell that there is the equalizing regional policy within regions. As for the European equalizing policy as a whole we can tell that it's not efficient as scientists suppose.

Anyway, the equalizing policy is one of the main places among the directions of the European regional policy: one third of the annual budget of the EU is allocated in structural funds for this solving the goal of disparities reduction across regions for state's efficiency increase.

There has been a significant increase in spending on equalizing regional policy, which is primarily due to Spain's and Portugal's accession and the adoption of Greece into the EU, which has led to an increase in income inequality between poor and rich regions. This was reflected in the growth in the cost ofconducting equalizing regional policy from EUR 3.7 billion in 1985 to EUR 18.3 billion in 1992, in 1999 this figure was 33 billion euros, which was 0.45% of the GDP of Europe. Transfers to the Cohesion countries (Greece, Ireland, Portugal and Spain) accounted for 3% of GDP at the end of the 20th century. National regional policy is also important in some countries, such as France, Italy and Germany. (Pflueger, Suedekum, 2004)

The EU has the Cohesion Fund for conducting the equalizing regional policy, also there are two more structural investment funds that are closely linked to this direction of policy: the European Social Fund (ESF) and The European Regional Development Foundation (ERDF). (Eurostat, ec.europa.eu/regional_policy)

The Cohesion Fund is a fund which is aimed to reduce economic and social inequalities and promote sustainable development. To receive support from this structural fund, country must have the rate of GDP per capita less than 75% of the EU average and a difference of 90% between GNI per capita in the country and the EU average.

For period of 2014-2020, there arecountries singled out among the countries that the foundation primarily helps. They are Bulgaria, Croatia, Cyprus, the Czech Republic, Estonia, Latvia, Lithuania, Hungary, Malta, Portugal, Poland, Romania, Slovakia and Slovenia. In 2015 EURO 63.4 billion were allocated (according to Eurostat this is 0.223% of GDP in 2015) to address the following objectives of the fund: development of transport networks, development and implementation of infrastructure projects in the regions, environmental protection. Moreover, the European policy makers are interested in ecologically efficient projects such that projects related to transport and energy must be energy efficient with the use of renewable energy. (Eurostat, ec.europa.eu/eurostat)

The European Social Fund is aimed at improving the situation of the poor population.It is engaged in the development and provision of employment and education opportunities in the EU for those category of population. This fund accumulatedEURO 80 billion in 2015 for solving tasks, including promoting employment and supporting mobility of labor, promoting social integration and combating poverty, investing in education, skills and learning and effective public administration. (Eurostat, ec.europa.eu/eurostat)

The specialization of the European Regional Development Fund is in the achieving economic and social cohesion in the EU by correcting the imbalance between the regions by investing in innovation and digital technologies, supporting small enterprises, and developing a low-carbon economy. What is more, it is assumed that the distribution of resources by region corresponds to their category. Thus, for the most developed regions, at least 80% of the resources from the fund must go to these tasks, for regions occupying a middle position, 60%, for the less developed regions - 50%. (Eurostat, ec.europa.eu/eurostat)

For the Russian Federation the issue of conducting the equalizing regional policy is relevant in view of the current situation in the unequal distribution of income between municipal districts in the regions of the country. The conducting the equalizing regional policy in Russia differs much from European policy. The main problem is in development of the territory, high territorial economic concentration and the difficulties in modernization. Moreover, the agglomeration has administrative nature which have negative influence on the state development.

According to our calculations made in the previous course work, conclusion about the existence of unequal income dictribution within regions was made in the distribution of income by subjects of the Russian Federation and we get the Gini index for each region and the average rate of the Gini index reach 0.5 (Fig. 4).Also looking back on the graph (Fig 3) we get that the Gini index grow since 1990^th. It can be explained by some factors: the USSR disintegration, interests lobbying by policy makers of particular region and inefficient equalizing regional policy (not spatial item in budget for this kind policy as in the EU).

Fig. 4 Gini Index for Russian data

One more economic reason for such inequality is the tendency for companies to be located and for population migrating to central cities. According to the data of migration population in 2013 taken from Russian Federal Statistics Service, there is a tendency for the increase of the outflow of population from peripheral regions to urban settlements, during the period from 2010 to 2014, the rural population decreased by 1.043 million. (Rosstat, gks.ru) Also, due to the decline in economic activity, many enterprises in small towns and rural areas went bankrupt, which resulted in a reduction in the number of jobs and a new wave of migration to the central areas which leads to a differentiation In incomes between municipal districts in the region. The existence of backward regions is one of the problems for the economic growth of the country. Thus, achieving the equal income distribution is one of the priorities in the conductingthe regional policy in Russia.

Unlike the EU where the equalizing independent regional policy, the equalizing policy in Russia is part of the state's social and economic policy, whose goals at the federal level are the following: raising the level and quality of life of the population, ensuring approximately equal conditions for social development in all regions of the Russian Federation, the full use of regional factors for the formation the effective socio-oriented economyin the regions. (MorozovSI, 2010)

This also has confirmation in legal instrument such as the "Concept of long-term socio-economic development of the Russian Federation for the period to 2020" and the development strategy of the subjects of the Russian Federation. According to this concept p. 4.2 "Innovative and social orientation of regional development", one of the social directions of the long-term socio-economic development of the Russian Federation is the significant reduction in the level of the interregional and intraregional differentiation and quality of the social environment and income of the population between the central regions and the peripheral one. (Order of the Government of the Russian Federation of 17.11.2008 № 1662-r)

As it was noticed earlier there is no definite relationship between the volume of allocated investments to regions with a high level of inequality in income distribution, the Gini index. Accordingly, the equalizing regional policy in the Russian Federation is not as revealed and effective as in the EU, where there are special funds in the field of this question. This is due to the fact that the EU is more interested in equal across regions and some other features (like special requirements for region setc).

Anyway, the Russian regional policy has two directions: stimulating (30%) and leveling (70%) which are controlled by the Ministry of Regional Development of the Russian Federation. The Fund for financial support of the regions (FFSR) is engaged in the leveling direction and is allocated 30% deductions of the federal budget. Also there are other funds which conduct the regional policy by different social transfers. They are the Compensation Fund and the Fund of co-financing of social expenses. As for the stimulating policy, the Federal targeted investment program is responsible for this and allocated with some other federal targeted programs 5-6% of budget. The leveling policy is more preferable way to conduct the equalizing regional policy because investments are assigned for the more perspective regions: business prefers to invest in territories with competitive advantages (scale effect, advantageous location, the best institutions that reduce barriers to development and higher-level human capital). (Zubarevich, 2008)

However, there exist many difficulties in conducting efficient equalizing regional policy in Russia. They are depopulation, concentration of the population in the richer regions and in the largest agglomerations, the lack of human and financial resources for the extensive type of spatial development. (Zubarevich, 2008) The problems of the equalizing regional policy in Russia are the large presence of depressed regions, the preservation of administrative management methods with lobbying interests, which are obstacles to achieving the objectives of regional policy. (CherkashnevR.Yu., 2013)

One more problem is a problem of underdeveloped regions in the absence of the stable development because of dominating the non-market services of the state in their structure of GRP. Moreover, the Ministry of Regional Development has plans which aren't correlated with the possibilities of regional industries for whole country development. To solve all these problems the Ministry of Regional Development should develop regions by increase of the natural agglomeration effect, human capital and modernized institutions for the regional development and determine the spatial priorities of the development, taking into account the real goals, opportunities and limitations of the regional policy. (Zubarevich, 2008)

3. The analysis of efficiency of the equalizing regional policy

Pflueger and Suedekum (2008) find that even distribution of subsidies across regions need not be optimal. The market equilibrium has the bubble-shaped form which takes into account the case of partial agglomeration that is characterized for real economic situation. According to the model, there are the efficient directions of the equalizing regional policy that can be reached only in the case of very high or very low trade costs and in that case there will be the full agglomeration or symmetric population dispersion which is necessity for the social welfare optimum in this model. So the model show that for the real economic situation it's almost partial agglomeration when there can't be the social optimum and therefore, the equalizing regional policy isn't efficient and shouldn't be conducted.

To show that, they use a NEG model in which consumers have CES preferences. However, recent literature in imperfect markets and international trade (Feenstra, 2003; Thisse, Parenti, Ushcev, 2016,; Arkokias, Costinotetc, 2015; Behrens, K., Murata, Y., 2007) raises the issue that many findings based on CES preferences are fragile due to peculiar properties of this type of preferences. In particular, the assumption of monopolistic competition under CES preferences which are identical across consumers is incompatible with abundant empirical evidence which shows that markups are variable (Fajgelbaum, Khandelwal, 2016; De Loecker, J., Warzynski, F., 2012). Therefore, conclusions based on the CES definitely require thorough robustness checks. To see whether the results obtained by Plueger and Suedekum (2008) are robust, we modify the model proposed by these authors by introducing symmetric translog preferences (Feenstra, 2003) instead of CES preferences. We choose to work with a translog model because it is (i) flexible enough to generate variable markups, and (ii) gives rise to a homothetic preference so that the ideal price index for a differentiated good is still well defined.

Our model describes the economic situation with 2 symmetric regions (domestic and foreign) which have same preferences, technologies and initial factor supply, 2 types of households: skilled and unskilled workers who have wages W and R respectively. Also 3 types of sectors have their characterisrtics. Housing is unproduced and non-consummated good which has a fixed demand in each region. Agricultural good is homothetic and is produced with single production factor (unskilled labor). Manufacturing aggregate is a wide variation of goods. Each of them is produced by the both labor types. All population is normalized as 1, is the rate of skilled labor in domestic region and is for the relative rate the unskilled labor to the skilled one.

The preferences are symmetric and translog and the price index has the following form:



(1)

The indirect utility function shows the consumer's attainable utility in order of income related to the price index. The translog form of indirect utility is reflected below.

(2)

(3)

To explore whether the equalizing regional policy is efficient or not we need to get the condition of market equilibrium and the social optimum. In case of stable equilibrium with symmetric population dispersion condition ( there won't be sense of the equalizing regional policy because with agglomeration there isn't situation of symmetry and stability.

For this purpose we need to determine the equilibrium prices on the market. The equilibrium on the competitive market of housing requires the equality of demand to the supply (H). Then

(4)

According to the model settings, housing belongs to households; while manufacturing goods are produced to be paid then prices of these goods have strict relation to the agent's demand. Therefore, to get the household demand we need to use the Roy's identity:



(5)

Then we calculated the demand of households in domestic and foreign regions respectively (.

(6)

(7)

where N- domestic goods variety, N*-boundle of foreign goods,i,j-good variety and .

The profit equation has the following form:

(8)

And if this equation equal to zero, there is the zero profit condition. As we can see, profit has dependence on the population dispersion which is special for the new economic models which describes the situation of the equalizing regional policy. Combining the demand equations (6,7) and the zero profits condition, we get the equation of markups on domestic and foreign goods consequently.

(9)

(10)

To get the equilibrium manufacturing prices we need to solve equations with integrals taking into the account the following:

The steps of getting the price equations (p and p*) are presented in the Appendix as well. The prices on domestic and foreign goods are:

(11)

(12)

The wages to skilled workers in both regions can be determined by imposing the demand and price equations (6,7,11,12) for domestic and foreign goods and the zero profits condition. Then the wage of skilled workers in domestic region:

(13)

For foreign region it will be the following:

(14)

Combining the zero profits condition with these equations (13,14) we can determine the equation of domestic and foreign goods variety:

(15)

(16)

Then the equations of firm prices will be:

(17)

For foreign goods:

(18)

The equations of demand on domestic goods:

(19)

On the foreign goods:

(20)

The wages will be the following for both regions:

( (21)

(22)

The equilibrium in the long run is determined by the decision of skilled workers to move across regions. This decision reflects the difference in indirect utilities.

The utility differential for skilled workers has the following analytical ezpression:

(23

(24)

According to the analytical expression, the market equilibrium varies due to the migration and the changes in the level of trade costs. So we get the graph (Fig.5) which reflects the dependence of the utility differential on the share of skilled workers in regions. To get this graph we need to put the value of the following parameters: and в which are statistical parameters (. The value of shows the number of unskilled workers to the world population of skilled workers. .

The NEG scientists told that the level of trade costs should be taken into account for conducting the equalizing regional policy. As in the Pflueger and Suedekum model “Integration, agglomeration and welfare” the equalizing regional policy can be efficient in case of very high, very low and intermediate trade costs. We also determine this parameter for 3 values (very low where In our case we have stable equilibrium for all rates of population dispersion.

Fig. 5 The market equilibrium in the case of the conducting the equalizing regional policy

According to the plot, it is obvious that in case of symmetric population dispersion it will be stable market equilibrium. And the equalizing regional policy will be efficient. But before whole conclusion we need to check the social optimum and if we get the same results we can tell about its efficiency of policy.

To analyse the social optimum for our case we don't use Pareto-criterion because it isn't sufficient from a social perspective. According to the Pflueger and Suedekum model, Pareto-criterion couldn't rank different spatial structures because of conflicting interests among different groups of agents so we should use the utilitarian concept where a social planner maximises the un-weighted sum of individual utilities.

(25)

So the social optimum has following form of the equation:

(26)

Where

To analyze the optimality of policy from the social perspective we need to take the derivative of lambda.

(27)

For convenience all calculations as the calculations of market equilibrium equation are presented in Appendix 2. Here is the resultant equation of the social optimum:

(28)

Here we also need to put concrete numbers to our parameters and as in case of the market equilibrium here we also get three levels of trade costs (high, intermediate and low). The graph is reflected three conditions: without agglomeration, partial agglomeration and full agglomeration. And as we can see there is stable equilibrium in case of symmetric population dispersion (

Fig. 6 The social optimum in the equalizing regional policy condition

So according to these plots, we can tell that the equalizing regional policy will be conducted efficiently only in case of low trade costs. And in case of full agglomeration or pretty equal population distribution there will be the sense of regional policy.

Therefore, we could tell that our result is robust to the result in the Pflueger and Suedekum model. However, in our case this policy will be efficient only in case of the low trade costs because markups has also influence and skilled workers migrate taking this into account.



Conclusion

The equalizing policy takes important part in regional politics of many countries. The European Cohesion Fund accumulates 0,223% of GDP in 2015 which conducts this policy via subsidies to the regions with high income inequalities. But there is dilemma in the choice of the way of conducting the equalizing policy. When it is aimed to equalize the disparities between countries in the EU, it leads to more divergence in income within regions of separated country. According to the plots of the EU data, we can tell that more developed macro-regions of the EU such as the North and Western one has rather equal income dispersion while two other regions (South and Eastern) has worse situation, and if we search for plot of Gini index for the EU we see that there are inequalities not only within macroregions separately but for whole subject too.

As for Russian evidence, the equalizing policy in Russia is part of the state's social and economic policy, whose goals are raising the level and quality of life of the population, ensuring approximately equal conditions for social development in all regions etc. The equalizing regional policy is also determined in the "Concept of long-term socio-economic development of the Russian Federation for the period to 2020" and the development strategy of the subjects of the Russian Federation. However, there are serious problems in conducting this policy in Russia. They are development of the territory, high territorial economic concentration and the difficulties in modernization. That is more, the main problem is the approach of the Ministry of Regional Development to this because assessment of perspectives aren't correlated with the possibilities of regional industries for whole country development and as a result the policy is inefficient for country.

Therefore, we might suppose that conducting the equalizing regional policy doesn't make sense in many cases and in our work we test the hypothesis about its efficiency. To get some results we analyzed literature and solved the theoretical model.

A good example of exploring the efficient ways of the equalizing regional policy is the model of Pflueger and Suedekum “Integration, Agglomeration and Welfare”. According to it, the efficient way of this kind of policy exist in case of very high, very low and intermediate trade costs and only in case of symmetric population dispersion between regions or full agglomeration the social optimum could be achieved.

In our case we solve the similar model for the translog price index. We modify their model to check the robust of results and test the main hypothesis about the efficiency. We decide to work with model without the CES preferences because they are identical across consumers is incompatible with abundant empirical evidence. So we chose the translog model due to its flexibility to generate variable markups and the homothetic preference which let to define the ideal price index for a differentiated good.

As a result of the solutions of modified model, we get plots for market equilibrium and the social optimum for three cases of trade costs and test the hypothesis. According to them, we could tell that our results are robust to the Pflueger and Suedekum model so there exist efficient approach of conducting the equalizing regional policy. However, it can be realized only in case of symmetric or full agglomeration and for low trade costs because for case with very high trade costs the variable markups can influence on decision of skilled workers to migrate and as a result there won't be social optimum.

To sum up, the Pflueger and Suedekum model results are robust but they doesn't work in evident economic situation where the partial agglomeration exist and there are different trade costs which are as usual rather high. So we could reject our hypothesis about the existence of the efficient ways of equalizing regional policy.



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Appendix

Appendix 1 Plots of Gini index for European regions



Appendix 2 Calculations

The base model calculations:

Using the Roy identity to get the equations of demands on domestic and foreign goods:

Combining the profit equation and the demand equations:

- R

Getting markups for domestic goods from the zero profit condition:



Then using following equation we get the markup on domestic goods:

The same works for the foreign goods:

To get the optimal prices we need to solve integrals in the equation of mark up:

Then the price equation is:

The foreign price equation will differ in the value of trade costs Opening the brackets and its simplification gives:

To get the equation of variety we need to use the zero profits condition and the equation of wages:



(=0

We need to simplify it and solve equation with 2 unknown values:

Using the results via simplification we get new equations of prices, demands and wages which were used in the following part.

e.g. the simplification of the domestic price equation:

The simplification of the demand equation:



In the analogous way:

The calculations for getting the market equilibrium:

The utility differential for skilled workers has the following form:

So we solve it partly.

Let us find the

Then we use previous calculations and simplify equation:

We get the following:

Before solve the similar case for the price index we need to determine the logarithm relation which is:

ln

ln

= ln=

ln

ln

And this is the differentiation of logarithm relation of housing prices for both regions:



So we put all results in the indirect utilities differentiation:

ln'

Via simplification we get analytical result:

Calculations for the exploring the social optimum:

Here we need to find the following parts:

As we can see we can simplify following part:

Where one part was calculated when we solved the market equilibrium:

Using the wages equation we have this difference:

(

(

In previous part we also found the wage derivative from lambda:

Combining it all we get the part of social optimum equation:



We need to get the following part for this we use the equation of price index as well as prices equations:

Combining with price equations:



Then we found derivatives:

The same works for the and

and will be equal to 0 because they don't have any relations to the and have constants.

We can simplify the second part of the social optimum equation:

Put all results of prices derivatives we get:

Combining two parts of the social optimum equation together we get:



We need to make some simplifications to work with this equation for the plot.

This is the social optimum equation:

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