Measuring the Impact of Increased Product Substitution on Pricing and Capacity Decisions Under Linear Demand Models

Abstract

We consider two substitutable products and compare two alternative measures of product substitutability for linear demand functions that are commonly used in the literature. While one leads to unrealistically high prices and profits as products become more substitutable, the results obtained using the other measure are in line with intuition. Using the more appropriate measure of product substitutability, we study the optimal investment mix in flexible and dedicated capacities in both monopoly and oligopoly settings. We find that the optimal investment in manufacturing flexibility tends to decrease as the products become closer substitutes; this is because (1) pricing can be used more effectively to balance supply and demand, and (2) the gains obtained by shifting production to the more profitable product are reduced due to increased correlation between the price potentials of the substitutable products. The value of flexibility always increases with demand variability. We also show that, as long as the optimal investments in dedicated capacity for both products are positive, the optimal expected prices and production quantities do not depend on the cost of the flexible capacity. Manufacturing flexibility simply allows the firm to achieve those expected values with lower capacity, while leading to higher expected profits.

Impacts of earmarked private donations for disaster fundraising

“…Donor's utility function must satisfy three conditions: (a) represent donors' behavior in the situation with and without earmarked funds (b) capture substitution/complementary effects between funds and (c) be simple enough to allow for solution derivation and analysis. The quasi-linear utility function used in Lus and Muriel (2009) motivated by Singh and Vives (1984) satisfies these three aspects.…”

“…Donors' donation behavior is motivated by two major factors: (1) donors' utility from donating money (e.g., Rose-Ackerman 1982), and (2) costs to the donors, stemming from an aid agency's fundraising costs and administrative costs (e.g., Khanna et al 1995). Analogously, in the function by Lus and Muriel (2009), consumers' utility is increasing in their consumption of private goods and decreasing in the price that consumers have to pay for these goods. (b) The level of substitutability between special funds within one aid agency has not been analyzed so far.…”

Yield Management Models for Two Substitutable Products

“…Kocabiykoglu and Popescu [13], Kim [11], Lus and Muriel [15], Tang and Yin [22] and Yu [26]. Lee and Kim [7] developed an optimal pricing and production decision model with price-driven substitution alone, where a part of the demand lost in one market moves to the other market.…”

“…Lee and Kim [7] developed an optimal pricing and production decision model with price-driven substitution alone, where a part of the demand lost in one market moves to the other market. Lus and Muriel [15] considered deterministic pricing/quantity decision problems with two substitutable products and compared two alternative measures of product substitutability for linear demand functions. Tang and Yin [22] explored joint pricing and ordering policies for two substitutable products with deterministic pricedependent demand.…”

“…This type of demand movement is called price-driven substitution. The most generally known type of demand movement, which is called inventory-driven substitution, occurs when consumers substitute for a product that is out of stock by buying a similar substitutable product [1,2,5,6,11,15,17,19,20,7].…”