United States: Pay-Per-View Entertainment Revenue Management Research

Originally published December 2005

Lou Volpano heads ascertain-ment®, a consulting firm providing research and strategic analysis for entertainment companies based in Newport Beach, California. Previous clients include: Great Chefs Television and Publishing, Dick Clark Productions, and the House of Blues.

Pay-per-view events appear haphazardly priced, naively presuming that cost determines the price. Traditionally, a single-part price is set such that the revenue collected from that universe of customers (somewhere between .01% and 1% of all addressable households) known to purchase pay-per-view (PPV) events at least covers average cost. Indeed, once many of these events are produced, the production costs have been incurred (sunk), leaving distribution costs, which are often trivial. For example, the cost of selling another unit is approximately zero, being largely a billing cost.

Such pricing strategies are sub-optimal for several reasons. First, this presumes the goal is zero profit, as pricing is set so that revenue equals cost. Second, it ignores factors affecting willingness to pay. Third, it erroneously treats incurred and to-be-incurred costs symmetrically. Theoretically, prices should reflect intensity of customer demand: the more fully variation in demand can be exploited, the more profit will be generated. Furthermore, costs that are sunk should not impact price. To take an extreme case, if all costs have been incurred (sunk), then maximizing profit is equivalent to maximizing revenue: costs, in this case, therefore should be ignored.

Other evidence of sub-optimal pricing is the existence of ticket scalpers in the live event markets. That is, if live entertainment was priced more consistent with economic theory than it currently is, there would be less margin for scalpers to trade on and they would largely vanish. Hence, scalping indicates additional revenue could be captured through more advanced pricing strategies. While scalping is not feasible with PPV, it is difficult to argue that pricing is optimal for PPV and, at the same time, suboptimal for live entertainment, and that marketers choose to leave money on the table. It is easier to make the argument that all such event pricing is sub-optimal and should be reexamined. That is the goal of this proposal.

We apply this analysis to a 1992 PPV tennis event, where REQUEST TV cut price from $25 to $10 in several viewing areas (cells) to test elasticity of demand. We then propose a generalized study to allow the collection and integration of customer and attraction data into price setting. Specifically, an event is to be priced using traditional single-part PPV marketing techniques in one market, and using price discrimination techniques in a comparable market. Results from such tests will then provide statistical links between customer and attraction data and price. These links will then be used exploit this data in pricing PPV events, including controlled testing and refinement of the process.

Since the REQUEST TV PPV experiment did not involve market segmentation, we first develop the analysis for a firm marketing a single product at a uniform price to all buyers. The two PPV tests are then analyzed within this framework.

We assume that the goal of producers, marketers, etc., is to maximize profit. We also assume that the event has been produced or has been contracted for, so that production costs will be incurred regardless of sales. Since the incremental distribution costs of serving one additional PPV customer are approximately zero, we further restrict the analysis by assuming that distribution costs are also zero. Hence, profit maximization simplifies here to revenue maximization, and profit maximization is equivalent to revenue maximization (the focus of this paper).

The economic way to view revenue maximization is in terms of marginal analysis, that is, to examine the consequences of small changes in output for cost and revenue. Under a uniform pricing strategy, revenue maximization requires the firm to select output so that marginal revenue equals zero. Erroneously incorporating sunk costs into price setting will lead to less revenue than if these costs are ignored.

We apply this analysis to the 1992 REQUEST TV price test case conducted during the 1992 Jimmy Connors - Martina Navratilova tennis match. Since only crude controls are in place, the conclusions are to illustrate the pricing process rather than to suggest an optimal price. In addition, because of the study design, we are not able to determine how individual and attraction characteristics affect what people are willing to pay. (This is the focus of the next section.)

Price was cut from $25 to $10 in one of two matching cable TV cells, of approximately 5,000 subscribers, in San Diego, CA and Boston, MA. If these cells are selected so that customers in the cells are similar, then we have implicit controls for individual characteristics that affect demand.

Table 1 summarizes subscriber and price data for the four test cells. The Massachusetts cells were chosen as they exhibited similar buy rates for two events: Holyfield vs. Holmes and Clash of The Legends. As can be seen, at this level of generality these cells are similar. Similar data for the San Diego cells is absent, as these cells were randomly selected; the only sampling criterion was that the number of subscribers per cell be equal.

Assuming identical test cell pairs allows us to interpret these price-quantity data as points on the same demand curve. (This assumption also prevents us from saying anything about how individual and attraction characteristics affect willingness to pay.) As can be seen in Table 2, the elasticities over this price range are estimated to be 0.67 and 0.49 in the test markets. Since demand is inelastic, we infer that the price cut was excessive; we cannot, however, conclude that no price cut should be made. That this is so is seen next.

We can extract additional information from this experiment by adding more structure to the problem. Specifically, assume that demand (identical for each pair) for such events is linear. This assumption, coupled with the price-quantity pairs, allows is to estimate demand, with which we can estimate the revenue maximizing price.

The estimated demand and marginal revenue curves for each case are given Table 2. (See Appendix A for the derivations.) In the Massachusetts case, this occurs at q* = 37.50, with a corresponding price of p* = $21.28. Total revenue per cell (the product of the two) is $805.xx, compared with actual revenues of $800 and $580. (Actual and maximized profit would be found by subtracting total cost from these revenues.) The last column presents the same analysis for the California case. In the California case, this occurs at q* = 14.15, with a corresponding price of p* = $26.60. Total revenue per cell is $439, compared with actual revenues of $375 and $230. Hence, price should have been lowered somewhat in Massachusetts market and raised in the California market.

Several caveats apply. First, we assumed that the sample selection procedures generated similar sets of customers in each cell. This is necessary to interpret the price-quantity data from each cell pair as reflecting the same demand. To the extent that this was not so, the estimated optimal price will deviate from its true value in each market. Since the point of this analysis is to develop a price setting procedure, as opposed to an optimal price, the estimates themselves are of little importance, and so such sampling issues are not important here. Second, we have assumed a linear demand. To the extent that demand is not linear, there may be more profitable prices. Having multiple prices in such tests would be useful here. Third, we have yet to establish how the optimal price depends on the customer and attraction characteristics. This analysis (at best) holds these important characteristics constant. We now address these points.

The previous section examined revenue maximization under uniform treatment of customers. In addition, we controlled for customer and attraction characteristics by sample selection. This is sub-optimal when there are differences across customers that may economically be exploited. That is, customers with higher (lower) demand for a PPV event may profitably be charged a higher (lower) price. This section generalizes the links between customer and attraction characteristics and the optimal price structure developed above, allowing prices to vary from cell to cell to exploit differences in demand. We first develop the theory underlying price discrimination, and then develop a marketing proposal to generate the information necessary to implement this pricing strategy.

Price discrimination involves selling a product at different prices to different customers, where these price differentials are related to demand differences but unrelated to cost differences. This naturally applies to PPV, as the cost of serving a buyer is independent of buyer characteristics. To implement this three conditions must be met. First, we must be able to sort customers based on intensity of demand. Second, we must be able to charge different prices according to intensity of demand. Third, we must be able to prevent resale. Since the third condition is met with PPV, we focus on the first two.

PPV demand depends on income, education, type of event, etc. Fundamentally, we want to charge people willing to pay a lot a high price and charge people willing to pay a little a low price. We first segment the market based on willingness to pay, where each segment is treated independently of other segments. Then each segment is charged a different profit maximizing price consistent with the analysis above.

To implement this pricing strategy we suggest a three-stage proposal. First, data generation: a PPV event is marketed under a variety of prices to customers of known characteristics. Second, estimation: this data is used to generate parameter estimates linking customer and attraction characteristics to price. Third, implementation: another PPV event is marketed consistent with the empirical results to test and refine the model.

The first stage involves generating customer information. The Massachusetts-California study should thus be generalized so that a wide variety of customers of known attributes are charged a wide variety of prices in many cells. Individual characteristics might include the cost of homes, race, previous PPV purchases, number of phone lines, etc. PPV attraction characteristics might include the time since an attraction has last been exposed in the market, prices of substitutes, sales of videocassettes or compact discs, etc.

The second stage involves estimating the links between buyer and attraction characteristics and price. We estimate how changes in each characteristic affects buyer willingness to pay. Buyers will then be segmented into relatively homogenous groups. In the REQUEST TV analysis, this was (assumed to be) accomplished via sample selection. Here it will be accomplished based on buyer attributes. (Note that, unlike above geographical segmentation, buyers will be segmented according to demand characteristics.) In addition, now we know how these characteristics vary across groups, which was unknown above (or assumed constant across groups). The statistical results will then be used to generate estimates of the revenue maximizing price for each cell. Revenue estimates may also be generated and compared with actual revenues, allowing us to predict the extent of revenue increases.

The third stage involves implementing and refining this procedure via the marketing of another PPV event. This event should be marketed in two (ideally) identical markets. The first serves as a test case, where the event is marketed according to the pricing strategies outlined here. The second serves as a control group, where the event is marketed according to past pricing practices. The two are then compared to assess the profitability of our pricing strategy, as well as to refine the strategy.

Our analysis suggests a pricing strategy based on economic principles. Prices should not reflect sunk costs, while exploiting differences in buyer demand. This strategy is superior to other pricing strategies, especially those incorporating sunk costs while ignoring differences across buyers. To implement this strategy, we suggested a proposal to generate and analyze data. A subsequent marketing test with a control group should be conducted to test and refine the model. Such an optimal pricing strategy should raise revenue and, at the same time, reduce the margins that scalpers trade on (when applied to live events).

This appendix develops the pricing model underlying this analysis. We do this first for the simple case of a firm marketing a pay-per-view event in a single market. Controls for individual and event characteristics for current purposes will remain unspecified, but may be thought of as affecting the parameters of the demand curve. We then generalize this analysis to allow for this market to be segmented to exploit differences in buyer demand.

Consider a firm marketing a pay-per-view event in a single market. Suppose that the market (inverse) demand for this event is given by

(1) P(Q) = a - bQ,

where P and Q represent price and quantity, and a and b are positive constants. These constants depend on individual and event characteristics, though for now these characteristics will remain unspecified. Total revenue is simply price times quantity:

(2) R(Q) = P(Q)Q.

Production and distribution costs (at the time of distribution) are assumed to be

(3) C(Q) = c + dQ,

where c and d are also positive constants. The first component of cost, c, represents a fixed (sunk) cost, i.e., one that is independent of output. The second component of cost, dQ, represents yet to be incurred distribution costs. These costs are dependent on output.

Profit ( ) is the difference between total revenue and total cost:

(4) (Q) = R(Q) - C(Q) = (a-bQ)Q - [c + dQ] = -c + (a-d)Q - bQ².

Profit maximization requires that the first derivative ( ’(Q)) be zero and that the second derivative ( "(q)) be negative. The first condition yields

(5) ’(Q) = (a - 2bQ) - d = (a - d) - 2bQ = 0,

implying a profit maximizing quantity of Q* = (a-d)/2b. The first term (a - 2bQ) may be interpreted as marginal revenue and the second term (d) may be interpreted as marginal cost. This says that output should be chosen so that marginal revenue (the additional revenue from selling a pay-per-view event to one more buyer) equals marginal cost (the additional cost associated with selling that extra unit). Note that the optimal quantity (and price) does not depend on fixed cost (c). Hence, incorporation of these kinds of costs into the pricing analysis, to the extent that it affects quantity (and price), a quantity different from Q*, and thus lower profit. The corresponding price and profit are P*(Q*) = (a+d)/2 and Profit is thus * = (a-d)² - c.

The second order conditions (that insure we have a maximum rather than a minimum) require that the second derivative be zero at Q*. Since "(Q*) = -2b, Q* indeed a maximum.

We now apply this to the matched pairs of cells in the 1992 REQUEST TV test, where we have the following raw data:

We first estimate the demand curve in each market. The assumption that the matched cells are identical is crucial here, as it allows us to treat the price-quantity pairs are though they came from the same demand curve. Fitting the linear demand P(Q) = a - bQ to the data, we first find slope (b), found by differencing the price-quantity pairs. For the Massachusetts case, the slope is given by b = (25 - 10) / (32 - 58) = -0.58. The vertical intercept may then be found by plugging either data point into the equation for the demand curve: P(Q) = a - 0.58Q. Doing so for the data point (32,25) yields 25 = a - 0.58(32), implying a = 43.56. Hence, the demand curve for the Massachusetts test is estimated to be P(Q) = 43.56 - 0.58Q. The marginal revenue equation is then given by MR(Q) = 43.56 - 1.16Q. For California, the slope is given by b = (25 - 10) / (15 - 23) = -1.88 and the vertical intercept, using the data point (15,25), is given by 25 = a - 1.88 (15), implying that a = 53.20. Hence, the demand curve for California test is estimated to be P(Q) = 53.2 - 1.88Q, with marginal revenue MR(Q) = 53.2 - 3.76Q.

With demand and marginal revenue, we can now estimate the profit maximizing quantity and price, along with profit. We now make use of the assumption that the marginal cost of distribution is zero, so that profit maximization reduces to setting marginal revenue equal to zero. For the Massachusetts test we have

(6) MR(Q*) = 43.56 - 1.16Q* = 0,

implying Q* = 38, P* = $21.78, and R(Q*) = $817.88. Similarly, for the California test we have

(7) MR(Q*) = 53.2 - 3.76Q*,

implying Q* = 14, P* = $26.60, and R(Q*) = $376.36. Note that to get estimated profit in each case, costs must be subtracted from revenue.

As can be seen, given the assumptions employed, pricing in each market was suboptimal, and is consistent to allow conditions for scalping in the market. This analysis is limited in at least one important respect: we have not exploited individual and event characteristics for rate setting. Ideally, we would charge people willing to pay a lot a high price while at the same time charge people willing to pay a little a low price, that is, to segment the market. We now turn to this issue.

Essentially, we segment the market based on buyer demand. Hence, we need to replicate the above test, where observe buyer and event characteristics and price. We then statistically link willingness to pay to these characteristics, and then price the product in each segment accordingly. A simple example illustrates. Table A.2 presents fictitious data on two markets, a low demand and a high demand markets. If the segments are ignored, so the both types of buyers are treated the same, akin to each test pair in the Massachusetts and California test cases (though each pair is treated independently), the optimal price is $50, total sales is 60, and total profit is $1,800. If the markets are segmented into low and high demand groups, akin to the different treatment of the Massachusetts pair versus the California pair, the optimal prices are $40 and 60, optimal quantities are 20 and 40, and (combined) total profit is $2,000. Hence, by exploiting differences in demand it is possible to raise revenue. Again, the presence of scalping signals the opportunity for further market segmentation.

Table A.3 indicate what happens to profit if, while not exploiting demand differences, the high demand or the low demand group is favored. In either case, by trying to exploit one group or the other, while not segmenting the market, profit will be lower than by not attempting such exploitation.

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