# Setting the Price in the Face of Competitive Substitutes – An Economics Approach

### Introduction

Price setting of new offerings proves to be a challenging task. Understanding how to accurately define the price point that reflects the value created by the new product or service provides tremendous financial impact to a firm’s bottom line. Pricing too low may be useful for driving volume and gaining market share but comes at the cost of losing potential profit and inaccurately setting price-to-value expectations. Pricing too high may lead to greater reaped profit margins from infrequent transaction occurrences but usually result in lost profit from lack of volume and increased market interest from fringe firms. Ultimately, pricing errors are detrimental to profits, volume, and a firm’s market existence.

Cost-based pricing has been the norm ever since the presence of trade. In some instances, firms presently use cost-based pricing to meet current pricing needs. The cost paradigm hinges on understanding the marginal cost structure of production and marking up according to industry best practices to deliver price. Although, the efficiency of truly capturing a consumer’s willingness to pay and perceived value using off the cuff cost-based pricing strategies, is quite unrealistic. The evolution of price setting techniques in the business landscape has allowed firms to price closer to value realized.

Value driven pricing strategies have emerged to become the forefront in aligning product’s observed benefits with price capture. Reversing the normal cost-based value chain to fully understand customer dynamics first, allows for successful implementation of value-based pricing methods. Identifying the importance placed on products or services by consumers is the primary objective of value-based pricing. After defining value customers recognize, price can accurately be set accordingly. Cost feasibility based on the price arrived at determines if the product is profitable. After value has been identified, price set, and cost derived, the product is then offered if deemed necessary. When firms use value-based pricing the likelihood of product success and healthy profit margins being realized is quite promising.

### Price Setting Techniques

Price setting methodologies tend to mirror the offering and the maturity of the market. In the market for evolutionary goods, products that offer marginal enhancements to the status quo, conjoint analysis proves to be the most useful. Conjoint analysis provides statistical evidence on how different product features stack up in relationship to consumers’ part-worth utilities. Identifying prominent product components that add more value to the product as a whole allows firms to align benefits to price more accurately.

Exchange value models offer a range of potential price points between the exchange value and comparable alternative, defined by differential value. Exchange value models tend to provide the most insight in setting the price of revolutionary products. Developing the zone of possible prices starts by determining whether the new good offers more or less value than the comparable alternative. Based off the previous determination, positive or negative differential value can be assigned to better understand the change in consumer’s utility provided by the new offering. Differential value plus the price of the comparable alternative sets the exchange value. The price of a revolutionary product falling between the exchange value and the price of a competing alternative, delivers the best suited price according to value received. Value that cannot be captured or value left on the table gives indication on how close the actual price is to the exchange value.

Price optimization tends to be the favored approach to price setting in theoretical scenarios where elasticities of demand on the individual and industry level are transparent and converge. Mature markets where products are relatively commoditized allow the use of price optimization when determining which price maximizes profit. Price optimization techniques often lead to misstated prices because of the short-run perceived lens. The disparity of elasticities between industry and consumer levels as well as pinpointing the appropriate price elasticity challenges the efficacy of price optimization. Representing true marginal cost depends highly on which time frame the analysis is occurring. Firm decision makers must tread lightly when utilizing economic price optimization models when uncertainty is prevalent.

### Consumer Theory Price Setting: A Mixed Bag

Economic consumer theory represents how a demander allocates consumption behavior between two good to maximize utility under constraints such as prices, time, and income. Consumer theory rests on the simple foundation that individuals are utility maximizing entities with the driven purpose to make tradeoffs depending on preferences and constraints. Usually the end objective of consumer theory in general equilibrium is to define the consumption set that maximizes the utility function and still remains on the budget constraint. Other tangents can be followed to derive equally beneficial outcomes.

Price determination of new product offerings can be the product of consumer theory if massaged. This new way of theoretically thinking about price derivation fits best in the evolutionary product setting where marginal improvements are distinguishable. Assumptions outlining the approach to pricing through consumer theory are as follows:

- Prices are linear (Price discrimination cannot be implemented…single price model)
- Prices of comparable alternatives are known
- The value of all goods are well understood
- Consumers are considered price takers

### Perfect Substitute Case

The basic utility maximization problem facing consumers is outlined by

where X_{N} and X_{C} represent the quantity of new good consumed and the quantity of comparable alternative consumed, respectively. P_{N} and P_{C} stand for the prices of the new and comparable alternative. M stands for the income endowment of the consumer. Essentially, a consumer prefers to maximize their utility by consuming X_{N} and X_{C} subject to the budget constraint. A generic utility function that characterizes an evolutionary product market with perfect substitutes is

*α* and *θ* are strictly positive numbers that measure the value of the new good and comparable alternative to the consumer. These scalars show the rate of substitution between both products. In other words the ratio of scalars represents the slope of the indifference curve and could be compared to differential value in exchange value models. Any other monotonic transformation of the generic utility function would be a sufficient model for analysis.

### Exhibit 1: Optimal Choice

Lagrangian optimization techniques or setting the marginal rate of substitution along the indifference curve equal to the price ratio will not offer a unique solution due to the perfect substitute assumption. The equimarginal principle will deliver the consumption behavior, choice, and price using the current model. The marginal utility of the new product divided by its price must exceed or be equivalent to the marginal utility of the comparable alternative divided by its price. In this instance a consumer will choose to consume the new product due to marginal improvement in value according to a static change in price.

The theoretical derivation of the new product price provides a means to evaluate the value ratio or tradeoff factor between products and the price of the comparable alternative.

### Cobb-Douglas Case

Still under the assumptions outlined earlier and same budget constraints, but modifying the generic utility function to represent Cobb-Doulas preferences, price setting will occur through constrained maximization. The new utility function encompassing Cobb-Douglas preferences will offer a price determination that does not require goods to be perfect substitutes.

In this case, *α* and *θ* are taste parameters essentially leading to different slopes of indifference curves. Cobb-Douglas utility functions provide well-behaved indifference curves that prove to be easily algebraically managed. Exhibit 2 offers a visually means of determining optimal choice through setting the marginal rate of substitution (MRS) equal to the price ratio.

### Exhibit 2: Optimal Choice

At the optimal choice, the slope of the indifference curve (MRS) is equal to the slope of the budget constraint (Price ratio). Mathematically deriving the optimal choice and solving for the price of the new product offering proves useful in price setting. Taking the natural log of the utility function allows for easier manipulation and determination of the marginal rate of substitution.

The take away from the constrained maximization approach rests on interpreting the differential parameters, *α* and *θ*. The slope of the indifference curve, regardless of which case, defines the tradeoff between competing products. Managers understanding the taste parameters of consumers can better position their products according to benefits of competitor’s products. The price determination in each case shows the magnitude of differential power between products. Accurately estimating such differences allows executives to better price products.

The challenges posed by this price setting model are similar to those of economic price optimization. Capturing individual utility and ordinal preference relationships will be the primary downfall to the proposed technique. If such variables could be measured the price point realized by this model would fall between the boundaries defined by exchange value models.