In terms of income-expenditure relationships
for fresh beef and selected types of beef, the es-
timated relations are depicted in Figure 1. For a
household size of three, Figure 1 indicates that
the patterns of fresh beef expenditure in response
to income differ among income levels. For
example, household expenditures for fresh beef
increases rather rapidly as income increases from
$2,000 to $10,000, remains quite constant be-
tween the range of $10,000 and $24,000, and
again increases as household income increases
above $24,000 (Figure 1). Furthermore, the t-test
indicates that, for fresh beef expenditure, the
linear segments are statistically significant at
either the 0.05- or the 0.Ю-significance levels,
suggesting that the slopes are different among the
various income levels (Table 1). This implies that
the marginal propensity to consume is much
higher for the low- and high-income households,
as compared with the middle-income households
in the case of fresh beef.
220
200
180
160
- 140
ɪ 120
1 wo
uj 80
60
40
20
0' 2 4 6 8 10 12 Î4 16 18 20 22 24 26 28 30
Household Income (1,000 dollars)
FIGURE 1. Beef Expenditures as a Function of
Household Income (Household Size = 3)
The estimated income-expenditure relation-
ships also reveal a sharp contrast in the expendi-
ture patterns among ground beef, beef roasts,
and beef steaks (Figure 1). Household food ex-
penditure for ground beef reaches a maximum
approximately at the income level of $8,000 and
then gradually declines as income further in-
creases. Even though the ground beef expendi-
ture curve tends to rise slightly toward the higher
income levels, this pattern does not seem to be
significant. In general, expenditure for beef
roasts resembles the ground beef expenditure
pattern except for absolute magnitude differ-
ences. Nevertheless, a significant structural
change, unlike that of ground beef, is found at the
higher level of household income. In contrast to
ground beef and beef roasts, the expenditure
curve for beef steaks shows a steadily increasing
pattern as household income increases. Similar
to beef roasts, expenditure for beef steaks re-
flects a significant structural change when
household income approaches the $25,000 level.
In summation, the results clearly suggest that
beef purchasing behavior changes as household
income increases. Households with lower in-
come tend to spend more of their food dollars for
ground beef, with no appreciable difference be-
tween beef roasts and beef steaks. As income
increases, expenditures for beef steaks increase
over the income range, with some evidence that
expenditures for ground beef decline over the
middle-income levels. Hence, for the higher in-
come families, a greater proportion of beef ex-
penditures was spent for beef steaks, with no ap-
parent difference between ground beef and beef
roasts. More specifically, the results suggest that
different beef expenditure patterns emerge as
household income changes. This implies that
over the range of the lower incomes ($2,000-
$10,000), household food expenditures for beef
steaks and beef roasts are of about the same
magnitudes at each income level. However, as
income increases above the low-income levels,
household food expenditures for beef steaks are
greater than for beef roasts and ground beef,
which are of similar magnitudes at income levels
above $10,000.
CONCLUSION
This paper demonstrates the application of
spline functions to income-expenditure relation-
ships, using household food purchase data from a
consumer panel of approximately 120 families.
The use of standard regression procedures pro-
vides flexibility and convenience in the estima-
tion of spline functions. More important, the use
of spline functions to approximate behaviorally
determined income-expenditure relations illus-
trates that various beef expenditure patterns of
structural differences can be investigated without
sample stratifications.
The results of this analysis indicate a unique
expenditure pattern for each type of beef. Spline
functions, as an approximation for estimating
income-expenditure relations, provided a proce-
dure that showed that consumers react differ-
ently to an income increase at the low-income
level than to an income increase at the higher
income level. The analysis indicates that, as ex-
penditures for beef change with increased in-
come, the mix of the household’s beef expendi-
tures also changes. Thus, expenditure for ground
beef was found to be predominant in the low-
income households, increasing rapidly as income
increased to about the $8,000 level. In contrast to
ground beef, expenditure for beef steaks was
more responsive and predominant in the high-
income households. Moreover, the results of this
study suggest that the relative importance of in-
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