The Camera Shop sells two popular models of digital SLR cameras (Camera A Price:

Question

The Camera Shop sells two popular models of digital SLR cameras (Camera A Price: 200, Camera A Price: 300). The sales of these products are not independent of each other, but rather if the price of one increase, the sales of the other will increase. In economics, these two camera models are called substitutable products. The store wishes to establish a pricing policy to maximize revenue from these products. A study of price and sales data shows the following relationships between the quantity sold (N) and prices (P) of each model:

   NA = 198 - 0.5PA + 0.25PB

   NB = 305 + 0.07PA - 0.6PB

Construct a model for the total revenue and implement it on a spreadsheet. Develop two-way data table to estimate the optimal prices for each product in order to maximize the total revenue. Vary each price from $250 to $500 in increments of $10.

Max profit occurs at Camera A price of $ .

Max profit occurs at Camera B price of $ .

Explanation / Answer

Ans-

the overall sales of high-end Canon cameras to enthusiastic consumers increase only in the first 8 months after the price change but decrease over time, bottoming out at 0.6% by the end of the time. This is because, after the price change, many price-sensitive consumers will choose not to purchase or to delay their purchase of low-end Canon cameras. Thus, this demand system will end up with a smaller customer base of low-end Canon camera holders. Fewer enthusiastic consumers will learn their types through purchase, and fewer of these consumers will purchase high-end Canon or Nikon cameras in the long run, leading to the decreasing elasticities of high-end cameras among enthusiastic consumers. Due to switching costs across brands, the impact on the decreasing sales of high-end Canon cameras is larger than that of high-end Nikon cameras. For this 1% price increase of low-end Canon cameras, the overall sale of high-end Canon cameras will decrease to about 0.4% to 0.5% by the end of the time. As a result, the estimated demand model implies a dynamic complementary relationship of low-end and high-end products produced by the same firm. This is the key demand side finding that drives the supply-side pricing results. Finally, using demand estimates and a stylized supply model, I explore the consequences of the demand dynamics on firms’ pricing strategies. First, I find that, due to the complementary relationship on the demand side, forward-looking firms have incentives to invest in their customer bases using low-end products. Firms can then harvest the resolved uncertainty of valuation and switching costs using high-end products. Second, I find that increasing switching costs between brands leads the optimal prices of low-end (high-end) products to decrease (increase). This result means that switching costs increase the incentives of firms to invest in their customer bases to accelerate consumer learning. When the switching cost is 10 times the estimated value, firms compete so fiercely in pricing low-end/gateway products that, for example, Canon is even willing to price its low-end product below the marginal cost. This aggressive pricing of low-end products drives consumers to adopt DSLR cameras and increases consumers’ welfare. In addition, the quality of high-end products determines firms’ competitiveness in the high-switching-cost environment. Third, I find a merger leads the firms to reduce the number of products. The merger also drives down the price of the low-end product, while the price of the high-end product rises. The novelty of my model is that it integrates both consumer learning and switching costs into a dynamic demand framework for durable goods in order to predict the resulting observed pattens of consumer choice. I assume that a consumer who has never purchased a 4 DSLR camera before does not know in advance her subjective valuation of using the advanced cameras. A consumer learns her valuation/type by purchasing a camera, which causes her to behave differently when considering her repurchase decisions. In addition, a consumer pays costs if she switches to a new brand when repurchasing. Every period, a forward-looking consumer chooses whether or not to purchase a DSLR camera, forming perceptions of future market states. When a new camera is purchased, the utility that depends on characteristics of the camera model comes upfront at the moment of purchase. In addition, after purchase, the camera in inventory delivers flow utility each period. A key to the simplicity of the model is in the flow utility from the camera in inventory. This flow utility is assumed to depend only on two factors: the product-line group of the camera model (low-end or high-end) and the consumer’s type. This assumption simplifies the state space of the consumer’s problem. Its advantage is that I am able to break down consumer choice into two separate components: 1) a static problem of choosing camera models conditioning on brand and product-line group choices; 2) a dynamic problem of choosing brands and product-line groups. To estimate the model, I combine aggregate monthly sales data (1999 - 2006) in the US DSLR camera market with micro-level camera ownership transition data from Flickr. I embed the Micro BLP-style (see Berry, Levinsohn, and Pakes, 2004) estimation approach to match the model predictions of conditional dynamic choice probabilities to the moments in Flickr data, in addition to match the market shares using the BLP moments (see Berry, Levinsohn, and Pakes, 1995; Gowrisankaran and Rysman, 2012). I choose this approach because, from the aggregate sales data, repeated purchases can not be distinguished from initial purchases, nor can individual purchase history be observed. Thus, in order to study consumer learning and switching dynamics, I need to supplement the sales data with information on individual-level camera ownership transitions. For example, identification of the switching cost is obtained by matching the probabilities that consumers choose previous brands conditional on repurchasing. Identification of consumer learning is obtained by matching the changing probabilities that consumers choose product-line groups in initial purchases and in later repurchases. The contributions of this paper are threefold.

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