Marketing Spending Models - Innovation and Marketing in the Pharmaceutical Industry - page 569

In another physician-level model, Manchanda et al. ( 2004 ) specify the number of
prescriptions written by a physician as a negative binomial distribution (NBD) and
the mean of the conditional distribution to be driven by the number of sales calls. An
interesting feature of their model is the specification of the unobserved coefficient
of sales call effectiveness. The assumption that detailing is set by management with
partial knowledge of a physician's responsiveness implies that the independent vari-
able is no longer stochastic. By specifying a model for the marginal distribution of
detailing, which depends on conditional response parameters, the authors are able
to derive unbiased estimates of detailing responsiveness. Following the optimality
condition that marginal profits must equal the cost of an additional detail, the study
shows that the average physician is detailed at close to an optimal level, but indi-
vidual results vary considerably across physicians. At least 50 % of physicians are
not detailed at optimal levels. The authors do not provide an optimal allocation plan
that may be developed in future research.

Optimizing detailing expenditures across spend categories . The models above are
focused on the optimization of a single communication element, detailing, which
may be too restrictive in a world where managers have to balance expenditures
across several communication elements interacting with each other. In addition,
optimality conditions may be different depending on the extent and nature of com-
petitive interactions. Shankar ( 1997 ) proposes a model that takes into account these
types of interaction. He assumes a log-log sales response model for two competing
brands, the pioneer and a follower brand. Specifically, the model is specified as
follows:

f

a b c d f − g h i

S = e A ADDp p , with a = a − (19.9)

it i i i i i i

it it jt it jt it jt it i

T

it

where S it is units sales of brand i in period t , A it is the advertising spending, D it is the
sales force spending, P it is the unit price, and T it is the “time in market.” The terms
a-h , α, and ϕ are parameters to be estimated, whereas c , f , and h represent market-
ing cross-effects that are associated with competitor variables indexed with j .
Maximizing the profit function, Π, with respect to advertising, sales force spending
and price leads to:

Max
ADP

Π= −−− mS ADF (19.10)

it it it it it it

,,

where m it denotes the contribution margin. Shankar uses the theorem by Dorfman
and Steiner ( 1954 ) to derive the equilibrium levels of spending for advertising and
sales force, respectively:

* *

AbmS
i

= (19.11)

i i

* *

DdmS
i

= (19.12)

i i