Peak Versus Off Peak Operation

An important practical problem in many industries is how to deal with sharp variations between peak and off-peak demands. Telephones are more heavily used during business hours than during evenings or weekends; local transit demands are greatest in the morning and afternoon commuting hours; in the arid areas water is more intensely demanded in summer than in winter months; restaurants are busiest at regular mealtimes, and so on. For a firm facing both peak and off-peak demands for its product, the optimization problem is how to divide its efforts between the two.

Assume for simplicity that the peak and off-peak periods are equal duration. Under pure competition the firm would be a price-taker in both the peak and off-peak markets. In the peak market it would face a higher price and in the off-peak market a lower price—but, in either market, the price will be independent of the firm’s own level of output. An example might be a city served by a number of competing taxicab suppliers, daytime hours being the peak demand period and evening hours the off-peak demand period. The quoted taxicab fares do not usually vary with time of day. However, the effective price of taxicab service does vary. In peak periods taxi earn a higher effective price, since there is less “dead time” waiting for a customer. And similarly, the customers have to pay a higher effective price in peak periods, since on average they have to wait longer for taxi to become available.

In analyzing the peak/off-peak situation, it is essential to distinguish between “common costs” and “saparable costs.” Common costs are those that apply to both peak and off-peak service. On the case of taxicabs they would include the costs of providing the casbs themselves, of running the central dispatching system,, and so on. Saparable costs are those incurred in serving each specific market. For taxicabs they might include gasoline and drivers’ wages. The distinction between common and saparable costs is quite apart from the distinction between fixed and variable costs. Common costs can be fixed or variable, and the same holds for saparable costs.

The following additional assumptions are employed: 1) There are no common fixed costs at all; the marginal common costs (MCC) is a constant magnitude. 2) The separable costs include both fixed and variable elements, but the cost function is the same in either market. However the firm may want to operate at different points along the cost curves in serving the two markets. A taxicab firm, for example, may chose to put a larger number of cabs on the road during peak period.

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