Pricing and Revenue Optimization by Robert Phillips. Toggle navigation. Australia; Canada. It is one of many increasingly. Get instant access to our step-by-step Pricing And Revenue Optimization solutions manual.
There are a lot of customers who are more or less indifferent between our offering and that of the competition. In other words, price elasticity is highest when we are at or near the market price. This kind of consumer behavior generates a response curve of the general form shown in Figure 3. When we price very low, we receive lots of demand, but demand changes slowly as we change price.
At high prices, de- mand is low and changes slowly as we raise prices further. The price-response curve has a sort of reverse S shape. Larger values of b correspond to greater price sensitivity. Higher values ofb represent more price-sensitive markets. Asb grows larger, the market approaches perfect competition. In other words, the price-response curve increasingly approaches the perfectly competitive price-response function in Figure 3.
Some of the characteristics of the logit price-response function are shown in Table 3. Logit willingness to pay follows a bell-shaped curve known as the logistic distribution.
An example of the logistic w. The y-axis has been scaled by a factor of 20, This is a far more realistic w.
For that reason, the logit is usually preferred to linear or constant-elasticity price-response functions when the effects of large price changes are being considered.
Yet competition is an important—some may say the most important—fact of life in any market of interest. How should we factor competition into our calculation of price response? There are three different levels at which competition might be included in PRO. This is especially true in business-to-business markets, when the pocket price of the customer may include discounts that are never made visible to the competition.
But it is also true in many consumer markets. The answer is yes. First of all, the price-response function we will be using in a market will be based on history. To the extent that our competitors will behave in a similar fashion in the future as they have in the past, the price-response function will be a fair representation of market response—including competitive response.
What if the market has changed? If we have a competitor who responds more aggressively to a price action than in the past, this will be manifested in the demand we see in the next period. We have the opportunity to adjust our price-response function and re- optimize accordingly. This information is increasingly available, particularly for online markets.
For example, the Online Petroleum Phillips, Robert. How can this type of information be used by sellers in setting their prices? Consumer-choice modeling is based on the situation in which a number of competitors are providing similar products or services to some population of customers. Each of the competitors sets a price for the product. Each customer has a vector of willingnesses to pay or reservation prices , one for each product. These different w. Each customer purchases the product with the high- est positive surplus.
If none of the products has a positive surplus for a customer, she will not purchase at all. Audio Two or his favorite alternative Cacophonia. Rather, she purchases the alternative that yields the highest surplus. We would expect that each customer would have a different set of reservation prices based on the value she places on the various features of each alter- native or her preference for a particular brand.
As before, we can imagine that the reserva- tion prices would be distributed across the population in an n-dimensional bell-shaped curve. The market share of each alternative is between 0 and 1. Every buyer chooses some alternative. Increasing the price of a product decreases its market share. Increasing the price of a product increases the market share of other products.
The products are substitutes. It is easy to see that mi p in Equa- tion 3. The bj are a measure of price responsiveness for each alternative—a high value of bj means that alternative j is highly price sensitive, while a lower value of bj indicates a lower value of price sensitivity.
Relation of the multinomial logit to the logit price-response function. You may have guessed that there must be some relationship between the MNL and the logit price-response function. And indeed there is: In the case where competitive prices are constant, the MNL reduces to the logit price-response function. To see this, assume that prices p 2, p 3,.
Then we can replace the competitive-price term in Equation 3. If we anticipate that competi- tive prices will be largely stable, the MNL provides little or no additional predictive value over a logit price-response function. Strengths and weaknesses of consumer-choice modeling.
There is a vast literature on consumer-choice modeling, and the issues involved with estimating the parameters of consumer-choice models have been much studied. Statistical software packages such as SAS include procedures for estimating the parameters of the logit or probit market-share func- tions.
This is a great strength of the consumer-choice approach to price-response estimation. There are a number of weaknesses to consumer-choice modeling as well.
One is that, at least as we have posed it, the models assume that all customers purchase some alternative. However, it may be that some customers choose not to purchase at all, since their willing- ness to pay for every alternative may be below the price of that alternative.
Thus, the esti- mation of the total market D is not really independent of the prices being offered. Indeed, it seems intuitive that an aggressive discount by one supplier would not only siphon cus- tomers away from competitors but actually induce customers into the market who might not have purchased from any alternative.
Another drawback of the consumer-choice modeling approach is that, in theory, it re- quires information on all competitive prices.
Table Other surveys have shown that in many consumer markets three or four major brands dominate a category, although there may be scores of smaller competitors. In these cases, one commonly used approach is to derive a competitive index price by weighting the prices offered by the major competitors and using this index as a single competitive price in a multinomial logit. After all, if we are taking competitive prices into account in setting our prices, we should an- ticipate that our competitors will take our price into account when they set their prices.
If we drop a price, we should anticipate the possibility that competitors will match, possibly eras- Phillips, Robert. The results of raising a price would certainly be different depending upon whether or not our competitors decided to match. Attempts to predict competitive response and incorporate it into current pricing deci- sions falls within the realm of decision analysis, or game theory.
While these approaches have their applications to strategic pricing, they are far less relevant to the tactical decisions of pricing and revenue optimization. For example, there is a vast literature on the use of game theory in pricing. This literature has little application to the day-to-day tactical pric- ing issues that fall within the scope of pricing and revenue optimization.
There does not appear to be a single pricing and revenue optimization system that explicitly attempts to forecast competitive response using game theory as part of its ongoing operation.
There are many reasons for this, but I believe there is one that is particularly important. For example, if customers in a market choose a supplier based on the multinomial logit price-response model described in Section 3.
More sophisticated strategies cannot yield more. It is about making a little more money from each transaction. Many of the price adjustments called for by pricing and revenue optimization are likely to fall below the radar screen of the competition and may not trigger any explicit response whatsoever.
This does not mean that competitive response need never be considered in pricing. Previously, Hertz, like other national rent-a-car companies, had changed prices only rarely. Whenever one of the rental car companies dropped a price, the others were likely to follow immediately— often with even larger drops—precipitating an industrywide fare war. Hertz took great pains to communicate to the industry that its new system would be changing prices much more commonly than before—some prices would go up, some would go down, but all would change much more frequently.
The communication was successful: Hertz was able to initi- ate its revenue management program without inciting retaliatory price wars. Once Hertz initiated revenue management, it was able to generate additional revenue through thou- sands of small adjustments to prices that its competitors were unable to match. After all, a company may not know the price-response function it faces, but surely it should know its Phillips, Robert. Unfortunately, things are not quite so simple.
Calculating incremental cost for a customer commitment depends critically on the con- text and nature of the commitment. Here are some examples. Once he has bought the goods, he cannot return them and cannot reorder.
During the season he wants to set and update the prices that will maximize the total revenue he will re- ceive from the fashion goods. Since the cost of the goods is sunk and selling a unit will not drive any additional future sales, his incremental cost per sale is zero. Because sell- ing a unit will result in an additional unit order, the incremental cost for selling a bottle of shampoo is the wholesale unit cost.
From previous experience, the distributor knows that this hospital is an expensive customer requiring high levels of customer support, wide variances in orders, and high rates of product returns. The expected incremental cost of the contract includes not only the expected cost of the items the hospital will purchase, but also the expected cost of customer service, operating costs and holding costs driven by the wide variance in orders, and the expected costs of returns.
These examples illustrate some of the key characteristics of incremental cost. These char- acteristics can be summarized as follows. It is based on the effect a customer commitment will have on future costs. Costs that have already been taken or that are driven by Phillips, Robert.
It is the expected cost of making this customer commit- ment. The incremental cost of making this commitment may not be the same as the average cost of similar commitments made in the past. Only costs that change as the result of a customer commitment are part of the incremental cost.
As a result, the incremental cost of a customer commitment is usually less than the fully allo- cated cost. Trucking companies such as Roadway Express and Yellow Freight sell contracts to shippers. Each contract covers the next year and commits the trucking company to carry all the freight ten- dered by the customer at an agreed-on tariff. The incremental cost associated with one of these contracts is likely to be highly uncertain at the time the commitment is made.
First of all, the amount, timing, and origin and destination of the freight the customer will tender over the next year is uncertain. In each case, the calculation of incremental cost requires understanding the nature of the customer commitment and then estimating the additional costs that would be generated by making the commitment— or, equivalently, the costs that would be avoided by not making the commitment.
The methodology behind calculating incremental costs is closely related to activity-based costing ABC. Activity-based costing is a management accounting ap- proach to allocating costs to their underlying causes in order to give a clearer view of the real sources of cost within an organization. The sum of the margins of all products sold during a time pe- Phillips, Robert. Note that there is a fundamental lack of symmetry in the total-contribution curve: The supplier can lose money by pricing too low below incremental cost , but she can- not lose money by pricing too high—the worst that can happen is that she drives demand to zero.
Marginal price equals marginal cost. We can rewrite Equation 3. This is the amount of additional revenue the seller could achieve from a small increase in price. Typically, marginal revenue is greater than zero at low prices but less than zero at higher prices. When price is low, increasing price leads to in- creased total revenue because the reduced demand is outweighed by increased margin.
But at some price, the effect of raising price further is to decrease total revenue as demand be- gins to drop more quickly than margin increases. The term on the right-hand side of Equation 3. Note that marginal cost is always less than or equal to zero—an increase in price results in lower demand by the downward-sloping property , which in turn leads to lower total costs. Equation 3. The contribution maximizing price occurs where the marginal-revenue curve intersects the marginal-cost curve in Figure 3.
Total contribution is maximized in the basic price optimization problem at the price at which marginal revenue equals marginal cost.
If marginal revenue is greater than marginal cost, then the supplier can increase his contribution by increasing price. If, on the other hand, marginal revenue is lower than marginal cost, he should decrease his price to increase contribution.
Optimal contribution margin and elasticity. We can also relate the optimal price to point elasticity. Rewrite Equation 3. In Equation 3. In other words, If the point elasticity at our current price is less than 1, we can increase total contribution by increasing price. Of course, since point elasticity changes as we change price, we cannot expect total con- tribution to continue increasing forever as we increase price.
Typically, as price increases, elasticity will increase as well, until we reach a point where lost sales outweigh increased unit margins. We can express the corresponding condition in terms of point elasticity by com- bining Equation 3. It is known as the contribution margin ratio or sometimes as the gross margin ratio. In words, Equation 3.
Of course this is equivalent to At the optimal price, the contribution margin ratio is equal to the reciprocal of elasticity. This means he should price the televisions at 2. Imputed price elasticity. This can only be true if the price elasticity is 5. We use the notation x to denote the maximum of x and 0, where x may be either a single variable or a mathematical expression.
This linear price-response func- tion is shown in Figure 3. Substituting into Equation 3. A company with incre- mental cost of zero can maximize net contribution by maximizing revenue.
There are some service industries, such as movie theaters, video rentals, and sporting events, in which the incremental costs are close to zero. Some of these are discussed in Section 6. This is the situation faced by many fashion-goods retailers, who purchase inventory for an entire season ahead of time.
Once the inventory has been purchased, the incremental cost of a sale is zero—and the seller should set prices accordingly. Many of these situations count as markdown oppor- tunities and are discussed in Chapter Typically, marginal revenue is a decreasing func- tion of price at least in the region of the optimal price.
In this case, we can show how marginal revenue and marginal cost can be used to compute the revenue-maximizing and contribution-maximizing prices in Figure 3. The revenue-maximizing price can be found by solving Equation 3.
The decision that management needs to make in Example 3. Since the revenue-maximizing price is lower than the contribution-maximizing price, there is no guarantee that the revenue-maximizing price will provide a reasonable margin— or even a positive margin—if incremental cost is greater than zero.
For this rea- son, it is dangerous to maximize total revenue without including a constraint that ensures that the resulting price is greater than incremental cost. Values of a be- tween 0 and 1 will maximize a weighted combination of the two, with higher values of a resulting in a higher weighting for contribution relative to total revenue.
Applying some algebra to Equation 3. The price that maximizes a weighted combination of revenue and contribu- tion is greater than or equal to the revenue-maximizing price and less than or equal to the contribution-maximizing price.
In the absence of other constraints, we would only be interested in prices greater than the revenue-maximizing price and less than the contribution-maximizing price.
In other words, there is no reason for an unconstrained seller to consider pricing outside of this range. The core problem in PRO can be formulated as a constrained optimization problem where the objective function is to maximize total contribution.
The constraints are the result of either business rules e. A key input into any PRO problem is the price-response function that relates price to demand. The price-sensitivity function is typically nonnegative, continuous, and downward sloping. In many cases, price-response functions can be considered as the measure of the number of people whose maximum willingness to pay or reservation price is greater than a certain price.
In this case, a price-response function corresponds to a particu- lar distribution of willingness to pay across a population. For example, a linear price- response function corresponds to a uniform distribution on willingness to pay. Linear and constant-elasticity price-response functions are both commonly used in analysis.
However, both tend to be unrealistic when applied to large changes in price. In such cases, a reverse S-shaped model, such as the logit, may be more appropriate. There are three broad approaches to incorporating competitive pricing into price optimization. The second approach is to explicitly include competitive prices into a broader price-response model.
This is typically only done when a major pricing change is contemplated. The cost used in pricing and revenue optimization is the incremental cost of a cus- tomer commitment. It is the difference between the total costs a company would incur from satisfying the commitment. The incremental cost will vary with the duration and size of the commitment and is not a fully allocated cost. The following are equivalent optimality conditions for the unconstrained price op- timization problem: Marginal revenue equals marginal cost.
The derivative of total contribution with respect to price is zero. The contribution margin ratio is equal to 1 over the price elasticity. Any of these three conditions can be used to compute the optimal price.
However, these conditions may not hold if the price optimization problem is constrained. Constraints may be due to limits on supply or capacity or may be due to business rules limiting the prices that can be charged. The price that maximizes revenue can be found by setting marginal revenue to zero.
It is always lower than the price that maximizes total contribution unless incre- mental costs are zero, in which case they are the same. Consider a seller seeking to maximize contribution. Under what relative values of his current price p, his cost c, and his point elasticity P p should the seller raise his price to increase contribution? Under what conditions should he lower his price? Keep his price the same? He determines that the point price elasticity of this model of printer is 5.
If he wants to maximize net contribution, is he better off raising his price, lower- ing his price, or keeping it the same? If the elasticity of 5. What price will maxi- mize the total contribution? How many cars will she sell during the month? The only two foods he can stand to eat on a regular basis are beans and hamburger. He derives twice as much pleasure per protein unit from eating hamburger as he does from beans. What is the optimal consumption of beans and ham- burger in this case?
Note that his individual price-response function is indeed upward sloping. What is his price-response function for beans now? If not why not, and what might they be trying to do? Landsburg Varian , p. In economic terms, it means that what we are selling is a good—something people are willing to buy—rather than an illth—something people are willing to pay to get rid of.
This is not a restrictive assumption—we can convert an illth with negative price to a good with positive price by exchanging the buyer and the seller. In reality, strict continuity of price-response functions often does not hold. In par- ticular, prices for most items sold in the United States do not vary by less than 1 cent and most items are sold in discrete units. We will sometimes use piecewise linear price-response functions.
Several restaurants have noted that a disproportionate number of customers tend to order the second-cheapest chardonnay on the menu—and they tailor their pricing accordingly. Here, we will be considering own-price elasticity—the response of the demand for a product to its own price. An important exception is e-commerce, in which programs can actively track the number of visitors to the Web site or the number of people who clicked to get a price quote on an online loan. There is such a price-response function; it is called the probit.
Also, the two distributions and their corresponding price-response functions behave in a very similar fashion in the region around the market price. Because the logit is easier to work with and is much more commonly used in practice, we will couch the majority of our analysis here and in Chapter 11 in terms of the logit. Train and Aldrich and Nelson also provide good comparisons of logit and probit models.
For a fairly technical proof of this, see Vives See Chapter 10 for more details on pricing in this situation. Appendix A reviews some basic optimization theory. Figures from Wild Price differentiation refers to the practice of a seller charging different prices to differ- ent customers, either for exactly the same good or for slightly different versions of the same good. It also adds a new level of complexity to pricing, often creating a need to use analytical techniques to improve the calculation and updating of prices over time.
Tactics for price differentiation include charging different prices to different customers or groups of customers for exactly the same product, charging different prices for different versions of the same product, and combinations of the two.
The term price discrimination is used in the economics literature to refer to much the same thing. We use the term price differentiation, rather than the more common price discrimination, in part to avoid the negative connotations associated with the word discrimination.
There is both art and science to price differentiation. There is no one way to segment customers that applies to all possible markets. Instead, there is a variety of techniques that can be applied in different ways, depending on the characteristics of a market, the competitive environment, and the character of the goods or services being sold. The science lies in setting and updating the prices in order to maximize overall return from all segments.
We start by using a simple example based on the widget maker from Chapter 3 to il- lustrate the economic principles behind price differentiation. This is the area of region A in Fig- ure 4. The sum of the three re- gions is the total contribution that the widget maker would realize if he were able to charge every potential customer exactly at her willingness to pay.
Charging every cus- tomer exactly her willingness to pay is known as third-degree price discrimination in the eco- nomics literature. While it is unrealistic to assume that this total potential could ever be captured, the sheer magnitude of the potential gain means there is a powerful motivation for sellers to tailor dif- ferent prices to different buyers according to their willingness to pay.
These two price-response curves are shown in Figure 4. The sum of these two curves is the original price-response curve in Figure 3. These two segments taken together make up the same total market that the widget maker faced before. The difference is that now he can offer a different price to each of the two segments. We assume for this example that the widget maker can perfectly identify customers as belonging to one group or the other and can then offer each customer the appropriate price, without any opportunity for resale or arbitrage between the two groups.
Demand Demand 4, The widget maker can determine the optimal prices for each segment by solving Equa- tion 3. The results along with a comparison to the un- segmented case are shown in Table 4.
Dividing his customers between those with w. These customers are priced out of the market if the seller can only charge a single price. In this case, price differentiation is a win-win situation since the seller is certainly better off and all of the buyers are at least as well off as before.
However, price differentiation is not always such a boon for consumers, as we discuss in Section 4. The reason is that there are powerful real-world limits to price differentiation.
Imperfect segmentation. The brain-scan technology required to determine the pre- cise willingness to pay of each customer has not yet been developed. The best that can be done is to create market segments such that the average willingness to pay is different for each segment.
Example 4. The second means that price differentiation needs to be carefully planned and managed in order to be successful. In this section we describe some of the most common and effective approaches to price differentiation used in different markets.
Senior citizen dis- counts are predicated on the belief that senior citizens, as a whole, are more price sensitive than the public in general. This is necessary to avoid arbitrage—in which customers with access to low prices resell to customers who are quoted higher prices. While group pricing on the basis of age is broadly accepted, differentiating prices on the basis of other characteristics, such as race and gender, are controversial or illegal.
The Robinson- Patman Act prohibits many forms of group pricing that wholesalers might want to use to charge differential prices to retailers. Taken together, these criteria are so stringent that pure group pricing is relatively rare in direct consumer sales.
It is most common in services. Furthermore, many services, such as health care and haircuts, are intrinsically non- transferable, so arbitrage is not an issue. Pure group pricing is also common in business-to-business sales. In Chapter 11 we dis- cuss how businesses can estimate price responsiveness and develop customized prices for different business segments. As with other price differentiation schemes, there can be more than one reason why a seller might charge different prices through different channels.
One is cost—for many companies, selling through the Internet is cheaper than selling through traditional chan- nels. For personal loans, it has been shown that customers inquiring through the Internet are more price sensitive than those contacting a call center, who are in turn more price sensitive than those who apply for a loan at a retail branch. This is not surprising given the characteristics of the channels—it is generally easier and more convenient to shop and compare prices during a single Internet session than by making many phone calls.
Thus dif- ferential willingness to pay is also a motivation for channel pricing. After all, travelers at an airport are essentially a captive market and have few alternatives. It is often much more convenient to differentiate prices in ways that allow customers to self-select. The idea is that those willing to make the additional effort to get the discount are generally more price sensitive than those who are not. Any customer can obtain an item at a discount if she is willing to take some additional ef- fort.
Research has shown that users of coupons are more price sensitive than nonusers of coupons. Since these mechanisms are based on self-selection, they are far more acceptable to most consumers than mechanisms in which the seller unilaterally selects customers to receive discounts. The most notable of these is designing or developing products either virtual or real that may have only minor differences but enable the seller to exploit differences in price sen- sitivity among customer segments.
We will discuss examples of both strategies as well as their logical extension into the creation of a product line. Inferior goods. Consider the following cases. This is a term coined to refer to the situation in which a manufacturer or supplier cre- ates an inferior good by damaging, degrading, or disabling a standard good Deneckere and McAfee Since this process starts with the standard good, the supplier is actually pay- ing more to create the inferior good it will sell at a lower price.
One example is the SX processor developed and sold by Intel Corporation. The SX processor of Intel Corporation was initially produced in a curious way.
Intel began with a fully functioning DX processor, then disabled the math coprocessor, Phillips, Robert. There can be a tremendous gain from offering an inferior good at a lower price, even if the supposedly inferior product is more expensive to produce. Superior goods. Spendrups is the largest brewery in Sweden. Traditionally Spendrups brewed medium- or low-priced lagers aimed at the mass market.
In the s, they created Spendrups Old Gold, which they advertised as a premium beer and sold in a special, highly distinctive bottle.
This is the ob- vious complement to the inferior-good strategy: creating a superior good in order to extract a higher price from less price-sensitive customers. Another example of the superior-good strategy was employed by Proctor-Silex. The only difference between the two was that the top model had a small light in- dicating when the iron is ready to use. In some ways, a superior-good strategy is safer than an inferior-good strategy because it does not threaten cannibalization of existing sales.
Of course, it presumes an ability to create and establish a product that the market perceives as truly superior to the existing product and that there is a customer seg- ment willing to pay a premium for the superior product. Product lines. Establishing a product line is the natural extension of creating inferior or superior products. A product line is a series of similar products serving the same general market but sold at different prices. For our purposes, we will consider vertical product lines, where almost all customers would agree that a higher-priced product is superior to a lower- priced one.
This applies, for example, to a hotel that charges more for an ocean-view room than a parking-lot-view room—almost all customers would prefer the ocean view to the Phillips, Robert.
It also applies to personal computers offered by Dell, where each product in the line has higher performance faster CPU, more memory, etc. This can be contrasted to horizontal product lines, where different cus- tomers would prefer different products within the line, even at the same price.
This is a horizontal product line because no one of the products is unambigu- ously higher quality or more desirable than another. An example of a vertical product line is shown in Table 4. Yet the Enterprise Solu- tions package is priced more than 15 times higher than the Basic Edition. The establishment of a series of products allows Intuit to segment its market via self-selection on the part of its customers.
Another example of product-line pricing is illustrated in Table 4. By providing a menu of al- ternatives at different prices Hertz allows customers to self-select: There are those who are entirely budget-focused and will choose the Economy or Compact cars and those who pre- fer and are willing to pay for greater levels of driving comfort.
It is important to stress that the range of rates offered by Hertz for these different products is not driven by cost differ- ences.
Life-cycle costs do not vary much among models. More important, there is little or no difference in the daily incremental cost to Hertz from renting out an economy car or a Phillips, Robert.
A rental car company or a cruise line has the ability to oversell lower-quality car types and upgrade customers into higher-quality types. An important advantage of pric- ing differentiation by establishing a product line is that consumers perceive it as fair. The pricing menus offered by Hertz and Intuit are openly communicated and available to all comers. In each of these cases, companies have created differentiated products that allow customers to self-select. In the case of Amazon, customers who are willing to wait for delivery can pay less.
Of course, it may be that the higher price charged by Amazon for early delivery exactly matches the incremental cost. But it is highly likely that Amazon is also using time of deliv- ery as a segmentation variable, relying on the fact that some of their customers will willingly pay a premium in order to have the product in their hands sooner. Those traveling for leisure pur- poses are presumed to be more price sensitive than those traveling for business. This seg- mentation is the foundation of revenue management in those industries, and we discuss it in detail in Chapter 6.
The willingness of some customers to wait in order to purchase fash- ion goods at a discount is the basis of markdown management, which we treat in detail in Chapter We have treated product versioning and group pricing as separate strategies for price differ- entiation. In reality, there is no clear line separating the two approaches and many price dif- ferentiation strategies contain elements of both.
Is this group pricing or product versioning? Disgruntled customers might argue that it is simply group pricing, since different customers are paying different amounts for exactly the same service, namely, a roundtrip coach seat San Francisco—New York. In addition, managers will find the practical approach to the issue of pricing and revenue optimization invaluable. With updates to every chapter, this second edition covers topics such as estimation of price-response functions and machine-learning-based price optimization.
New discussions of applications of dynamic pricing and revenue management by companies such as Amazon, Uber, and Disney, and in industries such as sports, theater, and electric power, are also included. In addition, the book provides current coverage of important applications such as revenue management, markdown management, customized pricing, and the behavioral economics of pricing.
0コメント