Sanghak Lee

A Direct Utility Model for Asymmetric Complements

A symmetric complements refer to goods where one good is more dependent on the other, yet consumers receive enhanced utility from consuming both. Examples include garden hoses and sprinklers, chips and dip, and routine versus personalized services where the former has a broader base for utility generation and the latter is more dependent on the others presence. Measuring asymmetric effects is difficult when all that is observed are the purchase quantities present in a consumers market basket. We propose a direct utility model with a latent decision sequence for measuring asymmetric effects that allows us to capture differential responses to cross-category purchases and inventories. Scanner panel data of milk and cereal purchases are used to investigate the presence of asymmetric complementarity, and implications are explored through counterfactual analyses involving cross-price elasticities and spillover effects of merchandising variables.

Modeling Indivisible Demand

Disaggregate demand in the marketplace exists on a grid determined by the package sizes offered by manufacturers and retailers. Although consumers may want to purchase a continuous-valued amount of a product, realized purchases are constrained by available packages. This constraint might not be problematic for high-volume demand, but it is potentially troubling when demand is small. Despite the prevalence of packaging constraints on choice, economic models of choice have been slow to deal with their effects on parameter estimates and policy implications. In this paper we propose a general framework for dealing with indivisible demand in economic models of choice, and we show how to estimate model parameters using Bayesian methods. Analyses of simulated data and a scanner-panel data set of yogurt purchases indicate that ignoring packaging constraints can bias parameter estimates and measures of model fit, which results in the inaccurate measures of metrics such as price elasticity and compensating value. We also show that a portion of nonpurchase in the data e.g., 2.27% for Yoplait Original reflects the restriction of indivisibility, not the lack of preference. The importance of demand indivisibility is also highlighted by the counterfactual study where the removal of the smallest package size i.e., 4 oz mainly results in nonpurchase in the yogurt category instead of switching to larger package sizes.

Laminar Forced Convection at Zero Gravity to Water near the Critical Region

Numerical modeling is carried out to analyze the heat transfer and fluid flow for water in the critical region in laminar tube flow under zero-gravity conditions. The model considers variable density, specific heat, viscosity, and conductivity. The effect of proximity to the critical point is also considered. To accurately predict property distributions, the numerical grid is clustered in the region where property variation is severe. The results of the modeling provide heat transfer and flow characteristics including profiles of temperature and velocity, the heat transfer coefficient, and the friction factor in the developing region of the tube. Constant wall temperature and constant wall heat flux are considered, and pressure, inlet fluid temperature, and Reynolds number are used as parameters. The calculation results show differences compared from results based on constant properties, and provide insight into the effects of the large property variations on heat transfer.

A Category-Level Model of Asymmetric Complements

Asymmetric complements refer to goods where one is more dependent on the other, yet consumers receive enhanced benefit from consuming both. Examples include garden hoses and sprinklers, chips and dip, and routine versus personalized services where the former has a broader base for utility generation and the latter is more dependent on the others presence. Measuring the presence of asymmetries is difficult because it requires longitudinal variation of utility where the degree of inter-dependency changes. We introduce a utility structure with multiplicative demand shocks capable of identifying the origin of demand variation, and investigate the presence of asymmetric complementarity using scanner panel data of cereal and milk purchases. Implications are explored through counterfactual analyses involving cross price elasticities, and spillover effects.

Price Promotions in Choice Models

Promotions are commonly used in marketing to increase sales and drive profits by temporarily decreasing the price per unit of a good. Some price promotions apply to all quantities (20% off), some have limits on the number of units that can be purchased at a reduced price, and others only offer the discount if the volume purchased is sufficiently high. We develop a model of price promotions in the context of a direct utility model where its effects are incorporated through the budget constraint. Price promotions complicate the estimation and analysis of direct utility models because they induce kinks and points of discontinuity in the budget set. We propose a Bayesian approach to dealing with these irregularities, and demonstrate the ability of direct utility models to engage in counter-factual analyses of price promotions given a consumer’s utility function. We investigate the stability of utility function estimates for consumers under alternative price promotions, and find evidence supporting the assumption that price promotions only affect consumer choices through the budget constraint. We then explore the benefits of customization and show that firm profits can significantly increase by offering different types of promotions to different people.

A Direct Utility Model for Economies of Scope and Access

Economies of scope in direct utility models exist when consumers encounter costs and inconvenience in purchase and consumption. Travel time, product acquisition, training, expertise and skills are examples of factors that impact the ability of consumers to derive utility from offerings beyond the price of a good. Household production of these factors often share commonalities among choice alternatives, making it more likely that some products would be purchased and consumed in conjunction with others. We develop a model with scope economies for a latent time-related resource that constrains consumer purchases. The model is applied to a conjoint dataset of theme park demand, where we find that economies of scope lead to a better model fit, larger monetary budget estimates, smaller price sensitivities, and larger compensating value estimates relative to existing models of demand.

A Model for Mixed Decision Variables: Modeling Subscription versus Ownership of Consumer Goods

The decision to rent or own is prevalent in many consumer decisions, including what to wear, what to watch and what to read. A challenge to firms pricing these products is understanding whether renting, or having access through a subscription, is considered complementary to, or acts as a substitute to owning the product. The challenge in modeling access by subscription versus ownership is that the subscription decision is discrete whereas the ownership decision can take on positive quantities other than one. We propose a mixed discrete/continuous direct utility model, and associated estimation algorithms, for assessing the economic relationship between renting and owning and find support for their complementary nature in two conjoint studies involving music and videos. We explore the degree to which profit maximizing prices are dependent on correctly assessing whether goods are substitutes or complements.