Aggregate Growth Model Research Articles

Structural Change, Aggregate Demand and Employment Dynamics in the OECD, 1970-2010

The paper combines Baumol’s model of structural change with a model of aggregate demand growth in the Keynesian-Kaleckian tradition to predict the dynamics of aggregate employment. The model for the demand regime is estimated with – and Baumol’s model for the productivity regime is calibrated on – OECD data. The trajectory for employment predicted by the combination of the two models tracks the actual employment dynamics in the OECD over the period 1970-2010 remarkably well.

On the Nature of Suppes-Sen Choice Functions in an Aggregative Growth Model

This paper investigates the nature of paths in the standard neoclassical aggregative model of economic growth that are maximal according to the Suppes-Sen grading principle. This is accomplished by relating such paths to paths which are utilitarian maximal when an increasing (but not necessarily concave) utility function evaluates each period’s consumption. An example is presented in which an explicit form of a consumption function is described, which generates only Suppes-Sen maximal paths. This consumption function is shown to generate consumption cycles, and violate the Pigou-Dalton transfer principle.

A Turnpike Theorem Involving a Modified Golden Rule

In the current study, we investigate efficient capital accumulation in a stochastic neoclassical aggregate growth model. The underlying uncertainty is driven by Brownian-motion shocks and the major results do not rely on the specification of production functions. The stochastic balanced path of the capital- labor ratio is naturally derived by a martingale, and the corresponding modified Golden Rule path of capital accumulation is well-defined. The powerful martingale theory is thus employed, and a stochastic turnpike theorem involving the modified Golden Rule is proved. That is, the underlying path of capital accumulation is asymptotically efficient in the sense of consumption maximization. We focus on asymptotic turnpike theorems and our turnpike theorem only relies on the requirement that the modified Golden-Rule path of capital accumulation is reachable in any almost surely finite Markov time. Finally, it is asserted that the modified Golden-Rule path of capital accumulation indeed provides us with a robust turnpike under very weak assumptions.

Different types of phase separation in binary monolayers of long chain alkyltrichlorosilanes on silicon oxide

In the present work, we studied the growth and morphology of binary monolayers made with triacontyltrichlorosilane (C30H61SiCl3) as the long chain and hexadecyltrichlorosilane (C16H33SiCl3), octadecyltrichlorosilane (C18H37SiCl3) or eicosyltrichlorosilane (C20H41SiCl3) as the short chain according to the deposition conditions on silicon oxide, using mainly atomic force microscopy, ellipsometry, and contact angle measurements. We distinguished three types of different phase separation. Besides the classical phase separation by islands of long chains in a surrounding phase of shorter molecules, we observed a separation involving dendritic “filaments” of long chains in a shorter chain phase, regardless of the couple of molecules studied. A third sort of phase separation also appears in the case of triacontyltrichlorosilane with octadecyltrichlorosilane or eicosyltrichlorosilane: formation of “holes”, i.e. islands of the shorter molecule in a surrounding phase of long chains. We obtained “hole” and “filament” type phase separation only by working below a critical temperature, which depends on the molecule length. Moreover, the level of ambient relative humidity was shown to have an impact on “hole” versus “filament” phase separation types. We then showed that for phase separation by islands or holes the composition of binary monolayers (RSAM) prepared at low humidity (18% RH) is almost the same as that of the silanisation solution (Rsol). Conversely, for SAMs prepared at high humidity (45% RH) RSAM is always lower than Rsol whatever the type of phase separation by islands or holes. Moreover, concerning phase separation with C30 filaments we observed that RSAM is independent from both the nature of the short molecule and the humidity conditions. Considering a diffusion limited aggregation growth model, we found that at high humidity the monolayer growth is mainly driven by the diffusion coefficient, while at low humidity the deposition rate from solution is the leading parameter of the growth. The efficiency of phase separation is also addressed.

On the nature of Suppes–Sen maximal paths in an aggregative growth model

This article investigates the nature of paths in the standard neoclassical aggregative model of economic growth that are maximal according to the Suppes–Sen grading principle. This is accomplished by relating such paths to paths which are utilitarian maximal when an increasing (but not necessarily concave) utility function evaluates each period’s consumption. Dynamic properties of Suppes–Sen maximal paths, which lie entirely above or entirely below the golden-rule, are analyzed. An example is presented in which an explicit form of a consumption function is described, which generates only Suppes–Sen maximal paths. This consumption function is shown to generate consumption cycles, and violate the Pigou–Dalton transfer principle.

Stochastic Versions of Turnpike Theorems in the Sense of Uniform Topology

In this paper, a stochastic endogenous aggregative growth model is constructed and two main results are established, based on endogenous horizon of the economy and endogenous terminal capital stock, which is also efficient capital accumulation in some sense. First, strong turnpike theorems under uncertainty and in the sense of uniform topology are obtained; second, inefficacy of temporary fiscal policy, which is chosen to be capital income taxation, has been demonstrated in comparatively weak conditions different from Yano (1998)'s.

Equivalence of utilitarian maximal and weakly maximal programs

For a class of aggregative optimal growth models, which allow for a non-convex and non-differentiable production technology, this paper examines whether the set of utilitarian maximal programs coincides with the set of weakly maximal programs. It identifies a condition, called the Phelps–Koopmans condition, under which the equivalence result holds. An example is provided to demonstrate that the equivalence result is invalid when the Phelps–Koopmans condition does not hold.

Rules of the population distribution of China and its evolution mechanism

The characteristics of the population distribution of China is analyzed based on the method of statistical physics. The results show that in the last 20 years, the total population of China increases roughly exponentially with time and the growth rate is found to be slowing down. The population distribution in provinces, cities or counties follows approximately the same rule: the population distribution changes slowly for small k, while it changes rapidly for large k and the distribution obeys the Zipf's law. This shows that the population distribution of China has self-similarity. A solvable model of migration-driven aggregate growth based on scale-free network is also proposed to simulate the population size distribution of China. It is found that the theoretical results are in good agreement with the realistic data.

Stimuli-Responsive Controlled Growth of Mono- and Bidimensional Particles from Basic Zirconium Sulfate Hydrosols

A thermostimulated sol-gel transition in a system prepared by mixing a ZrOCl(2) acidified solution to a hot H(2)SO(4) aqueous solution was studied by dynamic rheological measurements and quasi-elastic light scattering. The effect of temperature and of molar ratio R(S) = [Zr]/[SO(4)] on the gelation kinetics was analyzed using the mass fractal aggregate growth model. This study shows that the linear growth of aggregates occurs at the early period of transformation, while bidimensional growth occurs at the advanced stage. The bidimensional growth can be shifted toward monodimensional growth by decreasing the aggregation rate by controlling the temperature and/or molar ratio R(S). EXAFS and Raman results gave evidence that the linear chain growth is supported by covalent sulfate bonding between primary building blocks. At the advanced stage of aggregation, the assembly of linear chains through hydrogen bonding gave rise to the growth of bidimensional particles.

Asset Pricing and Productivity Growth: The Role of Consumption Scenarios

The paper analyzes the performance of asset prices implied by an aggregate macroeconomic growth model under two different consumption hypotheses: overlapping generations of agents with two period lives versus the infinitely lived agent. The production side of the economy is described by a random growth model with a competitive labor market and an exogenously given random dividend payout ratio. For an isoelastic technology with multiplicative production shocks this implies a random dynamical system for the firm's rate of profit with a unique asymptotically stable random fixed point for a large class of productivity growth and dividend payout ratio processes. Based on an extensive numerical study of stationary solutions we show that the two consumption scenarios imply a limited number of diverse effects regarding equity and bond returns and equity premia.

Kinetics of aggregation growth with competition between catalyzed birth and catalyzed death

An aggregation growth model of three species A, B and C with the competition between catalyzed birth and catalyzed death is proposed. Irreversible aggregation occurs between any two aggregates of the like species with the constant rate kernels In(n = 1,2,3). Meanwhile, a monomer birth of an A species aggregate of size k occurs under the catalysis of a B species aggregate of size j with the catalyzed birth rate kernel K(k,j) = Kkjv and a monomer death of an A species aggregate of size k occurs under the catalysis of a C species aggregate of size j with the catalyzed death rate kernel L(k,j)=Lkjv, where v is a parameter reflecting the dependence of the catalysis reaction rates of birth and death on the size of catalyst aggregate. The kinetic evolution behaviours of the three species are investigated by the rate equation approach based on the mean-field theory. The form of the aggregate size distribution of A species ak(t) is found to be dependent crucially on the competition between the catalyzed birth and death of A species, as well as the irreversible aggregation processes of the three species: (1) In the v < 0 case, the irreversible aggregation dominates the process, and ak(t) satisfies the conventional scaling form; (2) In the v ⩾ 0 case, the competition between the catalyzed birth and death dominates the process. When the catalyzed birth controls the process, ak(t) takes the conventional or generalized scaling form. While the catalyzed death controls the process, the scaling description of the aggregate size distribution breaks down completely.

Gold nanoparticles decorated with oligo(ethylene glycol) thiols: kinetics of colloid aggregation driven by depletion forces

We have studied the kinetics of the phase-separation process of mixtures of colloid and protein in solutions by real-time UV-vis spectroscopy. Complementary small-angle X-ray scattering (SAXS) was employed to determine the structures involved. The colloids used are gold nanoparticles functionalized with protein resistant oligo(ethylene glycol) (OEG) thiol, HS(CH2)11(OCH2CH2)6OMe (EG6OMe). After mixing with protein solution above a critical concentration, c*, SAXS measurements show that a scattering maximum appears after a short induction time at q = 0.0322 A-1, which increases its intensity with time but the peak position does not change with time, protein concentration and salt addition. The peak corresponds to the distance of the nearest neighbor in the aggregates. The upturn of scattering intensities in the low q-range developed with time indicating the formation of aggregates. No Bragg peaks corresponding to the formation of colloidal crystallites could be observed before the clusters dropped out from the solution. The growth kinetics of aggregates is followed in detail by real-time UV-vis spectroscopy, using the flocculation parameter defined as the integral of the absorption in the range of 600-800 nm wavelengths. At low salt addition (<0.5 M), a kinetic crossover from reaction-limited cluster aggregation (RLCA) to diffusion-limited cluster aggregation (DLCA) growth model is observed, and interpreted as being due to the effective repulsive interaction barrier between colloids within the depletion potential. Above 0.5 M NaCl, the surface charge of proteins is screened significantly, and the repulsive potential barrier disappeared, thus the growth kinetics can be described by a DLCA model only.

Competition between the catalyzed birth and death in the exchange-driven growth

We propose a three-species ( A , B , and C ) exchange-driven aggregate growth model with competition between catalyzed birth and catalyzed death. In the system, exchange-driven aggregation occurs between any two aggregates of the same species with the size-dependent rate kernel Kn(k,j)=Knkj (n=1,2,3) , and, meanwhile, monomer birth and death of species A occur under the catalysis of species B and C with the catalyzed birth and catalyzed death rate kernels I(k,j)=Ikjv and J(k,j)=Jkjv , respectively. The kinetic behavior is investigated by means of the mean-field rate equation approach. The form of the aggregate size distribution ak(t) of species A is found to depend crucially on the competition between species- B -catalyzed birth of species A and species- C -catalyzed death of species A , as well as the exchange-driven growth. The results show that (i) when exchange-driven aggregation dominates the process, ak(t) satisfies the conventional scaling form; (ii) when catalyzed birth dominates the process, ak(t) takes the conventional or generalized scaling form; and (iii) when catalyzed death dominates the process, the aggregate size distribution of species A evolves only according to some modified scaling forms.

Mutually catalyzed birth of population and assets in exchange-driven growth

We propose an exchange-driven aggregation growth model of population and assets with mutually catalyzed birth to study the interaction between the population and assets in their exchange-driven processes. In this model, monomer (or equivalently, individual) exchange occurs between any pair of aggregates of the same species (population or assets). The rate kernels of the exchanges of population and assets are K(k,l) = Kkl and L(k,l) = Lkl , respectively, at which one monomer migrates from an aggregate of size k to another of size l. Meanwhile, an aggregate of one species can yield a new monomer by the catalysis of an arbitrary aggregate of the other species. The rate kernel of asset-catalyzed population birth is I(k,l) = Iklmu [and that of population-catalyzed asset birth is J(k,l) = Jklnu], at which an aggregate of size k gains a monomer birth when it meets a catalyst aggregate of size l . The kinetic behaviors of the population and asset aggregates are solved based on the rate equations. The evolution of the aggregate size distributions of population and assets is found to fall into one of three categories for different parameters mu and nu: (i) population (asset) aggregates evolve according to the conventional scaling form in the case of mu < or = 0 (nu < or = 0), (ii) population (asset) aggregates evolve according to a modified scaling form in the case of nu = 0 and mu > 0 (mu = 0 and nu > 0 ), and (iii) both population and asset aggregates undergo gelation transitions at a finite time in the case of mu = nu > 0.

Poverty traps, aid, and growth

This paper examines the empirical relevance of the poverty trap view of underdevelopment. We calibrate simple aggregate growth models in which poverty traps can arise due to either low saving or low technology at low levels of development. We then assess the empirical relevance of these specific mechanisms and their consequences for policy. We find little evidence of the existence of poverty traps based on these two mechanisms. When put to the task of explaining the persistence of low income in African countries, the models require either unreasonable values for key parameters, or else generate counterfactual predictions regarding the relations between key variables. These results call into question arguments in favour of a large scaling-up of aid to the poorest countries that are premised on the existence of such poverty traps.

Aggregate growth driven by monomer transfer

We propose a solvable aggregate growth model with the rate kernelK(i;j;l)∝iμjνlϖ (ϖ⩾0), at which a monomer transfers from the A aggregate of size i to the A aggregate of size j only with the help of a B aggregate of size l. By means of the mean-field rate equation approach, we obtain the analytical solutions of the aggregate size distributions in several different cases. For a symmetrical system with μ = ν, the aggregate size distributionak(t) approaches the conventional scaling form in the μ<3/2 case; while for an asymmetrical system with μ≠ν, ak(t) takes the scaling form only in the case of μ<ν and μ+ν<2. As for the case with μ+ν>2 (μ≠ν) or μ>3/2 (μ = ν), the system may have a gelationlike transition. Moreover, we also study the kinetic scaling behaviour of the model with the generalized kernelK(i;j;l)~(iμjν+iνjμ)lϖ. The aggregate size distribution obeys a scaling law only in the μ+ν<3 case; while in other cases, the system may undergo a gelationlike transition after a sufficiently long time.

Synthesis of monodisperse fluorescent core-shell silica particles using a modified Stöber method for imaging individual particles in dense colloidal suspensions

Core-shell silica particles, with a diameter of 1.5 μm, containing a dye fluorescein isothiocyanate (FITC), are synthesized by the hydrolysis and condensation of tetraethylorthosilicate (TEOS). Sodium dodecyl sulfate (SDS) is added to synthesize fluorescent core particles with the diameter of approximately 1 μm. In the addition of SDS, the surface charge reduced by counterions (Na +) of the surfactant leads to a higher degree of aggregation of the primary particles and the formation of larger secondary particles. The particle growth kinetics confirms the aggregation growth model for the synthesis of monodisperse silica particles, and also shows the dependence of final particle size on colloidal stability resulting from the addition of SDS. Light and X-ray scattering data reveal that the final particles have compactly packed structures with smooth surfaces. The seeded growth technique is then used to form a silica shell layer on the fluorescent core. The added amount of water and NH 4OH has significant effects on shell formation. Finally, the final core-shell silica particles are modified by chemisorption of octadecanol at the surface to be dispersed in organic solvents. Octadecyl-coated silica particles are sterically stabilized in silica index-matching solvents such as chloroform and hexadecane to directly image separate particles using confocal microscopy. In chloroform, the organophilic silica particles disperse well, whereas in hexadecane they form a volume-filling gel structure at room temperature.

Dynamic Structure, Exogeneity, Phase Portraits, Growth Paths, and Scale and Substitution Elasticities

AbstractThe paper studies autonomous dynamic systems that allow for the existence of economic growth per capita without dynamically generating explosive solutions. The implications of any degree of homogeneity, including increasing returns to scale in production, must be carefully examined in two and higher dimensions. The necessity of introducing some exogenous state variables is demonstrated within homogeneous dynamic systems. The authors solve and demonstrate the dynamic implications of scale and the substitution elasticities in various basic (two‐factor) and augmented (multifactor) aggregate growth models.

Publicly Funded Education and Human Capital in the Presence of a Convex-Concave Education Function

This study investigates an aggregative optimal growth model in which short-lived individuals obtain their labour skill through education. The process of human capital formation is described by an increasing, convex-concave education function relating the success rate to the educational expenditure per student. The cost of education is publicly funded by an income tax imposed on adult workers. Despite the apparent regularity and rationality of this idealized economy, it is shown that the existence of the steady state of the model is not guaranteed. In fact, the steady state only exists for carefully chosen social time rates of preference. However, the steady state, if it exists, is unique and in terms of local stability, a saddle point.

液相におけるナノ粒子のサイズ形態制御機構に関する一考察

Insights have been given into basic problems in understanding of underlying mechanisms for size and shape control of nanoparticles in liquid phases on five major topics of current nanotechnology: applicable systems of the fundamental equation for size control, limits of Nielsen's chronomal analysis in its application to growth mechanisms, contradictions involved in the aggregative growth model of monodispersed particles, a new idea on the mechanism of particle growth in W/O microemulsions, questions on the soft-template model of surfactants for the anisotropic growth of metallic nanoparticles.