SOUTHERN JOURNAL OF AGRICULTURAL ECONOMICS DECEMBER, 1981
COMMENT: A THEORETICAL FRAMEWORK FOR ANALYZING SOCIAL
COSTS OF THE TOBACCO PROGRAM
Earl A. Stennis and M. J. Fuller
We commend Johnson and McManus on their
article, which presents a theoretical framework
for analyzing social costs of the tobacco program
and an application of that framework to current
policy issues.1 However, while we basically
agree with their approach in quantification of
“net reduction in social costs” (given their as-
sumptions), we perceive related matters that de-
serve further discussion.
Johnson and McManus apparently recognize
that, except under circumstances in which mark-
ups are a fixed percentage of raw product prices,
farm-level elasticity will be more inelastic than
retail elasticity. However, they do not appear to
recognize that the magnitude of the difference
will be mainly a function of marketing spreads,
and that a derived demand approach can be
utilized to reach empirically derived estimates of
elasticity of demand for tobacco at the farm
level. Their assumed value for farm-level de-
mand elasticity (-.6) was presumably based
upon their reported range of demand elasticity
estimates for cigarettes of - .3 (Sackrin, p. 86) to
-1.5 (Maier, p. 703). Marketing spreads for to-
bacco are substantial and largely fixed (Tobacco
Tax Council, p. viii; USDA, p. 98). This would
necessarily imply a farm-level demand elasticity
much more inelastic than assumed by Johnson
and McManus. Their assumed elasticity was also
notably less inelastic than that reported by Sut-
ton.2
In order to demonstrate the impact that an al-
ternative farm-level elasticity might have on
Johnson and McManus’ analysis, we assumed a
farm-level demand elasticity of - .05. Given this
value, if tobacco prices dropped 25 percent (to
the postulated competitive market equilibrium),
the calculated point on *D would be *P1 = .8445,
*Qι = 2,160,861.30.3 With the same assump-
tions, the calculated point on *D would be *P2 =
1.4638, *Q2 = 2,102,171.24 when price is in-
creased to the full cost equilibrium. Given the
estimate of supply elasticity (.45) and the as-
sumption that *S and *S' have the same slopes,
these equilibrium points were used to calculate
second points on *S and *S'.4 From the two
points on each curve and the assumption Oflinear
equations in the relevant range, equations for *D,
*S, and *S' were derived.5 With the use of these
equations and quantities for *Q0, *Q1, and *Q2,
the social cost areas in Johnson and McManus’
Figure 1 were estimated by integrating the func-
tions over the relevant intervals. The integral
equations and values (rounded to nearest thou-
sand) were as follows:
Public Costs
c *Q1 r *Q1
(1) AFHC=I *S'dQ-/ *SdQ
j *q2 j *Q2
= $39,240,000
Reduction in Public Costs
f*Q1 r*Qι
(2) BGHC = I *S'dQ - I *SdQ
∙7*Qo j*Qo
= $17,836,000
Producer-Consumer Surplus Loss
f*Qι f*Qι
(3) BCE = I *DdQ - I *SdQ
∙7*Qo ∙,*Qo
= $4,057,000
Net Reduction in Social Costs
f*Qι f*Qι
(4) CEGH = I *S'dQ - *DdQ
j*Qo j*Qo
= $13,779,000
Professor and Research Assistant, respectively, Department of Agricultural Economics, Mississippi State University.
Mississippi Agricultural and Forestry Department Station Journal, Ser. No. 4909.
The authors wish to thank, without implicating, the Journal's three anonymous reviewers for helpful comments and suggestions.
, It should be noted that the numerical data included in Johnson and McManus’ paper do not permit the reproduction of some of their findings. The authors have
inadvertently coded the production data in thousands (U.S.D.A.). The public costs, social costs, and producer-minus-consumer surplus yielded by their reported output
figures are their reported values divided by one thousand. Only by using corrected output (or properly decoding) can one reproduce their findings.
2 An unpublished dissertation by Russel W. Sutton reports a farm-level elasticity of -.031.
3 Johnson and McManus’ procedures were used for all calculations, with only the assumption for demand elasticity varied. Similarly, their coding convention for quantity
was retained. All values associated with the alternative analysis are noted with an asterisk (*).
4 The calculated points were: on *S (P = .7952, Q = 2,102,171.24) and on *S' (P = 1.5131, Q = 2,160,861.30).
5 Thesupplyequations were: *S (P = -.9715 + 8.404 × 10~7 Q), and *S' (P = -.3029 + 8.404 × 10~7 Q), where P = dollar price per pound and Q = thousand pounds. The
demand equation *D was P = 23.646 -1.0552 × IO-5 Q.
157