This note analyzes a simple Cournot model where firms choose outputs and capacities facing varying demand and price-cap regulation. We find that binding price caps set above long-run marginal cost increase (rather than decrease) aggregate capacity investment. (author's abstract) / Series: Working Papers / Research Institute for Regulatory Economics

We consider the problem of capacity expansion in telecommunication networks under uncertain economic conditions with various market structures. We assume that the demands for network capacity have constant price-elasticity, and demand functions are parameterized by an economic condition that is modeled by a discrete time Markov process. We apply dynamic programming to obtain a state-dependent capacity expansion strategy that maximizes expected total discounted cash flow. We incorporate partial reversibility of investment by differentiating the purchasing cost and the salvage value of the capacity. This partial reversibility makes the value function non-differentiable and divides the solution space into BUY, KEEP, and SELL regions. By identifying certain structural properties of the optimal solution, we perform sensitivity analyses on the optimal investment decisions with respect to market parameters. Under the condition that the level of cost depreciation is larger than that of the downside movement of the economic condition in each time period, we are able to obtain an analytical expression for the optimal capacity level and reduce the multi-period investment decision problem into a single-period myopic problem. As a result, optimal capacity increment depends only on the current economic condition. We study this problem under both monopolistic and oligopolistic market structures. In particular, we investigate investment decisions by two firms in a duopoly setting with Cournot competition. We prove the existence and the uniqueness of the Cournot equilibrium strategies in the duopolistic capacity investment problem. In addition, we show how competition between firms affects total available capacity in the market, capacity price, consumer surplus, expected time to a certain level of price reduction, and expected time to the first investment. We perform an empirical analysis to test a theoretical prediction obtained from our model through linear regression utilizing historical market data. By examining several alternative indices as a proxy to the economic condition considered in our model, we show that the Civilian Employment is the best proxy to use in validating the linear relationship between telecommunications capacity expansion and the economic indicator.

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This dissertation consists of two self-contained studies. The first study, in the domain of stochastic inventory theory, addresses the structure of optimal ordering policies in a periodic review setting. We take multiple sources of a single product to imply an ordering cost function that is nondecreasing, piecewise linear, and convex. Our main contribution is a proof of the optimality of a finite generalized base stock policy under an average cost criterion. Our inventory model is formulated as a Markov decision process with complete observations. Orders are delivered immediately. Excess demand is fully backlogged, and the function describing holding and backlogging costs is convex. All parameters are stationary, and the random demands are independent and identically distributed across periods. The (known) distribution function is subject to mild assumptions along with the holding and backlogging cost function. Our proof uses a vanishing discount approach. We extend our results from a continuous environment to the case where demands and order quantities are integral. The second study is in the area of capacity planning. Our overarching contribution is a relatively simple and fast solution approach for the fleet composition problem faced by a retail distribution firm, focusing on the context of a major beverage distributor. Vehicles to be included in the fleet may be of multiple sizes; we assume that spot transportation capacity will be available to supplement the fleet as needed. We aim to balance the fixed costs of the fleet against exposure to high variable costs due to reliance on spot capacity. We propose a two-stage stochastic linear programming model with fixed recourse. The demand on a particular day in the planning horizon is described by the total quantity to be delivered and the total number of customers to visit. Thus, daily demand throughout the entire planning period is captured by a bivariate probability distribution. We present an algorithm that efficiently generates a "definitive" collection of bases of the recourse program, facilitating rapid computation of the expected cost of a prospective fleet and its gradient. The equivalent convex program may then be solved by a standard gradient projection algorithm.