Cost reducing investiment, competition and industry dynamics

We characterize the dynamic equilibrium path ofa competitive industry with free entry and exit, where atomistic fmns undertake investment over time in order to reduce their future production costs. Investment reduces both total as well as marginal cost of production; however, the associated dynamic scale economies are eventually bounded. Cost reduction is deterministic and there are no inter-firm spill-overs. Marginal cost in any time period is stricdy increasing in output and active firms incur a positive fixed cost even if no output is produced. The industry equilibrium path is socially optimal. Equilibrium prices are (weakly) decreasing over time. Firms invest in cost reduction and eam negative net profit when they are young. In later periods, they face prices aboye their mínimum average cost, produce beyond their mínimum efficient scale and eam strictly positive net profit. No frrm enters after the initial time periodo Though all fmns are ex ante identical, sorne fmns may exit before others (shake-out). Exiting fmns have relatively "small size" compared to incumbents; as the industry matures, concentration and the average size of incumbent fmns increase. Heterogeneity in behaviour and size of fmns emerges endogenously through differences in their length of stay in the industry

Dynamic optimization with a nonsmooth, nonconvex technology: The case of a linear objective function

This paper studies a one-sector optimal growth model with linear utility in which the production function is only required to be increasing and upper semicontinuous. The model also allows for a general form of irreversible investment. We show that every optimal capital path is strictly monotone until it reaches a steady state; further, it either converges to zero, or reaches a positive steady state in finite time and possibly jumps among different steady states afterwards. We establish conditions for extinction (convergence to zero), survival (boundedness away from zero), and the existence of a critical capital stock below which extinction is possible and above which survival is ensured. These conditions generalize those known for the case of S-shaped production functions. We also show that as the discount factor approaches one, optimal paths converge to a small neighborhood of the capital stock that maximizes sustainable consumption.Nonconvex, nonsmooth, and discontinuous technology, Extinction, Survival, Turnpike, Linear utility

A Nonsmooth, Nonconvex Model of Optimal Growth

This paper analyzes the nature of economic dynamics in a one-sector optimal growth model in which the technology is generally nonconvex, nondifferentiable, and discontinuous. The model also allows for irreversible investment and unbounded growth. We provide sufficient conditions for boundedness, extinction (convergence to zero), survival (boundedness away from zero), and unbounded growth. These conditions reveal that boundedness and survival are symmetrical phenomena, so are extinction and unbounded growth. Since many of the conditions are only local, it is possible that extinction occurs from small capital stocks, while unbounded growth occurs from large capital stocks. We also show that in most cases, if the discount factor is close to one, any optimal path from a given initial capital stock converges to a small neighborhood of what we define as the golden rule capital stock. If this stock is not finite, i.e., if sustainable consumption is maximized at infinity, then as the discount factor approaches one, unbounded growth at least almost occurs.Nonconvex, nonsmooth, and discontinuous technology; Optimal growth; Unbounded growth; Extinction; Neighborhood turnpike

A nonsmooth, nonconvex model of optimal growth

This paper analyzes the nature of economic dynamics in a one-sector optimal growth model in which the technology is generally nonconvex, nondifferentiable, and discontinuous. The model also allows for irreversible investment and unbounded growth. We develop various tools to overcome the technical difficulties posed by the generality of the model. We provide sufficient conditions for optimal paths to be bounded, to converge to zero, to be bounded away from zero, and to grow unboundedly. We also show that under certain conditions, if the discount factor is close to one, any optimal path from a given initial capital stock converges to a small neighborhood of the golden rule capital stock, at which sustainable consumption is maximized. If it is maximized at infinity, then as the discount factor approaches one, any optimal path either grows unboundedly or converges to an arbitrarily large capital stock.Nonconvex, onsmooth, and discontinuous technology; Optimal growth; Unbounded growth; Extinction; Neighborhood turnpike

Cost reducing investiment, competition and industry dynamics.

We characterize the dynamic equilibrium path ofa competitive industry with free entry and exit, where atomistic fmns undertake investment over time in order to reduce their future production costs. Investment reduces both total as well as marginal cost of production; however, the associated dynamic scale economies are eventually bounded. Cost reduction is deterministic and there are no inter-firm spill-overs. Marginal cost in any time period is stricdy increasing in output and active firms incur a positive fixed cost even if no output is produced. The industry equilibrium path is socially optimal. Equilibrium prices are (weakly) decreasing over time. Firms invest in cost reduction and eam negative net profit when they are young. In later periods, they face prices aboye their mínimum average cost, produce beyond their mínimum efficient scale and eam strictly positive net profit. No frrm enters after the initial time periodo Though all fmns are ex ante identical, sorne fmns may exit before others (shake-out). Exiting fmns have relatively "small size" compared to incumbents; as the industry matures, concentration and the average size of incumbent fmns increase. Heterogeneity in behaviour and size of fmns emerges endogenously through differences in their length of stay in the industry.Cost Reduction; Investment; Learning; Dynamic Competitive Equilibrium; Shake Out;

Investment, Externalities & Industry Dynamics.

We provide an alternative theoretical explanation for a number of empirical regularities relating to the dynamics of industry structrure (product life cycle) and changes in size and age distribution of firms over time. We explain why entry may continue over a considerable period of time, why shake out of firms occur in mature industries and why exiting firms are likely to be younger and smaller in size than incumbents. Unlike the existing theoretical literature, this explanation is not based on uncertainty, structural non-stationarity or incomplete information. We consider an infinite horizon, complete information, deterministic competitive industry with continuum of firms and stationary market demand. Firms have perfect foresight, may enter or exit the industry at any point of time and active firms undertake investment which reduces their future cost of production. Investment by active firms also leads to the growth of an industry-wide capital that reduces production cost of all firms (externality). The marginal cost curves are upward sloping and firms incur a fixed cost of staying in the industry. While all entering firms earn zero intertemporal net profit, their instantaneous net profit is typically negative when they are young and strictly positive when they mature. Positive profits may persist in the long run. Equilibrium prices decline over time while the level of positive industry-wide externality increases with time.The equilibrium path makes firms indifferent between alternative entry and exit decisions. Their investment levels after entry reflects their length of stay & the nature of industry environment (prices, externalities) over their period of stay in the industry. Heterogeneity emerges out of deliberate choice. The industry stabilizes in the long runIndustry Dynamics, Entry, Shake out, Cost Reducing Investment, Learning, Spillovers, Competitive Industry.

THE ECONOMICS OF CONTROLLING A BIOLOGICAL INVASION

The paper develops a simple economic model of a biological invasion. The natural growth of the invasion is non-convex and the immediate cost of controlling the invasion depends on the level of current control as well as the current size of the invasion. Greater control raises control costs today while reducing damages - now and in the future. In addition, by decreasing the size of the invasion, increased control today raises the marginal cost of control in the future. As a consequence, the optimal path of an invasion is not necessarily monotonic. When the marginal control cost declines sharply with the size of invasion, it may be optimal to allow an invasion to grow naturally before it is controlled. We characterize conditions under which it is optimal to eradicate an invasive species (immediately and eventually) and conditions under which it is optimal to manage an invasion without complete eradication.Resource /Energy Economics and Policy,

On Prevention and Control of an Uncertain Biological Invasion

This paper examines how optimal prevention and control policies depend on the economic and biological characteristics of a randomly introduced biological invasion where the objective is to minimize the expected social costs from prevention, control, and invasion damages. The results characterize how optimal prevention and control policies vary with the initial invasion size, the invasion growth rate, and the probability distribution of introductions. The paper also examines the conditions under which the optimal policy relies solely on either prevention or control, the conditions under which it is optimal to completely prevent new introductions, and the conditions under which eradication of established invasions is optimal.Resource /Energy Economics and Policy,