Transaction Utility and Quality Choice

Sajeesh Sajeesh; Sang-Young Song

doi:10.1515/roms-2016-0030

Published by De Gruyter August 23, 2017

Transaction Utility and Quality Choice

Sajeesh Sajeesh and Sang-Young Song

From the journal Review of Marketing Science

https://doi.org/10.1515/roms-2016-0030

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Abstract

This paper uses a game-theoretic model to examine the role of reference price for firms that vary in their quality positioning in competing for customers. Reference prices provide consumers with additional components of utility. Building on previous research on the impact of consumer decision making on firm strategies, we focus on how firms choose their positioning when consumer utility is driven not only by acquisition utility but also by the transaction utility associated with the purchase and how this, in turn, affects firms’ pricing decisions and profits. Considering a competition between two firms, this paper shows that the firm with higher product quality provides greater discounts to consumers. We also show that when firms are allowed to set a high ‘regular’ price, product differentiation is greater between the firms, and price competition is less intense. Furthermore, under some conditions, the profits of both firms can be higher than the benchmark case (when the effects of transaction utility are ignored).

Keywords: transaction utility; reference prices; product positioning

Appendix

Equating consumer utility, the location of the marginal consumer is given by

(A.1)θ˜p1,p2,λ1,λ2=p2−p11+λ1+λ2−λ1αcs22+λ1αcs12s2−s1.

Therefore, the demand observed by the two firms is given by

(A.2)D1=1b−ap2−p11+λ1+λ2−λ1αcs22+λ1αcs12s2−s1−a,

(A.3)D2=1b−ab−p2−p11+λ1+λ2−λ1αcs22+λ1αcs12s2−s1.

Now,

(A.4)pˆ1=maxp1p1−cs12D1,

(A.5)pˆ2=maxp2p2−cs22D2.

Setting the derivative of π1 w.r.t p1 to zero and setting the derivative of π2 w.r.t p2 to zero, the first-order conditions (FOC’s) for profit maximization lead to the following equilibrium prices,

(A.6)pˆ1=b−2as2−s1+2cs121+λ1+λ2+cs221+λ1+λ2+cαλ1s12−s223λ1+3λ2+3,

(A.7)pˆ2=2b−as2−s1+cs121+λ1+λ2+2cs221+λ1+λ2+cαλ1s22−s123λ1+3λ2+3.

The choice of quality level can be found by solving the following maximization problem:

(A.8)s1∗=maxs1pˆ1−cs12D1pˆ1,pˆ2,

(A.9)s2∗=maxs2pˆ2−cs22D2pˆ1,pˆ2.

Setting the derivative of π1 w.r.t s1 to zero and setting the derivative of π2 w.r.t s2 to zero, using the FOC’s for profit maximization and solving, we get eqs (8) and (9) The second-order conditions (SOC’s) are given by d2πidsi2|(s1=s1∗,s2=s2∗)=12c−λ1−λ2+αλ1−1λ1+λ2+1 for i=1,2. The SOCs are satisfied for α<1+1+λ2λ1.

Substituting the equilibrium locations, the equilibrium prices are given by the following:

p1∗=16449a21+λ1+λ2+25b21+λ1+λ2−58ab1+λ1+λ2−24αλ1a−b2λ1+λ2+1c−λ1−λ2+αλ1−12,p2∗=16425a21+λ1+λ2+49b21+λ1+λ2−58ab1+λ1+λ2−24αλ1a−b2λ1+λ2+1c−λ1−λ2+αλ1−12.

Therefore,

p2∗−p1∗=38b2−a2c1+λ1+λ2−αλ12,dp2∗−p1∗dα=34cλ1b2−a2λ1+λ2−αλ1+13>0.

Not surprisingly, the higher-quality firm charges a higher price. As α increases, the difference in equilibrium prices between the high-quality and the low-quality firm also increases. The equilibrium market share of each firm is 12b−a>0. The conditions α<1+1+λ2λ1 and b<5a also ensures that the equilibrium prices are greater than 0 and dp2∗−p1∗dα>0.

Verifying that firms do not have an incentive to deviate from the equilibrium locations given in equations (8) and (9)

Given s2∗, when Firm 2 is the higher-quality firm, profits for Firm 1 is given by

(A.10)π1s2∗=−14608a−5b+8cs1+8cλ1s1+8cλ2s1−8cαλ1s117a−13b−8cs1−8cλ1s1−8cλ2s1+8cαλ1s12a−bc−λ1−λ2+αλ1−1λ1+λ2+1.

If Firm 1 deviates to choose a higher-quality than Firm 2, then Firm 2 becomes the lower-quality firm. The profits for Firm 1 under this scenario can be found by interchanging s1 and s2 in π2. In such a deviation, the profits of Firm 1, π1ds2∗ is given by

(A.11)π1ds2∗=−14608a−5b+8cs1+8cλ1s1+8cλ2s1−8cαλ1s117a−13b−8cs1−8cλ1s1−8cλ2s1+8cαλ1s12a−bc−λ1−λ2+αλ1−1λ1+λ2+1.

Using the first-order condition for profit maximization, the profits in the two settings is given by

(A.12)π1s2∗=3(b−a)216cλ1+λ2+1λ1+λ2+1−αλ1,and

(A.13)π1ds2∗=1144b−a2cλ1+λ2+1λ1+λ2+1−αλ1.

Since π1s2∗>π1ds2∗, firm 1 has no incentive to deviate and offer quality higher than Firm 2. Thus, the local equilibrium is the global product quality equilibrium.

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Published Online: 2017-8-23

Published in Print: 2017-9-26

From the journal

Review of Marketing Science

Volume 15 Issue 1

Journal and Issue

Articles in the same Issue

Frontmatter

Transaction Utility and Quality Choice

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