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We consider the problem of capacity expansion in telecommunication networks under uncertain economic conditions in various markets. We assume that the price-demand function has constant price-elasticity of demand and is parameterized by the index of a general economic condition that is modeled by discrete Markov processes. We use dynamic programming to find the state-dependent capacity expansion strategy that maximizes expected total discounted cash flow.
Our cost structure incorporates partial reversibility of investment by differentiating the buying price 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. In addition, with the non-differentiable value function, it is hard to obtain an analytical solution in general. By identifying some properties of the solution structure, we can perform a series of sensitivity analyses of optimal investment decisions with other market parameters. Under a typical condition, the cost depreciation is steeper than the movement of the economic condition, which shows the following: Capital investment can be analytically expressed. The multiple-time investment decision problem is reduced to a one-time investment decision. Increases are dependent on the economic condition of the current period and not on expected future economic conditions.
We study this problem in both the monopolistic and oligopolistic markets. In particular, we investigate investment decision of firms in duopoly markets, assuming that firms follow Cournot competition behavior. We attempt to prove the existence and the uniqueness of the Cournot equilibrium point in a duopoly market. In
addition, we show how competition between firms affects the market properties through total market capacity, market price, consumer surplus, expected time to a certain price reduction, and the expected time to the first investment decision. Finally, we perform a linear regression analysis using market data and attempt to validate our model by showing the relationship between capacity expansion and economic indicators.
