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1 econstor Make Your Publications Visible. Service of Wirtschaft Centre zbwleibniz-informationszentrum Economics Nalbach, Eva Conference Paper Sharing Economy: Dynamic General Equilibrium Effects Beiträge zur Jahrestagung des Vereins für Socialpolitik 28: Digitale Wirtschaft - Session: Growth III, No. C3-V2 Provided in Cooperation with: Verein für Socialpolitik / German Economic ssociation Suggested Citation: Nalbach, Eva (28) : Sharing Economy: Dynamic General Equilibrium Effects, Beiträge zur Jahrestagung des Vereins für Socialpolitik 28: Digitale Wirtschaft - Session: Growth III, No. C3-V2, ZBW - Leibniz-Informationszentrum Wirtschaft, Kiel, Hamburg This Version is available at: Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. Sofern die Verfasser die Dokumente unter pen-content-lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in EconStor may be saved and copied for your personal and scholarly purposes. You are not to copy documents for public or commercial purposes, to exhibit the documents publicly, to make them publicly available on the internet, or to distribute or otherwise use the documents in public. If the documents have been made available under an pen Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence.

2 Sharing Economy: Dynamic General Equilibrium Effects Eva Nalbach Werner Roeger bstract: Developments in digital technologies enabled the emergence and rapid growth of the sharing economy predicted to account for up to 5% of EU GDP in coming years. This paper contextualises these developments within a dynamic two sector model of the economy and analyses the effects of efficiency gains in the sharing sector on growth, income distribution and employment. We identify three sources of technological progress in the sharing sector and find that an expansion of this sector, in line with recent predictions, will lead to modest GDP growth and declines in both wage share and employment, if sharing is organised by profit maximising firms. We compare this solution to a case where households organise sharing directly and find that the sharing sector will be larger under the same technological conditions in the latter case. Keywords: Neoclassical Growth Model, Two Sector Growth Model, Technological Change, Macroeconomic Model, ggregative Model, GDP, Sharing Economy, Wage Share, Employment. JEL Code: 4, E, J2 ffiliation: Eva Nalbach (evanalbach@gmail.com);werner Roeger EU Commission (Werner.Roeger@ec.europa.eu). The views expressed in this paper are those of the authors and do not necessarily represent those of the EU Commission.

3 Introduction Recent technological developments have facilitated sharing of durable goods via digital platforms (see, for example, Dhar and Sundararajan (27) and Sundararajan (26)). Sharing of the consumer durable can be done across various time dimensions. There can be sub periods when a durable good such as a car or an apartment is temporarily not used by its owner. In this time it can be made available to others who are in need of the good, provided it is possible to match the supply of idle durables with the demand across location and time. lternatively, certain durables can only be used by their owners over a fraction of their lifetime (e. g. baby clothes) and will afterwards be sold on a market for used goods. Though sharing is not a completely new phenomenon, new technological developments have the potential to facilitate matching owners and users or buyers and sellers of consumer durables. Though the sharing economy is still small, a recent study for the EU Commission estimates the size (measured in the value of transactions) in the range between.5% and % of GDP in 25 (see Vaughan et al. (26). However, the growth of the share economy is enormous, with growth rates in recent years of around 25%. Recent forecasts predict that the sharing economy could eventually add between a 6Bn and 6Bn Euro to European GDP, this could be up to 5% of EU GDP (see Lilico et al. (26)). ne of the most interesting features of sharing is the possibility to increase the utilisation of durable goods with close to zero marginal cost, as for example noted by Rifkin (24) (this requires that the depreciation of durables is not a function of the intensity in which it is used). In this literature also claims have been made that this could be the end of capitalism. The question arises whether increasing consumption via sharing at zero marginal cost can be organised efficiently by private firms or whether there exist cooperative solutions among households which would be superior to the market solution. This paper is an attempt to shed some light on this issue. In this paper we present a two sector economy. There is a production sector which is producing a durable good and there is a utilisation sector. The physical production sector, is characterised by a constant returns to scale (CRS) technology and perfect competition. Prices for physical goods are equal to marginal cost. Firms in the sharing sector offer alternative variants in which the durable good can be utilised. Households regard these as imperfect substitutes. For example, a car can be used partly as a taxi (Uber), or the owner of the car can invite additional 2

4 passengers who want to go from one location to another at the same time (Lyft), or the idle car can be made available to neighbours (Getaround) or it can be given to a rental company for part time use. However the different ways of using the car are rivalrous, i. e. the physical good can only be made available for one type of use at a given time. It is assumed that sharing is essentially organised via dedicated digital platforms which can be operated at a fixed cost (per period), but there is no marginal cost up to the physical limit in which a durable good can be utilised. There are matching technologies (platforms), which allow coordinating the supply and demand for idle durable goods (sharing) among households in various different ways. The technology in the sharing sector differs from physical production. Utilisation can be extended up to a maximum limit at zero marginal cost. The firm in the utilisation sector only faces a per period fixed cost for operating the sharing platform and has to pay a price for the sharing technology when entering the market. There is free entry into the sharing sector. However entry requires a design. Such designs are created by a sub sector. The number of designs created per period is proportional to the labour input in this sector. This sub sector is assumed to be perfectly competitive. The sharing platforms can be run by profit maximising firms which are owned by the households or they can be run by household cooperatives where household members provide labour input for operating the platform on a voluntary basis and share the revenues. Technical progress in the sharing sector can take three forms. First there can be a positive technology shock to the creation of new platform designs, which lowers their price, second there can be innovations in platform operation which reduce fixed costs, and third there can be innovations which allow to increase the utilisation rate of durables. Technical progress in the physical economy is characterised by a labour saving technology shock. There are a number of questions which are often raised in discussions about the effects of an emerging sharing economy. How strongly will sharing reduce the physical production sector? r phrased differently, what is the net growth effect of a rise of sharing? The answer to these questions depends on a number of factors, such as the labour supply response and the reasons for a growing share economy, 3

5 which can be manifold. (increased technological possibilities for sharing (um) reduced costs for operating sharing platform (Lu), the invention of novel modes of sharing (ua). What are the distributional effects of a growing share economy? ften the opinion is raised that sharing platforms are by nature monopolies. However, if monopoly rents attract entry of new firms which offer alternative ways of using consumer durables, large rents could be the exception. Distributional effects also depend on the ownership structure, namely whether sharing is organised by profit maximising firms or household cooperatives. s a follow up to this one can ask the question, how will the growth with an expanding sharing sector look like. Will the stylised growth facts survive (growth associated with stable employment share and stable wage share) or will new growth patterns emerge? This paper tries to provide an analytical framework which allows to address these questions. We borrow heavily from the literature on endogenous growth, and here in particular from Romer (99) and Grossman and Helpman (992) for modelling the expanding sharing opportunities. However, our model differs in one important aspect from this literature. The intermediate goods producers in this literature usually operate with positive marginal cost and make pricing decision as monopolistic competitors. Firms in the utilisation sector we are looking at face a fixed per period operating cost and zero marginal cost up to a production limit. Here we follow Nalbach (26). The paper is organised as follows. In section one we present the model, section 2 provides a discussion on how different forms of technical progress in the sharing sector affect the wage share and the employment rate in this economy. Section three provides quantitative information on the impact of the currently expected expansion of the sharing sector on GDP, employment and the wage share and how these effects depend on the source of technical progress. This discussion is concentrating on the case where profit maximising firms organise sharing. In section 4 we introduce household cooperatives and discuss the steady state of this economy and how it compares to the capitalist solution. 4

6 . The Model We analyse a two-sector economy, with a sector for physical goods, a sector which organises the utilisation of those physical goods in times they are not used by their owners and an R&D sector developing new sharing technologies. Physical goods are produced with a CRS production function. This sector exhibits constant marginal cost. The utilisation sector is comprised of a two-stage production process. There is a production function for new platforms, which uses labour as input. The number of new platforms is proportional to labour input in platform production. Platforms are sold to entrants in the digital sector. Entrants buy the platform and receive revenues from selling digital services to the household sector. part from the purchase price of the platform there is a fixed cost of operating the platform every period. There are no other costs associated with the provision of digital services, i.e. digital services can be provided a zero marginal cost. Households There is a continuum of households h distributed over the unit interval h (,). Household h maximises an intertemporal utility function over a consumption aggregate C ht and labour L ht. U h = β t (log(c ht ) ω ) with β = t= (a) +ξ (L ht L ht +ξ ) +ρ The household is indifferent between owning a physical durable good C ht and utilising/sharing a bundle of different services from a pool of physical goods C S ht. In order to simplify notation we do not explicitly distinguish between durable and non durable consumption, but assume that the time period is long enough (t= years) such that we do not explicitly have to model depreciation. C ht = (C ht + C S ht ) (b) The household has CES preferences over the alternative utilisation variants of the physical good and u hj is the rate in which household h is utilising service j and ε denotes the elasticity of substitution between alternative utilisation variants. The utilisation rate is expressed in terms of the aggregate durable (or the pool of durables). Here it is assumed that the utilisation service 5

7 provider disposes of a technology which allows to match idle durables across a subset of households with the temporary demand for those durables of a disjoint subset of households. C ht t j= S = [ ( u hjt t C t ) ε dj] /ε with ε > (c) However, the different ways of using a durable good is rivalrous, i. e. the physical good can only be made available for one type of use at a given time. Therefore, if the number of possible ways in which the durable can be used increases, this reduces the utilisation rate per type of use. The household receives labour income W k k t L t kε{, S, } from the physical production sector (), from the utilisation sector (S), from the research sector/platform developer () and profit income π jt from the firms operating in the utilisation sector. We assume that each firm in the utilisation sector must buy the knowhow for operating the sharing network for that specific service from a firm which specialises in the creation of new sharing variants. part from the business idea this also includes the software which allows to set up and operate the specific sharing platform. We denote the price for such a patent with P jt. t each period the household must make an investment decisions over the number of new patents t and an investment decision over capital in physical production K t. The investment in capital for physical production K takes the usual form. The additional constraint to utility maxmisation of the household takes the usual form: K t = ( δ)k t + I t (2) I t = K t ( δ)k t with depreciation δ [,] Let P t and P u jt be the price of the physical good and the utilisation service j. Henceforth we use P t as numeraire. In order to simplify the optimisation we follow the endogenous growth literature (see Romer 99) and treat the index of different types of patents as a continuous variable, this avoids taking explicit account of integer constraints. 6

8 L = t= β t U(C(C t, C S t ), L t ) t= β t λ t (B t + P jt dj ( + i t )B t + P C t C t t W k k k t l t π jt dj t t P jt dj) (2) with kε{, S, } The consumption and utilisation decision of the household U h C = ht (C ht +C S ht ) = λ t P t (3a) U h u hjt = (C ht +C ht S ) C ht S (/ε) ( u hjt t C t ) /ε = λ t P tj u (3b) Under symmetry: u hj = u M and C h = C S = [ ( u hjt C t ) α t α dj] = ε u M t C t (4) C ht j= t S The utility for utilisation services C ht has a taste for variety feature and is a positive function of the number of services. Notice, for < ε < 2 utility is a convex function of, for ε > 2, it becomes a concave function. s will be shown below, stability requires concavity of C S ht, i. e. a sufficient degree of substitutability between utilisation services. Preferences for consumption goods and utilisation imply the following relationship between P t and P u tjt. P α t u t = P tjt (5) Because >, the relative price of utilisation increases with the number of service α varieties. Utilisation services get more attractive to the household as variety increases. In the special case =, P t = P u tjt, 7

9 We follow the literature and define the price index for utilisation services P S as a measure for the least expenditure on services which buys one unit of the consumption service index. This price index can be obtained from the following optimisation problem Min L = P u j ( u j C ) dj P S t [ ( u j C ) α dj] α (6) Solving this problem yields P t S = P t The relative price between the physical durable good and the index of all service varieties is equal to one. ptimal savings is determined by the following FCs L C t = C t λ t P t C = (7a) L B t N = λ t + βλ t+ ( + i t ) = (7b) L = λ t P jt + λ t π jt + βλ t+ P jt+ = (7c) t L K t = λ t + βλ t+ ( δ) + βλ t+ R t = (7d) This defines a relationship between the risk free rate of interest and the discount factor /( + i t ) = βλ t+ λ t (8a) /(R t + ( δ t )) = βλ t+ λ t (8b) a relationship between capital depreciation and capital rents, the discount factor and the risk free rate of interest can be established: βλ t+ λ t = /( + i t ) = /(R t + ( δ t )) 8

10 We can now express R t in terms of depreciation and rate of time preference: (due to our normalisation convention the nominal interest rate equals the rate of time preference) i t = ρ R t = (ρ + δ) nd the price of patents for utilisation services P jt = π jt + βλ t+ P λ jt+ = π jt + P t (+i t ) jt+ (9) The household is indifferent between working in the production, the utilisation or the research sector and labour is homogeneous. L t = L t + L t S + L t () ptimisation w.r.t. labour yields ω ( L t ) +ξ L t ξ = W t k P t C C t = W t k with kε{, S, } () These three FCs imply that wages are equalised across sectors. Technology and market structure for the physical good and utilisation The physical goods sector: We assume that the physical good is produced under perfect competition, with firms using a cobb-douglas production technology Y t = (u t L t ) α K t ( α) with α < (2) where u t is an efficiency parameter and L t is labour input in the physical sector and K t denotes the capital input in physical production. 9

11 The maximisation problem of the physical firm now becomes: L = P t Y t W t L t R t K t (4) The physical firm will operate at the level where input prices are equalised with their marginal productivity: L L t = α Y t L = W t t P t (5a) L K = ( α) Y t t K = (ρ + δ) t (5b) We can express K t,y t and W t in terms the parameters and variables of interest: K t = [ α ρ + δ ] αl t u t = (ΘK)L t u t Y t = [ α ] α L ρ + δ t u t = (ΘY)L t u t W t = α[ α ρ + δ ] αu t = (ΘK)u t Equilibrium conditions in steady state can be rewritten in terms of parameters and variables of interest: Y t = C t + I t = C t + δk t So that: C t = Y t δk t = (ΘY)L t u t δ(θk)l t u t = [(ΘY) δ(θk)]l t u t

12 GDP: Y t = C t + C t S + δk t = C t ( + t ε u M ) + δk t = [(ΘY) δ(θk)] ( + t ε u M ) L t u t + δ(θk)l t u t = (ΘY) ( + t ε u M ) L t u t t ε u M δ(θk)l t u t = (ΘY)L t u t + (ΘY) t ε u M L t u t δ(θk) t ε u M L t u t = (ΘY)L t u t + [(ΘY)L t u t δ(θk)l t u t ] t ε u M The utilisation sector: Here we follow the idea that utilisation services are scalable up to a time limit over which the physical good can be used over the period. In order to organise the utilisation in an efficient way across individual households the service provider needs to set up a platform which allows the coordination of demands for available physical goods across time and space. For this the service provider faces two types of costs. First, a per period cost for the fixed labour input L j u required for operating the sharing platform. Thus, fixed per period costs of service firm j are given by Cost u u jt = W t L jt (5) Second, when entering the market the start up has to pay a price P t for the platform, which is provided by a competitive research sector. nce the platform is in place and staffed, firm j can sell utilisation services at zero marginal cost up to the time limit which the consumer durable C t can be used. We denote the upper bound with u M u j u M (6)

13 Given preferences for utilisation services, the utilisation provider faces a demand function u jt u C t = ( P jt t P t S) ε C t S (7) With ε > the service provider maximises revenue by offering the maximum utilisation u j = u M Revenue of firm j is a positive function of the pool of physical goods, their maximum utilisation rate, and a negative function of competing service providers, under the assumption that the elasticity of substitution between alternative service variants exceeds 2. Rev j = (P u um C t ) = ( ε u M C t ) (8) Revenue of firm j is a positive function of the pool of physical goods, their maximum utilisation rate, and a negative function of competing service providers, under the assumption that the elasticity of substitution between alternative service variants exceeds 2. The period profit of service provider j is given by π j = ( ε u M C t WL j u ) (9) Finally, it must be noted that a feasibility constraint operates in the form that L j u must be sufficiently small such that profits of firms in the sharing sector are non negative (π j ). Production of user platforms: There is a research sector which continuously creates new ideas on how to share the durable consumption good. The flow of new platforms is constrained by a linear knowledge production function, which characterises how new platforms t are created with labour input L t and where u t is an efficiency parameter 2

14 t = u t L t (2) Platforms are produced under perfect competition. The zero profit condition P t t = W t L t (2) determines the platform price P t = W t u α α[ = (2b) ρ+δ ] αu t u = αθku t u which a new entrant in the market for utilisation services must pay. s shown above, arbitrage in capital markets requires that the return on an investment of size P jt is equal to that of a riskless loan and therefore P jt = π jt + P (+i t ) jt+ (9) This arbitrage condition can also be interpreted as a free entry condition into the market for utilisation services. Suppose because of a favourable technology or preference shock, there is an increase in profits π jt. This yields higher returns on patents and entry occurs until π jt has fallen enough (note profits are a negative function of ) such that the arbitrage condition holds. Labour market We assume that the household sector is indifferent between working the physical good, the service sector and the research sector, which equalises the wage rate across sectors. The wage rate is effectively determined by the marginal productivity condition in the production sector of the economy. Labour market equilibrium requires that labour supply is equal to labour demand from the physical production sector, the demand for fixed labour input from the utilisation sectors and the demand from the research sector L t = L t + L t u + L t (22) Labour supply is given by 3

15 L t = (L t ) +ξ ξ ( W t ) ω P C t C t ξ () Note, for ξ labour supply becomes inelastic at L t = L t. The dynamical system in terms of P t and The two dynamic variables are P t and. Therefore, we can study the dynamics of P t and in a two dimensional phase diagram. This requires however that we come up with a system of two dynamic equations which is only a function of V and and all exogenous variables P ε t = ( t u M C t α[ α ρ + δ ] αu t L u j ) + P + i t+ t P ε t = ( t u M [u t (L t t L u j L t )] α K ( α) t α[ α ρ + δ ] αu t L u j ) + P + i t+ t t = u t L t P t = α[ α ρ + δ ] αu t u t 2. Technological change in an economy with a sharing sector In this section we show how technical progress in the sectors of this economy affect key economic aggregates. It is well known that the standard neoclassical growth model for an economy with constant returns to scale and labour saving technical progress generates growth with a constant employment and wage share. The relative constancy of these two variables in the long run has been noted by Kaldor (96) and he has labelled them as stylised facts. However, while often taken as a justification for the neoclassical model, e. g. by RBC economists, the strict constancy of these two ratios has always been questioned. lso recently the question has been raised to what extent the emergence of a digital economy and associated production technologies with increasing returns and high fixed costs could change these 4

16 patterns. In this section, we therefor analyse how technical progress in the sharing economy as identified in this model affects growth, the wage share and the employment rate. Technical progress in this economy can take various forms. Besides the standard increase of technology u t in the physical production sector, there are three alternative ways in which the sharing sector can expand. Technical progress can reduce fixed operating costs, via a reduction in the fixed labour input L u j. Second, the time limit for using the durable u M can be increased (e. g. by shortening the time between different uses) and finally the efficiency by which new platforms are invented u can be raised. In this section we first identify the various channels in which these types of innovations affect growth, the wage share and employment. t a purely theoretical level we are able to characterise the transmission channels however we cannot derive completely unambiguous results, therefore we resort to model simulations of a calibrated version of our model. The theoretical discussion proceeds in two steps, first we analyse the impact of technical progress in the sharing economy and in the physical production sector on the number of utilisation variants and then analyse how each technology shock affects our variables of interest directly and indirectly through the number of utilisation variants. First, we look at the impact of technological progress on growth and the wage share under the assumption of inelastic labour supply, in a second step we discuss the steady state impact of technology shocks on the employment rate. In our quantitative model experiments we calibrate the size of the technology shock such that our model economy generates an increase in the sharing economy size from % of GDP to 5% of GDP. The added value of these experiments is that apart from the qualitative results we obtain an estimate of the impact of shocks of this size on the long run level of GDP, the wage share and the employment rate. 2a. nalytical Results First, we derive steady state results under the assumption of a constant employment rate. In the following we assume ε > 2. We proceed in two steps. We first show how the number of utilisation variants depends on the technology shocks and then we show how our variables of interest: level of output, wage share and employment rate depend on and technology shocks. 5

17 In the steady state = from which L = and K t = K t+ Equilibrium condition in the physical sector in steady state can be rewritten in terms of parameters and variables of interest: Y t = C t + I t = C t + δk t So that: C t = Y t δk t = (ΘY)L t u t δ(θk)l t u t = [(ΘY) δ(θk)]l t u t From the free entry condition P = αθku t u = r ( ε u M C αθku t L j u ) (9a) αθku t u = r ( ε u M [(ΘY) δ(θk)]l t u t αθku t L j u ) αθku t u (r + L M u j u ) ε = [(ΘY) δ(θk)]l t u t we obtain a solution for the number of sharing firms as a function of u, u M and L j u. The entry condition can be rearranged to αθku t u (r + L M u j u ) ε = [(ΘY) δ(θk)](l L u j )u t (9b) This allows us to determine the number of utilisation variants as a function of the underlying technological factors graphically (see Figure ). The right hand side of this expression shows how revenues of utilisation firms are constrained by the availability of physical goods. The term (L L u j ) gives the steady state labour input into the production of the consumer durable. Revenues in the utilisation sector depend positively on the availability of consumer durables. s can be seen an increase of utilisation variants reduces the labour input in the production of physical goods and therefore has a negative impact on revenues in the utilisation sector. The 6

18 RHS therefore provides a supply constraint for the sharing sector. The two terms in brackets on the LHS give the two types of fixed costs in the utilisation sector plus the cost in terms of lost market share associated with entry of new firms. First we can see from eq (9b) that the level of technology in the physical sector u cancels from this expression. The level of technology in the physical production sector is therefore irrelevant for the determination of. Figure : Determining the number of utilisation variants Increase of u M : LHS shifts down. Profits of firms in the sharing sector rise, this increases entry of new firms. The entry is limited by the supply constraint for physical goods ( increases). Increase of u : LHS shifts down Cost of patents fall, entry costs decline, this increases the number of firms. ll firms need less profits in order to cover entry costs. Stock market value of each utilisation firm declines. Reduction of L j u : LHS is shifted down, while RHS is shifted up. This unambiguously increases. This is intuitively plausible, as profits per firm increase, leading to entry, whilst reducing counteracting effects from the supply constraint. 7

19 Increase of u : Why is an increase in u not affecting. n increase in u is increasing C but it is also increasing W and therefore also increases fixed costs (also costs for patents are increased). The linear technology for C implies that revenue and cost increase at the same rate. This discussion establishes a positive link between positive technology shocks in the sharing sector and the number of firms/variants in the sharing sector. The total GDP effect of an expanding sharing economy: Because of high substitutability between sharing and physical consumption it is likely that sharing will lead to some crowding out of physical production. This section discusses the net growth effect of technical progress in the sharing sector. Given our normalisation assumption (P = ), total output (Y), measured in terms of the physical consumption good is given by GDP: Y t = C t + C t S + δk t = (ΘY)L t u t + [(ΘY)L t u t δ(θk)l t u t ] t ε u M (23) and can be expressed in terms of technology parameters and number of utilisation variants, as follows Y = u (L L j u )(ΘY + ε u M (ΘY δ(θk)) (23a) It is evident from this expression that an increase in efficiency in physical production (u ) unambiguously produces a growth effect. reduction in fixed costs (reduction of L u j ) and efficiency gains in the utilisation rate (u M ) also have direct growth effects. However, since they also increase the number of utilisation variants, the growth effect becomes ambiguous. s shown in the first term of eq. (23a) a rising number of utilisation variants represents an efficiency loss. This occurs due to rising overall fixed costs, as each new entrant faces the same per period cost structure. n the other hand, rising numbers of utilisation variants can also lead to growth effects through love of variety, as is shown in the second term of eq. (23a). n increase in the choice between sharing variants increases the real value of the sharing bundle relative to the physical consumption good. The magnitude of the growth effect produced through an increase in variety depends, however, on the elasticity of substitution between the different utilisation options ε, so that for a high elasticity of substitution it is conceivable that the efficiency loss dominates the indirect effect. n increase in the efficiency in platform production does not have a direct positive steady state GDP effect but only affects GDP indirectly via an increase in. We would therefore expect that in constellations where the efficiency loss dominates 8

20 the variety effect, an increase in the efficiency of platform production could yield negative long run GDP effects. The effect of technical progress in the sharing sector on profits and the wage share In the steady state we get the following arbitrage condition for an individual sharing platform j rp = αθku t u = π j = ( ε u M [(ΘY) δ(θk)]l t u t αθku t L j u ) i. e. profits increase with a rise in u and free entry reduces profits if there is a decline in the platform price due to an increase in u. reduction of fixed cost and an increase in the utilisation rate leads to entry such that profits of firm j in the new steady state remain constant. Since the number of firms increases, total profits increase. In contrast, with an increase in u, the fall in the platform price reduces profits of individual firms under free entry. Therefore, the effect on aggregate profits is ambiguous. Since the wage share is defined as total wages over total income and total income is the sum of total wage and profit income WS = Wages = W o L = Wages+Capital Rents+Profit W L+R K +π j αθku t L αθku t L+(ρ+δ)(ΘK)L t u t +(ε u M C t αθku t L u j ) = αθku t L αθku t L+(ρ+δ)(ΘK)L t u t +(ε u M [(ΘY) δ(θk)]l t u t αθku t L u j ) Note: ΘY = [ α ] α = ΘK[ α ρ+δ ρ+δ ] αθku t L ΘKu t (αl + (ρ + δ)l t + ε u M L t [ α ρ + δ ] δl t αl u j ) = = αl (αl + (ρ + δ)l t + ε u M L t [ α ρ + δ ] δl t αl u j ) αl (L L j u )(α + ρ + ε u M [ α ρ + δ ] ) 9

21 It follows that the wage share is not affected by technical progress in the physical production sector, it declines with a reduction in fixed labour and an expansion in the utilisation rate. There is some ambiguity concerning the effect of rising efficiency in platform production. The employment rate and technical progress in the sharing economy ptimisation w.r.t. labour yields ω ( L t ) +ξ L t ξ = W t C t = αθku t C (+ε u M ) = αθku t [(ΘY) δ(θk)]l t u t (+ε u M ) = α ([ α ρ+δ ] δ)(l L u )(+ε u M ) (b) This allows to analyse the steady state impact of technology shocks in the sharing economy on the employment rate in a graphical way. Like in the discussion of technology shocks on the wage share we note that the constancy of employment w. r. t. technology shocks in the physical production sector is preserved in this economy. In contrast, the technology shocks which directly affect efficiency in the sharing economy and therefore the size of the sharing economy will in general not be neutral on employment. We start our discussion by analysing the effects of a reduction of fixed costs. To better understand the effects it is useful to proceed with the discussion in steps. First we assume that the effect of a reduction of Lu on is negligible and discuss only the direct effects of a reduction in fixed costs. In this case we obtain a downward shift of the RHS of eq (b) and a reduction in the employment rate. s discussed in Nalbach (26) in the case of a static economy this reduction of employment can be interpreted as a wealth effect associated with higher profits in the sharing sector. However, we know that an increase of profits in the sharing sector stimulates entry, this reduces profits (first bracket in the denominator of RHS) and mitigates the reduction of employment. However, there is a third effect, namely a rising marginal utility of consumption (second bracket in the denominator of RHS) which reduces employment. Increasing the utilisation rate and also first neglecting also reduces the employment rate. This can again be interpreted as a wealth effect from increased profits. But like in the previous 2

22 case, a rise in entry associated with an increase in the rate of utilisation has positive and negative effects on employment. Without entry, an increase in efficiency of platform production has no effect on employment, but because of offsetting wealth and utility effects from entry also in this case the effects on the employment rate are theoretically ambiguous. Figure 2: Employment and technical progress in sharing 3. Quantitative analysis 2

23 In the following we show the dynamic effects of technical progress in the utilisation sector in the case of a high elasticity of substitution between utilisation services. It turns out that the qualitative results on the wage share are not sensitive to the elasticity of substitution. In the following we show how total GDP, employment and the wage share adjust to technical progress associated with sharing. In order to provide some realism we assume that each shock will lead to a long run increase of the share economy by about 4% which appears to be an upper bound estimate for the future expected size of the sharing economy as % of GDP. The annex to this paper contains information about the calibration of our model. 3. Increasing the utilisation rate Increasing the sharing economy via an increase in the utilisation rate of durables (by 4%) increases GDP (total consumption) by about 2.5% in the long run. The net increase of GDP is less than the direct effect from increased sharing because of a reduction in physical production and a small decline of employment. lso the wage share declines by about 2PP. Figure 3: Increase of sharing economy (4%) via increased utilisation 22

24 4 x_a 2 x_lc x_lco x_lcs -2 5 x_lo x_la x_ls x_ws.2 5 x_l x_a: absolute change in variety; x_lc: per cent change of total consumption (GDP) (in per cent) x_lco: per cent change of physical consumption (production) (in per cent) x_lcs: per cent change sharing consumption (in per cent) x_lo: change of employment, production sector x_la: change of employment, platform design x_ls: change of employment, sharing sector x_ws: change of wage share x_l: change of total employment 3.2 Reducing fixed costs in the utilisation sector Results on GDP, employment and the wage share a qualitatively similar to the previous case. This is to be expected since both technology shocks affect the sharing sector in a similar way. Figure 4: Increase of sharing economy (4%) via reduced fixed costs 23

25 x_a 2 x_lc x_lco x_lcs x_lo.2 x_la x_ls x_ws.2 x_l Increasing efficiency in platform creation This case differs from the previous two cases in on dimension. Increasing efficiency in platform design does not reduce the employment rate. This suggests that the wealth and utility effects on labour supply cancel each other. 24

26 Figure 5: Increase of sharing economy (4%) via more efficient platform creation x_a 2 x_lc x_lco x_lcs -2 5 x_lo x_la x_ls x_ws x_l Sensitivity nalysis s discussed in section 2, an increase in the efficiency of platform production has possibly ambiguous effects on growth and income distribution. Especially in the case of a high elasticity of substitution between alternative utilisation variants the efficiency loss can dominate the variety effect. This can lead to a fall in GDP and in total profits or an increase in the wage share. s shown in Figure 6, with an elasticity of substitution equal to, increasing efficiency in platform production leads to excess platform growth a fall in total steady state output/consumption. Since this is associated with a decline in profits the wage share increases. 25

27 Figure 6: More efficient platform creation with high EoS ( ε = ) 4. The cooperative household solution In this section we discuss the household optimisation problem under the cooperative solution. Households organise sharing among themselves. They still charge each other a utilisation fee (a market price, which has an important coordinating function in the case of scarcity. I. e. there must still be a mechanism which allocates the good to those households which are in most urgent need of the good). However, what is different is the way in which production is organised. Individual households supply labour to a cooperative producer (sharing company) and they do not receive a wage. However, they receive the revenue from the user fees, in proportion to the labour input. The profits of the cooperative firm in sector j are now given by π j C = (P u um C t ) = ( ε um C t ) = ( ε u M C t ) (2) 26

28 Notice, in contrast to the capitalist firm, the cooperative firm does not pay any wages for fixed labour input per period, therefore period profits are equal to revenue. The decision problem of the household differs in one important way. While under the capitalist solution the household makes a separate investment decision into the optimal number of designs and total labour input. Under the cooperative household solution the household makes a joint decision on and the labour input supplied to the sharing sector. In making this joint decision, the household takes into account that a change in has implications on the marginal revenue from labour in the sharing sector. In particular the household takes into account that total labour input in the sharing sector is given by L t S = t L j u (3) nd the household optimisation problem can be formulated as follows L = t= β t U(C(C t, C S t ), L t ) t= β t λ t (B t + P jt dj ( + r t )B t + P C t C t t W k k k t L t π C jt dj t t P jt dj) (4) with kε{, S, } The FCs are identical up to the derivative w. r. t. L t S L LS = U t t P jtdj t C dj π LS λ t t LS + λ jt P t t LS + βλ jt+ t+ t LS = (5) t t dj This yields the following steady state solution for L = β t U(C(C t, C t S ), L t ) t= t β t λ t (B t + P jt dj ( + r t )B t + P C t C t W k k t L t t= t t π C jt dj P jt dj) k kε{, S, } 27

29 The FCs are identical up to the derivative w. r. t. Ls L S L = U S t L λ t t t t P jt dj π S + λ t L C jt dj P S + βλ t+ t L jt+ dj S = t L t t The individual derivatives are given as follows t P jt dj t S = L P jt S t L dj + P jt S t L = P jt S t L t t π C jt dj t S = ( L t ε ) ε 2 u M C t S L t t π C jt dj S = L t ε ε dj + ε u M C t L t S ε u M C t S L + ε u M C t S t L t t π C jt dj S = 2 ε u M C t S L t L t L S L = U S t L λ tp jt S t L + λ t2 ε u M C t S j L + βλ t+p jt+ t L j S = U L t S = W t = u t λ t = P t C C t = βλ t+ λ t = + r 28

30 This yields the following steady state solution for rp t = WL S + 2 ε u M C t rp t = WL S + 2 ε u M C t r u u u + W = 2ε u M C L t S j L t r u u L j u + u = 2 ε u M u (L L j u ) L t S r u u + u L j u = 2 ε u M u (L L j u ) (r u + L j u ) ε = 2u M (L L u j ) (r u + L j u ) ε = 2u M (L L j u ) (6) This cooperative steady state solution for can be compared to the firm solution. The following graph compares both solutions with each other Figure 7: The number of sharing services under the firm and cooperative solution 29

31 Under the cooperative solution, the utilisation sector offers more sharing varieties than under the market solution. Why is this the case? Consider the market solution. In this case workers in the utilisation sector get paid a wage which is equal to u, and owners of the firms in the utilisation sector receive a return for the provision of the durable good (and the investment made into the technology (a return is paid proportional to P ) ). Under the cooperative solution, profits are shared proportionally to the labour input, the wage in the utilisation sector exceeds the market wage for the equilibrium level of under the market solution and households are willing to increase sharing services (add varieties) until the marginal return from sharing is equal to u. t this stage it is not clear whether the cooperative solution is welfare improving. Both solutions are not dealing optimally with the externality in this economy. The externality consists of the fact that only those goods which are produced can be shared. socially optimal solution would have to deal with this externality. The market solution adds a second distortion to this economy, namely a monopoly rent due to imperfect substitutability of sharing variants. This restricts entry into the utilisation sector (the marginal product of labour in the utilisation sector exceeds the marginal product of labour in the physical production sector). However, restricting entry has the side effect of keeping the physical production sector large. The cooperative solution on the other hand allows for an equalisation of the marginal product of labour in the sharing and the physical production sector. However, because of a labour supply constraint, this reduces employment in the physical production sector and increases the externality problem. The provision of more sharing variants has an independent impact on 3

32 increasing consumer welfare, however this effect is likely to be small because of restrictions on the substitutability (lower bound on substitutability (ε > 2)) 5. The Social Planner Solution In order to compare the two proceeding organisational forms of the sharing economy in a meaningful manner, this section identifies the Social Planner Solution. This is especially important because the specific technological structure of sharing leading to ambiguous welfare effects and trade-offs. By technological structure we refer to; firstly, the fixed costs associated with platform acquisition and per period fixed costs of running the platform in absence of marginal costs, and secondly, the added welfare produced by more intensive use of the existing durable good constituting a positive externality. The trade-offs in welfare then occur, as on one hand introducing new sharing activities increase the number of sharing variants and increases consumer welfare. n the other hand, there is a resource cost associated with more variety, since platforms compete with each other for the use of a durable good (externality associated with the durable good is reduced). Therefore, it is interesting to ask whether the market solution leads to the optimal outcome and if not what policies should be invoked in order to achieve the optimum. It is also interesting to see how the capitalist solution compares to the cooperative solution. Since we know that the cooperative solution yields a larger number of varieties/platforms compared to the capitalist solution, this question boils to asking where the optimal number of variants is located. The social planner problem can be formulated in the following way L = β t log (C t + [ ( um C α α t= t ) dj] ) t= β t λ t (C t u t L t ) t t= β t θ t ( t u t L t ) t= β t φ t (L t L t L u t dj L t ) (7) So that the social planner maximises total utility of consumption, whilst taking into account that it is constrained by the durable good, the technology for producing new platforms and resource constraint on labour. 3

33 The social planer optimises w. r. t. C t, t, L t and L t β t We consider the problem where the social planer takes the symmetry of the solution into account. L = β t log (C t + C t [ α t u Mα α t= ] ) λ t ( K t u θ t L θ t K ( θ) t= t C t + ) t= β t θ t ( t u t L t ) t= β t φ t (L t L t t L u t L t ) δk t (7a) The resulting F..C. are L C = t C = λ t (8) t L K = λ t +λ t ( θ) Y t t K + βλ t+ ( δ) = (???) t L t = (+[ α t u Mα ] α ) α 2 u M βθ t+ + θ t + φ t L t u = (9) L = λ Y t L t L u t + φ t = t (2) L L = θ tu t + φ t = (2) In steady state, rearranging the resulting entry condition in terms of number of sharing variants and technology parameters then yields the following expression (ε )( + ( t ε u M )) u M ( u t ρ + L t u ) ε = (L t L t U ) (22) 32

34 Comparing the LHS of this equation with eq (9b) it is easy to see that it intersects with the RHS at a lower level of, which shows that the welfare optimising number of sharing variants * lies below both the market and cooperative results. Figure 8: The number of sharing services under the firm and social planner solution RHS /LHS RHS* RHS LHS This result implies that the number of sharing variants that optimise the externality of the available durable good through sharing and reduces the supply constraint, lies below the two organisational forms of sharing we discussed above. With a cooperative of households organising sharing among themselves being sub optimal to the market solution. Furthermore, the optimal number of sharing variants is highly dependent on the elasticity of substitution between the emerging sharing firms and reduced for higher substitutability between options. Conclusion 33

35 Sharing of durable goods is an expanding economic activity, made possible by new digital technologies. Sharing allows a more intensive use of durables at close to zero marginal cost. We have presented a model of a multi sector economy with physical production of a durable good and a sharing sector. The production sector is conventional and subject to marginal cost pricing, while the sharing sector operates at zero marginal cost (up to the time limit on usage of the durable). However, sharing is not costless for firms and requires to set up dedicated platforms at a sunk cost and there are positive per period fixed costs associated with operating the platform. We model a dynamic economy with entry into the sharing sector. Given consumer preferences for owning and sharing, prices on sharing are determined in equilibrium. We use the model to analyse how a rising sharing economy might change the stylised facts on growth. We identify three sources of technical progress in the sharing economy, namely a reduction in fixed cost for operating sharing platforms, reduced costs for platform design and an increase in the rate in which consumer durables can be utilised and we analyse their respective effects on growth, distribution (wage share) and employment. In our quantitative analysis we explore the impact on GDP, the wage share and employment in case some recent predictions on the eventual size of the sharing sector materialise. We find that an expanding sharing sector will be associated with modest net growth of GDP, a small decline of the employment rate and a small decline of the wage share. While this analysis assumes that sharing is entirely organised by profit maximising firms, the following section of the paper compares the firm solution to a case where sharing is organised by households directly. We find that with a cooperative household solution the sharing sector will be larger under identical technological conditions. The last section of the paper presents the welfare optimising solution, in which a social planner takes into account that physically produced consumer durables have additional value through sharing, which represents a positive externality not accounted for in the market and cooperative solutions. In addition, the social planner takes into account the supply constraint on sharing as the number of sharing firms increases competing for the available durable good and labour supply. We find that it is socially optimal to have fewer sharing variants than both the market and the cooperative organisations of sharing would produce, with the market solution being closer to the social optima than the cooperative. This analysis shows that the introduction of new production and consumption possibilities brought about by technological developments, that enabled the emergence and growth of the 34