a 10 consecutive day average (September 11-
22,1978)’ as reported in the “yellow sheet” [4],
with the exception of beef trim which is repre-
sented by an estimated salvage price of $0.26
per pound. The costs of diverting the primal
cuts—loin, rib, round, and chuck—to ground
beef are the estimated deboning costs’ per
pound of bone-in primal. The coefficients repre-
senting fat and bone content and the percent-
age of carcass going to each primal are based
on an assumed yield grade 2-3 carcass weigh-
ing approximately 600 lbs.
The linear programming formulation of the
current beef market shown in Figure 1, though
an extreme simplification of the actual market
and submarkets, is a realistic representation of
the aggregate decisions to be made by the in-
dustry. This contention is supported by the op-
timal solution of the model for which the activi-
ty levels are shown in Figure 1, row 12. The op-
timal solution calls for 40 percent of the beef
sold to be ground beef, made up of 58 percent
domestic manufacturing beef, 15 percent im-
ported beef, and 27 percent beef trim. These
figures differ slightly from the previously men-
tioned estimates of (1) the percentage that
ground beef contributes to total beef sales and
(2) the composition of sources of ground beef.
The differences, at least in part, are due to the
total exclusion of block beef in the composition
of ground beef in the model solution. In actual
beef market situations, some block beef nor-
mally is diverted to ground beef at the retail
level (i,e., chuck marketed as “ground beef”
and some “over-aged” beef from all primais
which is salvaged as ground beef). Though
these are legitimate sources of ground beef,
they are provided by the retailer and thus are
outside the processor-wholesaler market repre-
sented by the model.
Beef Diverted from Block Beef Trade
To examine the impact of reducing cow, bull,
and other nonfed beef slaughter by 30 percent
from current levels, the model was first ad-
justed by decreasing the availability of domes-
tic manufacturing beef by 30 percent (to 164
lbs.) with all other coefficients remaining con-
stant. The solution to the adjusted model
(Figure 1, row 13) calls for ground beef to be re-
duced to 31 percent of total beef sales (down
from 40 percent) with corresponding increases
in the sales of other beef products from fed beef
carcasses. In an actual market situation one
would expect a reduction of this magnitude in
the sales of ground beef to be accompanied by
an increase in its price. Likewise, the increases
in the volume of sales of the other beef prod-
ucts would, ceteris paribus, be accompanied by
decreases in their market prices.
To further examine the relationship between
the prices of ground beef and other beef prod-
ucts in the restricted model, the price of
ground beef was increased in increments of
$.01 per pound until the optimal solution ac-
tivity levels changed. The new solution (Figure
1, row 14) is at a ground beef price of $.926 per
pound (up from the original $.866 per pound)
with the availability of domestic manufactur-
ing beef again restricted to 164 lbs. In this
solution, ground beef makes up 46 percent of
the volume of total beef sales and is produced
from 13 percent imported beef, 35 percent
domestic manufacturing beef, 27 percent beef
trim from fed beef carcass, and 25 percent from
beef rounds converted to ground beef.
Another change in the optimal solution acti-
vity levels can be induced by increasing the
price of ground beef to $.966 per pound (from
$.926). At this price of ground beef, with all
other prices remaining constant, the optimal
solution (Figure 1, row 15) calls for 69 percent
of the volume of beef sold to be ground beef,
being composed of 8 percent imported beef, 24
percent domestic manufacturing beef, 18 per-
cent beef trim, 33 percent chuck converted to
ground beef, and 17 percent round converted to
ground beef.
Reliable estimates of the price elasticities of
ground beef and the other beef products at the
wholesale level are not available, but price elas-
ticity estimates of ground beef and fed beef
products at the retail level have been reported
by Freebairn and Rausser and others [6, 10].
Assuming that the estimated retail level price
elasticities of —.43 for ground beef and —.83
[from 6] for fed beef products are representa-
tive of the elasticities of these products in the
current processor-wholesaler markets,7 one can
further assume that each 1 percent reduction
of the quantity of ground beef exchanged will
be accompanied by a 2.3 percent8 increase in its
price. Thus, a reduction in the volume of
•This two∙week period was selected when this article was written in September and October 1978. The period was chosen as being representative of the relative
prices of the various beef products during the portion of the year 1978 that had then elapsed. Since then the model has been run with prices from other periods, includ-
ing average annual prices for 1978. The results indicate no changes in the conclusions reported.
eThepercentageofbonein the primal cuts is assumed to be 16 percent for chuck, ISpercentforround, 16 percent for rib, and 12 percent for loin. Deboningcosts are
based on the assumption that labor costs $7.50 per hour and overhead costs $5.00/cwt. of bone-in product and the boning rates per man hour of 9 chucks, 14 rounds,
16 ribs, or 10 loins.
7Theoretically, one would expect wholesale prices to be somewhat more inelastic than retail prices. Certainly, the retail elasticities should serve as upper bounds on
those of the corresponding wholesale markets.
eIn this case, because substitutes exist and the market is at the wholesale instead of the retail level, this figure must be regarded only as a lower limit on the ab-
solute value of the price flexibility at the wholesale level.
24