416 PART • Market Structure and Competitive Strategy Profit F IGURE 11.11 TWO-PART TARIFF WITH MANY DIFFERENT CONSUMERS Total profit p is the sum of the profit from the entry fee pa and the profit from sales ps Both pa and ps depend on T, the entry fee Therefore p = pa + ps = n(T)T + (P - MC)Q(n) where n is the number of entrants, which depends on the entry fee T, and Q is the rate of sales, which is greater the larger is n Here T* is the profit-maximizing entry fee, given P To calculate optimum values for P and T, we can start with a number for P, find the optimum T, and then estimate the resulting profit P is then changed and the corresponding T recalculated, along with the new profit level Total a s T* T Figure 11.11 illustrates this principle The firm’s profit p is divided into two components, each of which is plotted as a function of the entry fee T, assuming a fixed sales price P The first component, pa, is the profit from the entry fee and is equal to the revenue n(T)T, where n(T) is the number of entrants (Note that a high T implies a small n.) Initially, as T is increased from zero, revenue n(T)T rises Eventually, however, further increases in T will make n so small that n(T)T falls The second component, ps, is the profit from sales of the item itself at price P and is equal to (P − MC)Q, where Q is the rate at which entrants purchase the item The larger the number of entrants n, the larger Q will be Thus ps falls when T is increased because a higher T reduces n Starting with a number for P, we determine the optimal (profit-maximizing) T* We then change P, find a new T*, and determine whether profit is now higher or lower This procedure is repeated until profit has been maximized Obviously, more data are needed to design an optimal two-part tariff than to choose a single price Knowing marginal cost and the aggregate demand curve is not enough It is impossible (in most cases) to determine the demand curve of every consumer, but one would at least like to know by how much individual demands differ from one another If consumers’ demands for your product are fairly similar, you would want to charge a price P that is close to marginal cost and make the entry fee T large This is the ideal situation from the firm’s point of view because most of the consumer surplus could then be captured On the other hand, if consumers have different demands for your product, you would probably want to set P well above marginal cost and charge a lower entry fee T In that case, however, the two-part tariff is a less effective means of capturing consumer surplus; setting a single price may almost as well At Disneyland in California and Walt Disney World in Florida, the strategy is to charge a high entry fee and charge nothing for the rides This policy makes sense because consumers have reasonably similar demands for Disney vacations Most people visiting the parks plan daily budgets (including expenditures for food and beverages) that, for most consumers, not differ very much