Optimal Customer Acquisition and Customer Retention over the Business Cycle. Gerasimos Lianos 1 and Igor Sloev 2. Abstract

Transcription

1 Optimal Customer Acquisition and Customer Retention over the Business Cycle Gerasimos Lianos 1 and Igor Sloev 2 Abstract We study the problem of optimal allocation of the marketing budget between customer acquisition and customer retention by a firm over the trade cycle. In line with the Schumpeterian idea of creative destruction, we find that under perfect capital markets customer retention increases with the state of the trade cycle (pro-cyclical) and customer acquisition decreases with the state of the cycle (counter-cyclical). In the case of imperfect capital markets, however, customer retention may be decreasing and customer acquisition may be increasing with the cycle. Keywords: customer acquisition, customer retention, creative destruction, marketing budget. JEL classification: M20, M30, M31 1 Corresponding Author. School of Business Administration, University of Miami, 517-N, Jenkins Building, 5250 University Drive, Coral Gables, FL 33146, USA. glianos@bus.miami.edu, Phone: Fax: Higher School of Economics, National Research University, 33 Kirpichnaya Str., Moscow, , Russia. isloev@hse.ru

2 1. Introduction In economic recessions marketing budgets of business are slashed more than other functional budgets, σο the optimal allocation of the marketing budget during the business cycle is a matter of utmost importance. Marketing decisions are investment decisions (Srivastava et. al. 1999) and the subject of marketing, customers, are assets (Gupta and Lehman 2003) and the allocation between customer retention and customer acquisition is an asset allocation decision between different vintages of value-producing assets. The Schumpeterian view of the business cycle maintains that the continuous process of creation and destruction of productive units that results from product and process innovation is at the center of the dynamics of the capitalist business cycle (Schumpeter 1939, 1942, Caballero and Hammour 1994, Aghion and Howitt 1991, Jovanovic and Lach 1989). Recessions have the consequences of "cleansing" obsolete and unproductive productive units, firms of older vintages of capital goods, or whole economic sectors. In the present paper we study the structure of optimal customer acquisition and customer retention of a firm over the trade cycle. We build on Aghion and Banerjee 2005, Aghion et. al. 2010, and Lianos and Sloev 2014 and study the intertemporal problem of the representative firm inside a competitive industry under contest for customer acquisition and customer retention. Customer retention as a decision giving its return in the short term and customer acquisition as giving returns in the long term. We consider the possibility of a re-investment or liquidity need with respect to the long-term decision, which may also be interpreted of a previously unforeseen change in the preferences of customers, a marketing failure, or a need to reformulate the customer acquisition strategy or campaign. As in Aghion and Banerjee 2005, we set up a twoperiod problem for the representative firm in the industry. The customer retention and customer acquisition decision take place at the beginning of the first period. Customer retention gives its returns at the end of the first period. Customer acquisition gives its return at the end of the second period. We formulate the re-investment need of the firm that may occur at the beginning of the second period. In particular, we assume that the firm can realize the returns from customer acquisition only if it meets the re-investment need. The question of the allocation of marketing expenditure between customer acquisition and customer retention has been studied from the perspective of an isolated firm as well as of a firm in a competitive industry. We follow

3 Blattberg and Deighton 1996 in the specification of the return funcions in the model of maximization of Customer Lifetime Value. The organization of the paper is as follows: In Section 2 we present the baseline model of optimal allocation of the marketing budget between customer acquisition and customer retention. The firm enters the industry with a marketing budget and the initial customer base. At the beginning of the first period the firm observes the first-period realization of the profitability of the current customer base. At the beginning of the first period the firm forms expectations about the realization of the profitability of the newly acquired customers. The firm decides on the allocation of the marketing budget between the short-term customer retention and the long-term customer-acquisition decisions. Optimal customer retention is increasing with the state of the business cycle (pro-cyclical) and customer acquisition decreases with the state of the business cycle (counter-cyclical). In Section 3 we present the extended model. There is a re-investment need occurring at the beginning of the second period after the realization of the first-period returns, and must be met before the firm continues to operate in the second period. The probability of meeting the re-investment need depends on the size of the shock, the realized return on the initial customer base and the customer retention, the degree of capital markets perfection, and the extent that the probability distribution function depends on the first-period wealth. If capital markets feature a high degree of imperfection, customer acquisition decreases and customer acquisition increases with the state of the trade cycle. In order to be able to meet the random re-investment need in the second period, the firm must retain a larger part of the initial customer base even if the initial customer base is less profitable than the newly acquired customers are expected to be. In Section 4 we conclude. 2. The Basic Business Cycle Model We consider a firm that lives for two periods. The firm starts the first period with a customer base of unity and a flexible marketing budget. Customer profitability is a random variable and it is realized at the beginning of each period. The realized value of the random variable in the first period is and in the second period,, with the law of motion:, with, ε ~ ), Firms decide over the retention of existing customers and acquisition of future customers. The customer retention expenditure is R and the customer

4 acquisition expenditure A. Without loss of generality, we assume that after the end of the first period all previous customers leave the firm. These customers may be thought of as retiring from the industry, or as changing profitability type and becoming the target for acquisition of the first in the second period of operation. The customer retention expenditure and customer acquisition expenditure relative to the industry are defined as: and:. If the firm spends the relative amount in customer retention, the firm s gross realized profits at the end of the first period is:. Similarly if the firm spends the relative amount in customer acquisition, the firm s gross realized profits at the end of the second period is given by: Both expenditures are incurred at the beginning of the first period, after the realization of the random customer profitability is observed. Customer retention gives its return at the end of the first period. Customer acquisition gives its return at the end of the second period. The problem of the firm is to choose the mix of customer-acquisition and customer-retention expenditures to maximize the sum of the two-period cash flows subject to the marketing budget constraint, and the stochastic process for customer profitability. The firm solves: ( ) ( ). ( ) The first-order condition with respect to the choices for R and A are given by:

5 In the symmetric equilibrium of the industry we have: and:. We have:. Using these conditions the first-order conditions give that the optimal policy functions as follows: The acquisition-to-retention expenditures ratio is given by: The quantity measures the elasticity of the optimal relative marketing expenditure share with respect the current customer profitability. The elasticity depends on the persistence parameter,. If the persistence of the profitability state is very high, the optimal marketing expenditures ratio is irresponsive to the state of the business cycle. If the persistence of the profitability state is very low,, the optimal marketing expenditure ratio moves proportionately to the cycle. Figure 1 shows the marketing budget B as a function of the state of the economy s for the parameter values: and rho=0.3 rho=0.6 rho=0.9 total marketing budget current state of business cycle Figure 1 Figure 2 shows the ratio R/A as a function of s for the parameter values:,,, and ρ and.

6 retention-to-acquisition expenses ratio rho=0.3 rho=0.6 rho= current state of business cycle Figure 2 The above relations have the following implications for the cyclical properties of the marketing budget: Proposition 1. The total marketing budget, economy s., is pro-cyclical, i.e. B increases with the state of the Proposition 2. The retention-to-acquisition-expenditures ratio,, is pro-cyclical, i.e. increases with s. 3. The Model with Liquidity Shocks We assume that after the allocation of the marketing budget and before the realization of the second period's return, the firm is subject to a shock that affects the acquisition of the customers in the second period. The shock is in the nature of a liquidity shock, which implies an additional cost for acquiring new customers due to a defect in the product line, a failure in the design of the marketing campaign for new customers, a random change of preferences, reducing the effectiveness of the acquisition process, or any other unforeseen contingency at the moment of the initial allocation of the marketing budget. We assume that the firm will be able to realize the second period profits only if it meets the liquidity shock. The probability of the firm surviving

7 the shock depends on the current wealth made from the first-period customer base. (In the Section 4 we will give a possible alternative interpretation in terms of the marketing concepts of customer-loyalty or a reputation effects.) The dependence of the survival will depend on the current wealth in two ways: (a) the degree of leverage of current wealth for borrowing in the capital markets, with. (b) The degree that the distribution function depends on the current wealth,, with. The timing of events is as follows: after the allocation of the marketing budget, the random liquidity shock is realized. It is (0, ), with distribution function. We assume that:, so that φ is the local elasticity of F. After ζ is realized, the firm is able to realize the acquisition of customers only if and only if, where is end-of-current-period return obtained from the existing customer base. The probability of the firm continuing into the second period is: The problem of the representative firm in the industry is to find the allocation of marketing budget into customer retention R and customer acquisition A to maximize the sum of cash flows to the firm. The firm solves the following problem: ( ) ( ) ( ) ( ) The first-order conditions of the problem are given by: ( )

8 Using the symmetric equilibrium conditions:, and, the optimal policy functions are given by: The retention-to-acquisition-expenditures ratio is given by: Figure 3 show the total marketing budget,, as a function for the parameter values:,,,, and fi=0.1 fi= total marketing budget current state of business cycle Figure 3 Figure 4 shows the ratio as a function for the parameter values:,,,, and.

9 14 12 fi=0.1 fi=0.9 retention-to-acquisition expenses ratio current state of business cycle Figure 4 From the above relations we immediately obtain the following propositions: Proposition 3. The total marketing budget, economy s., is pro-cyclical, i.e. B increases with the state of the Proposition 4. The retention-to-acquisition-expenditures ratio,, is pro-cyclical, i.e. increases with s, if. is counter-cyclical, i.e. decreases with s, if. 4. Conclusions We consider the problem of optimal allocation of the marketing budget between long-term customer acquisition and short-term customer retention of a firm inside a competitive industry and over the business cycle. In line with the neo-schumpeterian model of investment, we find that under perfect capital markets customer retention is pro-cyclical and customer acquisition is counter-cyclical. In the case of sufficiently imperfect capital markets and the possibility of a liquidity shock, optimal allocation of the budget results in counter-cyclical customer retention and pro-cyclical customer acquisition.

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