Optimal Capacity Choice Research Articles

Investment timing, capacity choice and optimal floors and ceilings

We develop a model for determining the optimal timing and capacity choice of investment under floors and ceilings (collars). We study how a welfare maximizing finite-lived collar can be optimally designed. Our findings show that for a linear demand function, multiple collar arrangements are optimal, including pure floors and fixed price regimes. Departing from previous literature, our results suggest that pure ceiling regimes are not optimal. When the demand function is isoelastic, optimal schemes are not attainable.

Investment timing and capacity choice in duopolistic competition under a jump-diffusion model.

This paper aims to apply the real options game theoretic to study the impact of sudden events on the optimal investment timing and capacity choice in a duopoly market. We model the market demand and investment cost as the geometric Brownian motions with jumps driven by the Poisson processes. A new computing method independent on specific distribution functions is proposed for the real option models with jump processes of random frequency and amplitude. Based on this method, we find that both firms delay investment with a larger capacity as uncertainties of demand and investment cost increase. We also demonstrate that two firms both invest later and the optimal capacity relationship between them is ambiguous in the presence of two sources of uncertainty. Numerical simulation reveals that upward (downward) jump in demand and downward (upward) jump in investment cost cause the firms to invest earlier (later) with a larger (smaller) capacity. Finally, in a duopoly with symmetric firms, the first investor invests earlier than in an asymmetric duopoly due to the threat of preemption.

Optimal timing and capacity choice with taxes and subsidies under uncertainty

We develop a real options model that examines the effect of government’s subsidies and taxation policy on the timing and size of investments. We find that a higher depreciation rate or subsidy, or a lower tax rate, accelerates investments. The effect of subsidies on the investment size depends on whether the subsidy is fixed or variable: a fixed subsidy induces smaller size investments, whereas a variable subsidy encourages larger size investments. The tax and depreciation rates do not affect the size of the investment. For revenue-neutral incentive packages, the effect of changes in the above variables on the investment timing and size is not necessarily monotonic and it depends on the instrument of the tax-subsidy policy that is used to keep the new policy revenue neutral. There are also economic contexts in which an increase in the tax rate can accelerate investments of a larger scale.

Optimal timing and capacity choice under the rate-of-return renewable energy support

This article presents a stylized renewable energy (RE) investment project profitability analysis under a rate-of-return RE support type. We use a dynamic programming approach to value the real options. While the method is widely used in RE policy analysis, the rate-of-return support is presented in this framework for the first time. We formulate a stylized RE project under the rate-of-return regulation in the dynamic programming framework and solve for optimal investment timing and project size.•A stylized renewable energy (RE) investment under rate-of-return RE support is presented in the dynamic programming framework;•The system is solved for optimal capacity choice in the presence of the electricity price uncertainty. We also comment on the optimal investment timing, which turns out to be a now-or-never decision in this case.

Investment timing and capacity choice under rate-of-return regulation for renewable energy support

Abstract This study analyzes a renewable energy (RE) support scheme recently introduced in Russia and compares it to the most frequently applied policy measures, feed-in tariff (FiT) and feed-in premium (FiP) schemes. In particular, we present an analytical formulation of the problem set-up and study optimal investment timing and capacity choice employing a real options approach. In addition, we conduct detailed sensitivity analyses to highlight how different policies shape investment behavior. The contributions of this paper include modeling the Russian RE support mechanism in a dynamic programming framework that allows us to show that such a RE support design offers a strong case for transferring market risks away from the investor and has potential for a unique combination of effectiveness and cost efficiency.

When and how much to invest? Investment and capacity choice under product life cycle uncertainty

While empirical research indicates that innovations typically follow a product life cycle that is subject to uncertainty in many industries, endless cash flow growth is still at the heart of most papers guiding investment decisions under uncertainty. This paper studies the effect of an uncertain technological life cycle on the decision to invest in new product introduction, taking into account the combined effects of flexible investment timing and optimal capacity choice. Based on a numerical example referring to investment decisions in facilities for the production of electric vehicle batteries, we find that the optimal investment threshold follows an S-curve over the product life cycle and derive the optimal capacity choice for the given investment decision.

Duopolistic Competition and Capacity Choice with Jump-Diffusion Process

This paper studies the effects of sudden events on the optimal timing and capacity choice in a duopoly market. According to the characteristics of economic environment, we assume that the product demand follows geometric Brownian motion with a Poisson jump process. Under the settings, the firms face the risk of a sudden drop in demand which is caused by sudden events. We develop the real option game model to derive the investment equilibrium strategies. Moreover, the effects of sudden events on investment decisions are obtained by numerical analysis.

Optimal investment timing and capacity choice for pumped hydropower storage

Pumped hydropower storage can smooth output from intermittent renewable electricity generators and facilitate their large-scale use in energy systems. Germany has aggressive plans for wind power expansion, and pumped storage ramps quickly enough to smooth wind power and could profit from arbitrage on the short-term price fluctuations wind power strengthens. We consider five capacity alternatives for a pumped storage facility in Norway that practices arbitrage in the German spot market. Price forecasts given increased wind capacity are used to calculate profit-maximizing production schedules and annual revenue streams. Real options theory is used to value the investment opportunity, since unlike net present value, it accounts for uncertainty and intertemporal choice. Results show that the optimal investment strategy under the base scenario is to invest in the largest available plant approximately eight years into the option lifetime.

Demand uncertainty and airport capacity choice

This study analyzes the effects of demand uncertainty on airport capacity choices. It shows that demand uncertainty will not change optimal capacity choice if demand variation is low and capacity cost is high; otherwise the optimal airport capacity under demand uncertainty will be larger than the case when a deterministic mean demand is considered. These conclusions are robust with respect to the different market structures considered in this study and hold for both profit-maximizing and welfare-maximizing airports. The moderating effects of commercial revenue, capital cost, and airport operation cost on airport capacity choice are qualitatively the same in the cases of uncertain demand and deterministic demand.

Optimal pricing and capacity choice for a public service under risk of interruption

We develop rules for pricing and capacity choice for an interruptible service that recognize the interdependence between consumers’ perceptions of system reliability and their market behavior. Consumers post ex ante demands, based on their expectations on aggregate demand. Posted demands are met if ex post supply capacity is sufficient. However, if supply is inadequate all ex ante demands are proportionally interrupted. Consumers’ expectations of aggregate demand are assumed to be rational. Under reasonable values for the consumer’s degrees of relative risk aversion and prudence, demand is decreasing in supply reliability. We derive operational expressions for the optimal pricing rule and the capacity expansion rule. We show that the optimal price under uncertainty consists of the optimal price under certainty plus a markup that positively depends on the degrees of relative risk aversion, relative prudence and system reliability. We also show that any reliability enhancing investment—though lowering the operating surplus of the public utility—is socially desirable as long as it covers the cost of investment.

Transport Infrastructure Investment and Demand Uncertainty

In transportation planning, there can be long lead times to adapt capacity. This article addresses two questions. First, in a one mode world (e.g., rail or road), what is the optimal capacity choice when faced with uncertain demand, long lead times, and congestion. Using a simple analytical model, it is shown that when demand is inelastic, it is socially optimal to invest more than if only the expected level of demand is taken into account. In this case, it may be beneficial to overinvest in capacity because congestion costs are an increasing function of relative use. This result holds with or without optimal tolling. The second question deals with 2 competing modes in which only one mode has long lead times for capacity, whereas the other has flexible capacity. This is typical for the competition between high-speed rail and air for the medium distance trips (500–1,000 km), or for the competition between inland waterways and trucks for freight. We find that overinvestment is less justified because the substitute mode can more easily absorb the high-demand outcomes.

Optimal Capital Structure, Capacity Choice and Product Market Competition

This paper develops a dynamic trade-off model to study the interaction between product market competition and capital structure. Firms make interdependent entry, investment, financing and default decisions. Trade-off between tax benefits, bankruptcy costs and strategic considerations in the product market determines optimal capital structure. The model delivers the following results that are consistent with empirical evidences: (1) Firms may have non-linear and non-monotonic reactions to their competitors' change of leverage, depending on their original levels of leverage; (2) The within-industry variation of leverage can be large, because incumbents and entrants use leverage strategically differently; (3) Entrants have higher leverage than incumbents in equilibrium, because the incumbents use lower leverage to gain strategic advantages over the entrants.

Investment timing and optimal capacity choice for small hydropower projects

This paper presents a method for assessing small hydropower projects that are subject to uncertain electricity prices. We present a real options-based method with continuous scaling, and we find that there is a unique price limit for initiating the project. If the current electricity price is below this limit it is never optimal to invest, but above this limit investment is made according to the function for optimal size. The connection between the real option and the physical properties of a small hydropower plant is dealt with using a spreadsheet model that performs a technical simulation of the production in a plant, based on all the important choices for such a plant. The main results of the spreadsheet are simulated production size and the investment costs, which are in turn used for finding the value of the real option and the price limit. The method is illustrated on three different Norwegian small hydropower projects.

Transport Infrastructure Investment and Demand Uncertainty

In transportation planning there can be long lead times to adapt capacity. This paper addresses two questions. First, in a one mode world (say rail or road), what is the optimal capacity choice when faced with uncertain demand, long lead times and congestion. Using a simple analytical model it is shown that when demand is inelastic, it is socially optimal to invest more than if only the expected level of demand is taken into account. In this case it may be beneficial to over invest in capacity because congestion costs are a convex function of relative use. This result holds with or without optimal tolling. The second question deals with two competing modes and where only one mode has long lead times for capacity while the other has flexible capacity. This is typical for the competition between High Speed Rail and air for the medium distance trips (500 to 1000 km), or for the competition between inland waterways and trucks for freight. We find that over investment is less justified because the substitute mode can more easily absorb the high demand outcomes.

The Debate on Net Neutrality: A Policy Perspective

The status quo of prohibiting broadband service providers from charging websites for preferential access to their customers—the bedrock principle of net neutrality (NN)—is under fierce debate. We develop a game-theoretic model to address two critical issues of NN: (1) Who are gainers and losers of abandoning NN? (2) Will broadband service providers have greater incentive to expand their capacity without NN? We find that if the principle of NN is abolished, the broadband service provider stands to gain from the arrangement, as a result of extracting the preferential access fees from content providers. Content providers are thus left worse off, mirroring the stances of the two sides in the debate. Depending on parameter values in our framework, consumer surplus either does not change or is higher in the short run. When compared to the baseline case under NN, social welfare in the short run increases if one content provider pays for preferential treatment but remains unchanged if both content providers pay. Finally, we find that the incentive to expand infrastructure capacity for the broadband service provider and its optimal capacity choice under NN are higher than those under the no-net-neutrality (NNN) regime, except in some specific cases. Under NN, the broadband service provider always invests in broadband infrastructure at the socially optimal level but either under- or overinvests in infrastructure capacity in the absence of NN.

Cost Considerations in Optimal Capacity Acquisition: An Option Pricing Approach

The optimal capacity choice is a tradeoff between the costs of shortage and excess capacity. This paper models the costs as the prices of an infinite number of European call and put options maturing continuously over the planning horizon. This approach allows a firm to consider the benefits of flexibility arising from delaying the acquisition of some capacity to a later time when more information about stochastic demand becomes available. The firm can then adjust the capacity to meet exact demand by purchasing in the spot market or reselling in the salvage market. The model determines optimal capacity by minimizing acquisition and capacity adjustment costs. I compare the model to extant models and discuss some special situations. Qualitative sensitivity analysis describes the impact of changes in model parameters on the optimal capacity. A Monte Carlo simulation compares this model with other models and results show that the Option Pricing model results in the lowest operating cost for all scenarios considered. A substantially simplified version of the model, which does not require complete understanding of option pricing methods, also performs well under certain conditions.

Pricing, Capacity Choice, and Financing in Transportation Networks

Abstract. This paper explores interrelations between pricing, capacity choice, and financing in transportation networks. We build on the Mohring‐Harwitz result on self‐financing of optimally designed and priced roads and investigate it in a network environment under various types of second‐best regulation. A small network model with endogenous car ownership demonstrates that optimal congestion pricing and capacity choice over an entire network may cause user prices to increase more in initially mildly congested areas compared to heavily congested areas. Furthermore, a flat kilometer charge under optimal capacity choice may result in first‐best efficiency gains.

Product Costing and Pricing under Long-Term Capacity Commitment

We develop a model to analyze optimal product-costing and pricing decisions in a dynamic information environment under long-term-capacity commitment. The arrival of new information about demand and cost parameters each period makes the problem complex. The optimal prices and capacity choices in our model cannot be decoupled as in Banker and Hughes' (1994) single-period model. The optimal prices are based on product costs that are adjusted each period to reflect changes in expected variable costs as well as utilization of fixed activity resources. The charge for each fixed resource is monotonically increasing in the expected demand for that resource in each state given the optimal capacity choice. The average optimal prices across periods and states are similar to Banker and Hughes' (1994) benchmark prices. Finally, we investigate a two-period version of the model to explore the optimality of carrying idle capacity. The optimal product-cost charge for fixed capacity is strictly less in the first period than in the second period when the firm expects demand growth.

Negotiated Transfer Pricing, Specific Investment, and Optimal Capacity Choice

This paper investigatesinvestment decisions in a divisionalized firm, in which an upstreamdivision supplies an intermediate product to a downstream division.The upstream division's investment includes two simultaneousdecisions. First, the division determines its capacity level,and second, it invests in a firm specific production technologythat lowers the marginal cost of production. Both the capacityand the specificity decision must be made before the actual demandfor the intermediate product is observable. Since the terms ofinternal trade are negotiated between the divisions, the upstreamdivision faces the well-known holdup problem and thus has incentivesto underinvest. It turns out that a simple contract stipulatinga minimum quantity and a transfer price for excessive quantitiesis sufficient to induce the efficient capacity and specificitydecisions.

Capacity choice in a two-stage problem under uncertainty

When choosing production capacity, a firm may not know which among mutually exclusive projects will be most profitable. It may be possible to await more information before committing given capacity to a project. We identify when shifts in project profitability and firm pecking order increase ex ante optimal capacity choice.