Creative Capital, Information &Communication Technologies, & Economic

Growth in Smart Cities

by

Amit BatabyalRochester Institute of Technology

&

Peter NijkampTinbergen Institute, Amsterdam

1. Introduction1.1. A definition

Definition of smart city in 2 parts:(i) vision of urban development whose goal is toutilize ICTs to manage city’s assets & improve itsperformance(ii) metropolitan area in which large share of adultpopulation has college degree

3 findings from literature review:(i) extant literature on smart cities is typicallyeither empirical or based on case studies(ii) literature paid almost no attention to workingof smart cities from theoretical standpoint(iii) even though smart cities possess abundanceof Florida’s creative capital, no theoretical studiesthat link use of creative capital & ICTs toeconomic growth in smart city

Objectives of this paper:(i) theoretically analyze nexuses between creativecapital, ICTs, & economic growth in stylizedsmart city

(ii) delineate dynamic model adapted fromMankiw et al. (1992) & derive closed-formexpressions for 3 growth related metrics

(iii) use metrics to show smart city convergesto BGP & compute growth rate of output pereffective creative capital unit on BGP

(iv) compute BGP values of ICT & skills pereffective creative capital unit

(v) study how heterogeneity in initial conditionsaffects outcomes on BGP by introducing smartcity into analysis; at time 2 key savingsrates in city are assumed to be twice as large asin city

(vi) compute ratio of BGP value of income percreative capital unit in city to value in city

(vii) for same values of 4 savings rates, computeratio of BGP value of skills per creative capitalunit in city to value in city

2. The Theoretical Framework

Consider stylized smart city that producesknowledge good at time

Knowledge good also final consumption goodwhose price is unity at all time points

Inputs used to produce knowledge good are ICTs& creative capital units denoted by &

Skills or smartness possessed by individualcreative capital units denoted by

In addition to ICTs, there’s another technologythat augments (makes more productive) individualcreative capital units

Creative capital augmenting technology is & denotes effective creative capital unit

Production function for output is

(1)

where &

Dynamics of 4 inputs used to produce knowledgegood given by

(2)

(3)

(4)

(5)

where &

is constant fraction of output of final

consumption good saved to create more ICTs(skills) in smart city

Initial values of 4 inputs & given & are all positive

Values of output, ICTs, & skills per effectivecreative capital unit (intensive values) are givenby &

3. One Smart City3.1. Three growth metrics3.1.1. An expression for q(t)

Substituting (1) into definition of we get

(6)

Using definitions of & rewrite (6) as

(7)

Simplifying (7), we get

(8)

3.1.2. An expression for

Differentiating defining equation for w.r.t.time & then simplifying, we get

(10)

Substituting from (2), (3) & (4) into (10) & thensimplifying, we get

(11)

Substitute from (8) into (11); we getexpression we seek

(12)

3.1.3. An expression for

Differentiating defining equation for w.r.t.time & simplifying, we get

(14)

Substituting from (2), (3), & (5) into (14) &simplifying, we get

(15)

Substituting from (8) into (15) givesexpression we seek

(16)

3.2. Convergence to a BGP

To show convergence, need to study properties ofpoints in space where &

Setting in (12), we get

(17)

Computations show locus is upwardsloping & concave in space

Setting in (16), we get

(18)

Computations show locus is upwardsloping & convex in space

Figure 1: Smart city converges to BGP

      c(t)                         dc/dt=0       

                                                                                         E 

                                                                                                 

                                                                                  ds/dt=0 

 

 

 

 

                                                                                                         s(t) 

Findings:(i) economy of smart city converges to stableBGP at point

(ii) excluding origin where stable BGP at is unique

(iii) is constant on BGP; so ICTper creative capital unit or mustbe growing at same rate as creative capitalaugmenting technology which is

(iv) skills or smartness per effective creativecapital unit or is constant onBGP; so, skills per creative capital unit or

must be growing at same rate ascreative capital enhancing technology which is

Analysis shows output of knowledge good percreative capital unit in smart city also grows atrate on BGP

3.3. BGP values of c(t) & s(t)

Denote two BGP values of interest by &

Working with (17), (18) & then performingseveral algebraic steps, we get

(21)

Substituting expression for from (21) into(17) & then simplifying, we get

(24)

4. Two Smart Cities4.1. Ratio of BGP value of income per effectivecreative capital unit in city A to city B

To study effect of heterogeneity, focus on 2 smartcities &

Smart city different from smart city in 2ways; & twice as large in city as in city

Need 2 more assumptions for tractable analysis:(i) apart from above 2 differences, cities & identical in all other respects

(ii) parameters &

Want to compare output of consumption good pereffective creative capital unit in cities &

Using (8), ratio of output of knowledge good onBGP in smart city to that in smart city is

(25)

Using & simplifying (21) & (24),we get

(28)

Substituting & in (28), we

get

Finding 1: even though smart city saves onlytwice amount that smart city does to createmore ICTs & skills, 2-fold initial difference leadsto 32-fold difference in BGP output per effectivecreative capital unit

Finding 2: relatively small initial differences in 2savings rates lead to magnified impact on BGPvalues of output per effective creative capital unit

One way of measuring extent to which city issmart is to look at skills or smartness possessedby creative capital units in this city

Question: how do initial differences in & in

cities & affect ratio of BGP value of skillsper effective creative capital unit in these cities?

4.2. Ratio of BGP value of skills per effectivecreative capital unit in city A to city B

Can show that BGP ratio of skills (smartness) incity to those in city is

(29)

Substituting & in (29), we get

Finding 1: even though smart city saves onlytwice amount that smart city does to createmore ICTs & skills, 2-fold initial difference leadsto 64-fold difference in BGP value of skills pereffective creative capital unit

Finding 2: relatively small initial differences in 2savings rates lead to magnified effect on BGPvalues of skills or smartness per effective creativecapital unit

Policy implications:(i) raising fraction of output of final consumptiongood used to generate more ICTs & skills increative capital units now will yield magnifiedbenefits in terms of increased output & skills pereffective creative capital unit later

(ii) consider smart city lagging another smart cityin terms of output & skills per effective creativecapital unit; for such city to get ahead, it will needto increase 2 constant fractions of output or,equivalently, 2 savings rates denoted by &

(iii) size of magnification effect on output & skillscan be computed by policymaker in smart city forgeneral case of m-fold initial difference betweenrelevant savings rates in any 2 smart cities

(iv) suppose & where is

arbitrary positive integer greater than 2; in this

case, &

5. Conclusions

examined nexuses between creative capital,ICTs, & economic growth in stylized smart city

showed smart city economy converged toBGP & computed growth rate of output pereffective creative capital unit on BGP

computed BGP values of ICT & skills pereffective creative capital unit

studied how heterogeneity in initial conditionsinfluenced outcomes on BGP by introducingsecond smart city into analysis

Extension 1: analyze economic growth in 2 ormore heterogeneous smart cities when cities arelinked either via trade over space or throughharmonization of, for instance, tax policy

Extension 2: embed economies of smart cities instochastic environment & analyze impactuncertainty in temporal evolution of ICTs &/orskills has on growth prospects of these economies