## The plant size problem and monopoly pricing

### Demichelis, Stefano ; Tarola, Ornella

This paper is concerned with the so called ”plant-size problem”: a demand increasing over time has to be served by a firm when there are economies of scale in plant construction. Generally the operating firm is assumed to be a cost-minimizer. We depart from this by supposing that it is a profit-maximizer, namely can manipulate demand through its own price. For the properties of a simultaneous... Plus

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- This paper is concerned with the so called ”plant-size problem”: a demand increasing over time has to be served by a firm when there are economies of scale in plant construction. Generally the operating firm is assumed to be a cost-minimizer. We depart from this by supposing that it is a profit-maximizer, namely can manipulate demand through its own price. For the properties of a simultaneous pricing and expansion capacity strategy to be exploited, we first fix the time points when the investment for adding capacity is undertaken and characterize the optimal policy in terms of the price and the size of investment. We show that the investment size is strictly smaller than the one realized if no price change is allowed. Then we proceed in the reverse way: we assume that the amount of investment is fixed and define the optimal policy in terms of the price regime and time points when the investment is realized and we prove that price manipulation induces the firm to postpone the increment of capacity. Indeed as for both the cases, prices are so charged to dampen demand and make it satified by the existing capacity at any time.