# This paper considers the decision problem of a firm that is uncertain about the demand, and hence profitability,

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5 Marketing Science 25(1), pp. 25 5, 26 INFORMS 29 Figure 1 Kellogg s Kenmei Rice Bran 6 3 Sales (mill. lb.) 4 2 Price (\$/lb.) Year Year Advertising (mill. \$) Year Advertising/sales ratio Year Figure 2 General Mill s Apple Cinnamon Cheerios 1 3 Sales (mill. lb.) 5 Price (\$/lb.) Year Year Advertising (mill. \$) Year Advertising/sales ratio Year

8 32 Marketing Science 25(1), pp. 25 5, 26 INFORMS This value is positive if and only if q> 1 / 2. For example, if the discount factor is 9, which roughly corresponds to an annual interest rate of 1%, the firm should scrap the product only if q< 9. The solution of the model considered below involves the same ideas that we just illustrated using a very simple model. The realism needed for an empirical application, however, requires consideration of many details, in particular on the demand function and also on the prior that contains the firm s information. We give a full account of these details below. Model Details States and Decisions. The firm s objective is to maximize the expected PDV of the stream of profits generated by a specific product, Ɛ =t t s t. 18 The objective function is maximized with respect to a sequence of decision variables t = E t A t, where E t denotes the exit E = 1 or stay E = decision, and A t is the current advertising level. These decisions are based on the state vector s t = h t t t g t. h t denotes the age of the product, i.e., the number of time periods passed since the product was launched. t and t index the current prior on the product quality parameter. As is explained in more detail below, in our model this prior is a normal distribution, represented by the normal probability density p t = p t t 2. g t is the current goodwill stock, a measure of the accumulated effect of advertising in demand. The expected flow of profits in period t is s t t = s t t f d A t k (1) t denotes current profits, gross of advertising, and the per-period cost factor k. k can be thought of as a fixed cost of production, which includes the value of the time managers devote to the specific product, and the opportunity cost of the shelf space in the supermarkets where the product is sold and in the warehouses where it is stored intermittently. The expectation in (1) is taken with respect to the distribution of, a vector of demand shocks. The shocks are i.i.d. across time and products, but possibly dependent across geographic markets. The gross profit function is derived from some underlying demand system. As will be explained in detail below, t incorporates a vector of equilibrium product prices, which are determined after the current state of the market is realized. In the framework considered here, product prices do not change the transition process of the state vector. Hence, pricing 18 In this formulation, managers are assumed to be riskneutral. has no dynamic effects on future profit flows, and can therefore be separated from the dynamic decisions, advertising and product exit. Product Demand. Product demand is modeled as a random coefficients logit demand system (Berry et al. 1995, Nevo 21). Our approach follows Nevo (21), who develops and estimates such a demand system for the case of the U.S. RTE breakfast cereal industry. Random coefficients logit models have several desirable properties. In particular, they allow for flexible substitution patterns among differentiated products that can be related to some underlying household heterogeneity structure, yet they can be estimated using market-level data only. Also, the potential econometric endogeneity of prices can be accounted for using instrumental variables. For a detailed discussion, we refer the reader to the aforementioned papers and Nevo s (2) very accessible user guide. More generally, our frameworkcan accommodate any product demand system that has the same underlying latent utility structure as our model. For example, this includes the case of a probit demand system. Even more generally, any demand system with an associated profit function of the form s t t t could be employed, although such a formulation may lose the computational tractability of our model. 19 We consider a market populated by a large number of households who choose among several differentiated products. Household l s indirect utility from product i in time period t is U l it = i l P P it + x i l x + g it A it + h it + it + l it (2) i is the quality of product i, i.e., the average valuation consumers assign to all unobserved product attributes. Everything else held constant, the market share of product i increases in i, which is the sense in which the term quality should be understood. P it is the product price, and x i is a K 1 -vector of observed product attributes that do not vary over time. P l is household l s marginal utility of income, and l x expresses household l s preferences for the product attributes in x i. Both the accumulated effect of advertising in the past and the current flow of advertising have an impact on demand through the function, which is specified in more detail below. h it is a preference shockthat systematically occurs h it periods after product launch. This term is a simple proxy for consumer learning, or variety seeking. 19 If the firm cannot infer from observed sales up to an additive error, the prior and posterior will generally not be conjugate, and hence it will be difficult to represent the prior in a computationally convenient form.

12 36 Marketing Science 25(1), pp. 25 5, 26 INFORMS Figure 4 Solutions of the DP: The Value Function V, the Optimal Advertising Policy A, and the Exit Rule E Value function Value function 2, 3, 1,5 2, 1, 5 1, 5 g 8 6 µ µ 4 Advertising policy Advertising policy g 8 6 µ µ 4 6 Exit policy 1.2 Exit policy g µ Note. The exit region of the state space is shaded gray. of the advertising copy, for example. Across products and time, the error terms are assumed to be independent. Under these assumptions, the signal t has a multivariate normal distribution, t N t t t t t = t t is an M-vector with all components equal to 1. Under Bayesian updating, the posterior p t t has a µ normal distribution with moments 28 t+1 = t + 2 t T 1 t t t (15) 2 t+1 = 2 t 1 2 t T 1 t (16) Equation (15) implies that t+1, conditional on the current information summarized in the state and decision vectors, has a normal distribution with mean t and covariance matrix var t+1 = t 4 T 1 t. Hence, t has a normal transition density f t+1 s t t = N t t 4 T 1 t. 28 See the exposition in DeGroot (1969).

20 44 Marketing Science 25(1), pp. 25 5, 26 INFORMS Figure 5 Top Row: Products Are Drawn from the Empirical Distribution of All Newly Launched Products. Bottom Row: Products Are Drawn from the Empirical Distribution of All Products in the Sample 12.5 (a) Relative profit loss 1. (b) Percent launched 1. (c) Exit rate \$ mill (d) Relative profit loss 1. (e) Percent launched 1. (f) Exit rate \$ mill drawn from all, the empirical distribution of all products, new and established, in our sample. The first distribution contains a larger fraction of unprofitable products than the second (Table 5). Figures 5(a) and (d) show L L, the profit loss under a specific (the standard deviation of the prior at the time of product launch) relative to the baseline profit under perfect information. 44 The profit loss can be large; at the estimated standard deviation = 1 31, it is \$11.8 million under new and \$8.4 million under all. As a percentage of the expected profit under perfect information, the loss is 37.5% under new and 5.7% under all. The reason for this difference is straightforward. Under the empirical distribution of all newly launched products the incidence of unprofitable products is higher than under the empirical distribution of all products in the market. Hence, the average profitability of a new product is lower (\$31.45 million versus \$ million), and the scope for making the wrong entry or exit decision is higher. Hence, relative to average profits under certainty, the value of information is higher under new. Optimal Entry and Exit Rates. We next turn to the question of how firms should change the fraction of 44 All profit numbers shown are in 24 dollars. new product opportunities launched under increasing demand uncertainty. Furthermore, we calculate the optimal exit rate. Figure 5 displays the percentage of new product opportunities launched and the product exit rate under new and all. 45 Under full information, 3% of all product opportunities are launched under new, and 78% of product opportunities are launched under all. 46 The difference in the launch rates reflects the underlying occurrence of profitable products under the two distributions. The percentage of products launched increases strongly in the degree of uncertainty. If products are drawn from new, 96.5% of all product opportunities should optimally enter the market at the estimated uncertainty, = Even under much smaller levels of uncertainty, more than 8% of all product opportunities should be launched. Consequently, firms incur large product exit rates; for example, under new close to 8% of all newly launched products exit if the initial uncertainty is larger than.25. Hence, optimal, forward-looking behavior can imply that under even 45 The exit rate is defined relative to all products that were actually launched, i.e., not including product opportunities that never entered the market. 46 In other words, 3% and 78% of all new products drawn from these two distributions are profitable.

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