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Indeterminacy, Bifurcations and Chaos in an Overlapping Generations Model with Negative Environmental Externalities
No full textWe analyze an overlapping generations model where agent’s welfare depends on three goods: leisure, environmental quality and consumption of a private good.
We assume that the production process of the private good depletes the natural resource
and that the consumption of the private good alleviates the damages due to environmental deterioration. In such context, we show that individuals’ reactions to environmental deterioration
may lead to complex dynamics, in particular to the rise of periodic orbits and chaos
Monopoly with differentiated final goods and heterogeneous markets
Full text linkThis work attempts to characterise the dynamic properties of a nonlinear model in which a monopolist produces a fixed amount of an intermediate good. The firm employs this good in producing two vertically differentiated final commodities, sold in two distinct markets. Consumers’ preferences are described by quasi-linear and quadratic utility functions respectively yielding isoelastic and linear demand functions. In addition, we assume that the monopolist adopts a gradient adjustment rule based on profit variation to adjust its choice about the amount of intermediate good to employ in the production of each final good. Two alternative scenarios emerge: in the first, there exists coexistence of two markets; in the second, the monopolist specialises on the production of a single final good. The dynamics show that the elasticities of market demands play an ambiguous role in affecting the stability of the equilibrium, whereas the speed of adjustment unambiguously destabilises the system. Moreover, the article investigates the role of the productive capacity and the gap in marginal costs in defining the different scenarios. In particular, economic dynamics may be chaotic and/or multiple attractors may appear
Water Resource Use and Competition in an Evolutionary Model
Full text linkOver the last few years water scarcity and pollution have been rapidly growing at both regional and global level. This has generated in many cases increasing intersectoral competition over the use of a limited amount of water resources. To examine the dynamics that such competition may generate in the economy, the present paper proposes a simple dynamic evolutionary model in which two sectors (A and B) compete for the use of water and studies the impact of water pricing on the dynamics of the two sectors in the presence of a population of interacting economic agents characterized by imitative behaviors. As it emerges from the model, when water is underpriced a self-enforcing process may be observed driving the economy towards a Pareto-dominated equilibrium. In such equilibrium the economy fully specializes in sector A, characterized by the highest negative impact on the water resource, at the expenses of sector B. The paper shows that a policy of fine tuning that increases water price through the endogenous water pricing mechanism examined in the model can inhibit the convergence of the economy to such an equilibrium point and can progressively shift the system towards the less water-consuming sector. Finally, assuming a Leontief production function and performing numerical simulations, it is shown how a change in water price can affect the dynamics of the model, and that the same results hold also in a more general, three-sector context
Effects of fixed and continuously distributed delays in a monopoly model with constant price elasticity
No full textLocal and Global Indeterminacy in an Overlapping Generations Model with Consumption Externalities
No full textNew sedimentoogical data from the Villafranchian deposits of Castelnuovo Garfagnana and Barga basins (Lucca, Tuscany, Italy)
No full textThe Castelnuovo Garfagnana and Barga basins are
located about 25 km north of Lucca along the
intramontane valley of the Serchio river. They are
about 5 Km wide, 15 and IO Km respectively long
and are separated by a structural high, known in
literature as "Soglia di Monte Perpoli" (Puccinelli,
1987). These basins constitute a tectonical
extensional depression, elongated in a NW-SE
direction, delimited southwest by the Alpi Apuane
and northeast by the Apennines. The geologica!
history of the Castelnuovo Garfagnana and Barga
basins, as the other depressions formed along the
Tyrrhenian margin of the Apennine chain, is related
to the Tyrrhenian rifting, active since late Tortonian,
and the counter-clockwise migration of the chainforedeep-
foreland system (Patacca et al., 1990). The
two basins, studied since 1800 for mining of lignite
and quarrying of clay, are filled with a remarkable
thickness of continental deposits, mainly of
Villafranchian age, generically interpreted in
literature as fluvio-lacustrine (Masini, 1936; Calistri,
1974). This study aims at offering a more detailed
reconstruction of the depositional history of these
deposits. A geologica! survey 1/ 10.000 scale,
together with sedimentological and compositional
analysis and paleontological data, allow to locate
five informai litostratigraphic units, whose
geometrica! relationships are shown in Fig. l. Within
each unit, a various number of lithofacies can be
seen (Miall, 1996 and, Sanchez-Moya et al., 1996
lithofacies code are used) and their association
allows to define some architectural elements (Miall,
1996). Their features and their geometrica!
relationships give rise to a more detailed and
complex reconstruction of the depositional history of
the Vi llafranchian deposits. Sixteen conglomeratic,
heterolithic, sandy and silty-clay lithofacies were
distinguished and grouped in nine architectural
elements belonging to channel belt elements and
overbank elements. The channel belt elements
consist of conglomeratic deposits (isolated channels
!C, grave! bar GB, debris flow deposit DF),
heterolithic and sandy elements (heterolithic bar HB
and sandy bar SB), while swamp (SP), pond (PO),
levee (L) and muddy-floodplain (M) constitute the
fine-grained overbank elements. On this basis four
alluvial depositional systems can be recognized. The
basai fluvial system, corresponding to
lithostratigraphic Uni t l , li es in disconformity o n the
substratum made by the metamorphic and nonmetamorphic
"Falda Toscana" units and subordinate
"Ligurian" units. !t is composed mainly of fine-
54
grained deposits, related to overbank elements with
intercalation of conglomeratic and sandy lithosomes
(Channel belt elements). Within overbank elements
SP deposits are characterized by widespread
presence of lignite (C lithofacies) and subordinate
intercalation of clays (Fm lithofacies). Tree trunks in
life-wise position have been observed. Vegetai
remains of G/yptostrobus sp., are consistent with
humid-subtropical climatic conditions. PO element is
characterized by rhythmical alternations of clay and
silt (Fh, Fsm and Fm lithofacies) containing freshwater
taxa like ostracodes (Candona spp. 1/yocypris
gibba), gastropods (Me/anoides curvicosta,
Prososthenia paulae Theodoxus sp. Laminifera
vi/lajranchiana), teeth of fish (Tinca sp., Leuciscus
cepha/us), together with charophytes oogonia and
leaves. L and M elements consist respectively of
rhythmical alternations of fine sand, silt, clay (Sh,
Fsm, Fm lithofacies) and clay and silty-clay (Fm,
Fsm lithofacies). Widespread presence of
hydromorphic paleosols (P lithofacies) containing
land taxa (e.g. Helix sp. , Pomatias e/egans, Discus
rotundatus) is observed mainly in M element.
Channel belt elements consist of isolated channels
(IC) and heterolithic bar (HB). IC element shows a
ribbon geometry and frequently "ailes d' etalement"
(sensu Friend et al. , 1979). Width-depth ratio is
consistent with stable channels. They are composed
of polygenic, grain-supported conglomerate (Gp, Gt
and Gcm lithofacies), frequently organized in fining
upward trend. HB element shows a plane-convex
upward geometry and consists of alternations
between sand and grave! (Ep, Et, St, Sp lithofacies)
organized in fining upward trend. They represent
bars migration within the channel. Compositional
data and paleocurrent analysis (northwest to
southeast direction) are consistent with a single
longitudinal (sensu Miall, 1996) fluvial course
flowing through the two basins. The whole acquired
data is consistent with the characteristic of cohesive
sediment anabranching river system, organo-clastic
sub-type (sensu Nanson & Knighton, 1996). The
second alluvial system recognized corresponds to
lithostratigraphic Uni t 2 (Fig. l). Unlike the
underlying system, Unit 2 is mainly composed of
conglomerates (channel belt elements), while finegrained
deposits (overbank elements) are
subordinate. GB and SB elements constitute channel
belt elements. GB element is made up of openwork
and matrix-filled conglomerates (Gp and Gt
lithofacies), frequently organized in fining upward
trend. Reactivation surfaces are frequently observed. SB element consists of medium to coarse-grained
sand (Sp and St lithofacies) sometimes containing
clay soft clasts. GB and SB associations are
interpreted to represent bars migration within the
channel. L and M elements constitute the overbank
elements. They are respectively characterized by fine
to medium-grained sand (Sh and Sr lithofacies) and
by drapes of clay (Fm lithofacies), while immature
paleosols (P lithofacies) are common in M element.
L and M deposits show strong affinities with the
actual overbank deposits of Serchio river. Deposits
belonging to this unit are related to a gravel bed load
braided system (sensu Sanchez-Moya et al., 1996).
Compositional and paleocurrent analysis point out
more or less the same longitudinal fluvial course,
flowing through the two basins, observed for the
underlying cohesive anabranching river system
organo-clastic sub-type. Along the Castelnuovo
Garfagnana and Barga margins, spatially limited
conglomeratic lithosome, showing latero-vertical
relationships with Unit l and 2 (Fig. l) are mapped.
Lithostratigraphic Unit 3 crops out along the
Apennine margin of the two basins. !t consists of
channel belt elements of very coarse massive
monogenic conglomerate (Gcm and Gmm
lithofacies), exclusively derived from the
surroundings "Macigno" F ormation. The same
textural characteristics were observed in the
litostratigraphic Unit 4 (Fig. l) cropping out in a
small area of the southwest margin of the Barga
basin. Besides "Macigno" clasts, the conglomerate is
also composed of deriving "Falda Toscana" and
Methamorphic units clasts. The close proximity of
source area and textural features are consistent with a
debris flow dominated fan (sensu Stanistreet & Mc
Carthy, 1993) developed transversally to the basi n' s
axis. The lithostratigraphic Unit 5 crops out in the
southwest margin of the Castelnuovo Garfagnana
basin and consists of channel belt elements.
Lithofacies Gp, Gt e Sm, (polygenic, clast supported
conglomerate and medium-coarse grained sand)
representing the composition of surrounding area are
associated in GB element. Paleocurrent analysis
shows a radiai pattem. This unit is interpreted as a
braided fluvial fan alluvial system (sensu Stanistreet
& McCarthy, 1993) developed transversally to the
basin 's axis. The whole acquired data lead to
delineate the depositional history of villafranchian
deposits cropping out in the Castelnuovo Garfagnana
and Barga basins. The results of this study can be
summarized in two principal points: i) onset, in a
humid sub-tropical climate phase, of a first alluvial
system, flowing through the two basins and related
to a cohesive sediment anabranching river (sub-type
organo-clastic) characterized by a prevalent finegrained
overbank organic-rich sedimentation. At the
same time coalescent debris flow dominated fan,
mainly derived from Apennines margin, forms
transversally to the basins axis. ii) Development of a
gravel bed load braided alluvial system,
characterized by prevalent gravelly channel belt
deposits, flowing through the two basins. The
erosive contact between this system and the
underlying one, is an abrupt facies change inferring a
possible disconformity surface. At the same time
debris flow dominated fans derived from the
Apennines margin continue to develop. Although the
proposed reconstruction involves the necessity of a
disconformity surface also within these deposits, the
spatially limited outcrops and the frequently
weathering do not permit to evaluate this hypothesis.
During this depositional phase a braided fluvial fan
derived from the Apuan Alps develops transversally
in the Castelnuovo Garfagnana basin. This
palaeoenvironment reconstruction implies that
Monte Perpoli high plays a different role compared
to that proposed by other authors. In our
interpretation, according to the sedimentological and
statistica! compositional data (Sodini M. et al.,
2002), this area acted as a sedimentary by-pass since
the opening (Lower Villafranchian) of the
Castelnuovo Garfagnana and Barga basins. This
interpretation is consistent with most recent data
about Alpi Ar uane uplift times (Molli G., 2001)
The Villafranchian deposits of the Castelnuovo Garfagnana and Barga Basins (Lucca, Tuscany, Italy): facies analysis and paleoenviromental reconstruction
No full textA facies analysis of the Villafranchian continental
deposits outcropping in the Castelnuovo Garfagnana and Barga
basins allow the reconstruction of their paleoenvironmental
evolution that differs significantly from the traditional fluvio-
lacustrine interpretation. We identify, at different stratigraphic
positions, two main river systems and some tributaries
which flowed longitudinally and laterally to the axis of
the two basins respectively, the latter fed both by the Apuan
and Apennine margins. The mapped deposits were subdivided
in five lithostratigraphic units (U1-5). Lying in disconformity
on the substratum U1 corresponds to a cohesive sediment
anabranching river (sub-type organo-clastic) developed
longitudinally to the axis of the two basins in a humid subtropical
climate phase. It is characterized by abundant fine
organic-rich deposits and lignite accumulation (overbank elements)
and by conglomeratic facies (channel-belt elements).
An abrupt facies change characterizes the contact between U1
and overlying U2 that is constituted by prevalent conglomeratic
deposits (channel-belt elements) and interpreted as a
gravel bed-load braided river. U3, U4 and U5 correspond to
coalescent fan systems developing transversally to the axis of
the two basins. U3 and U4 were interpreted as debris flow
dominated fans exclusively, (U3), or prevalently, (U4), constituted
by «Macigno» clasts while U5 corresponds to a braided
fluvial fan mainly characterized by a high variety of metamorphic
clasts. Their influence, as transversal tributaries of
the main longitudinal river systems, results both from compositional
statistical analyses of conglomeratic deposits and
from survey evidences. This paleoenvironmental reconstruction
implies that Monte Perpoli high («Soglia di Monte Perpoli
» Auctt.) acted as a sedimentary by-pass since the opening
of the Castelnuovo Garfagnana and Barga basins
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