Numerous studies have examined the effectiveness of producer-funded
generic promotion for milk and for cheese (among others, Blisard et al.
1999; Kaiser 1997, 1999; Kaiser and Chung 2002; Liu and Forker 1990;
Schmit and Kaiser 2002, 2004). The typical analysis estimates
econometric models of fluid milk or cheese demand as a function of own
prices, prices of related goods, demographic characteristics, and
generic advertising expenditure. While empirical findings vary across
studies and across products, promotion is typically found to generate
positive and significant increases in demand, as well as large returns
to producers' investment.
However, the typical approach, which models the market for the
advertised product in isolation, is incapable of capturing the effects
of commodity promotion on horizontally related markets (Alston, Carman,
and Chalfant 1994; Piggott, Piggott, and Wright 1995; Kinnucan 1996;
Kinnucan and Miao 2000; Alston, Freebairn, and James 2001). This
omission is particularly crucial for analysis of dairy product promotion
for two reasons. First, individual dairy products are linked on the
supply side through their common use of milk as key inputs. Thus, an
increase in demand for any given product will result in a higher price
for milk in all products and a reallocation of milk across product
markets. Second, dairy product markets are arguably related on the
demand side, so that prices and advertising for one product affect
demand for other products.
This paper develops an analytical, multi-market model of the dairy
industry that captures these horizontal linkages across dairy product
markets. We apply the model to trace the economic effects of generic
commodity promotion on markets for dairy products and the market for
milk. Comparative statics show that the effect of advertising on the
prices and quantities of milk depends on the horizontal demand and
supply linkages across markets. Further, we derive an expression for the
optimal advertising expenditures for alternative dairy products, and
then evaluate the importance of the horizontal linkages through the
numerical simulation. A key result is that ignoring the horizontal
relationships that link dairy product markets leads to errors in
measurement of the effectiveness of advertising. This is due to two
effects: a supply-side effect wherein increased derived demand for milk
in the advertised product results in a higher price of milk in all dairy
products and a reallocation of milk away from the non-advertised
products; and a demand-side effect wherein increased demand for the
advertised product comes, in part, at the expense of reduced demand for
dairy products that substitute for the advertised product.
A key contribution of this paper is the extension of work by
Alston, Freebairn, and James (2001) to link the markets for advertised
products through supply, as well as demand. This concept is applicable
to other industries where a single commodity is allocated to multiple
downstream markets. Examples may include the allocation of a farm
commodity in alternative processed markets, processed versus fresh
markets, or foreign versus domestic markets. As well, this paper
demonstrates that the empirical literature on generic dairy advertising,
most of which ignores horizontal markets, is missing important economic
effects and potentially misstating the returns to advertising.
A Multi-Market Model of the U.S. Dairy Industry with Per Unit
Check-Off Funding
A 1-input x 2-product Model of the Dairy Industry with Advertising
We develop an equilibrium displacement model (EDM) of the U.S.
dairy industry for the purpose of demonstrating analytically the role of
linkages between related markets for determining the effects of generic
promotion (see Alston, Norton, and Pardey 1995 for a recent treatment of
EDMs). To keep the exposition simple, we specify a model in which milk
is used in the manufacture of two distinct dairy products (e.g., fluid
milk and manufactured products), and an integrated post-farm gate
marketing sector combines processing and retailing functions.
The model is written in general form as follows:
(1) Milk supply M = M([W.sub.f])
(2) Production of fluid products [X.sub.1] = [g.sub.1]([M.sub.1])
(3) Production of manufactured products [X.sub.2] =
[g.sub.2]([M.sub.2])
(4) Fluid product demand [X.sub.1] = [X.sub.1]([P.sub.1],
[P.sub.2], [t.sub.1]M, [t.sub.2]M)
(5) Manufactured product demand [X.sub.2] = [X.sub.2]([P.sub.1],
[P.sub.2], [t.sub.1]M, [t.sub.2]M)
(6) Pricing of milk for fluid products [W.sub.1] = [g.sub.M1]
[P.sub.1]
(7) Pricing of milk for manufactured products [W.sub.2] =
[gM.sub.2] [P.sub.2]
(8) Price discrimination [W.sub.1] = [W.sub.2] + D
(9) Blend price of milk W = ([M.sub.1][W.sub.1] +
[M.sub.2][W.sub.2])/M
(10) The farm price [W.sub.f] = W - [t.sub.1] - [t.sub.2]
(11) Milk adding up condition M = [M.sub.1] + [M.sub.2].
Equation (1) expresses the supply of milk, M, as a function of the
farm price of milk, [W.sub.f]. Equations (2) and (3) are the production
functions that transform milk into dairy products, [X.sub.i]. Equations
(4) and (5) are the dairy product demands. Demand for each dairy product
is a function of prices for both products, [P.sub.1] and [P.sub.2], as
well as advertising expenditure for those products, [t.sub.1]M and
[t.sub.2]M, where [t.sub.i] is a tax or check-off levied on all milk
production for advertising for product i. Equations (6) and (7) express
the competitive equilibrium condition for milk, that the processor price
of milk for fluid products or manufactured products is the equal to the
value marginal product of milk, where [gM.sub.i] is the marginal product
of milk in product i. Equation (8) captures price discrimination by
Federal Milk Marketing Orders (FMMOs) and similar state programs, which
raises the price of milk paid by fluid products processors by a fixed
mark-up, D, relative to that paid for manufacturing milk. Equation (9)
defines the blend price of milk paid to all producers under FMMO
regulation as a weighted average of processor prices of milk for fluid
products and manufactured products. Equation (10) defines the net farm
price, as the blend price less the per unit check-off collected for
dairy product advertising, [t.sub.i]. Equation (11) is the market
clearing condition that supply equals demand for milk.
Totally differentiating equations (1) through (11) and converting
to elasticity form yields a system of equations linear in percentage
changes. Using the symbol E to denote percentage change, the model is as
follows:
(12) EM = [[epsilon].sub.f][EW.sub.f]
(13) [EX.sub.1] = [EM.sub.1]
(14) [EX.sub.2] = [EM.sub.2]
(15) [EX.sub.1] = [[eta].sub.11] [EP.sub.1] + [[eta].sub.12]
[EP.sub.2] + [[alpha].sub.11]([Et.sub.1] + EM) +
[[alpha].sub.22]([Et.sub.2] + EM)
(16) [EX.sub.2] = [[eta].sub.21] [EP.sub.1] +
[[eta].sub.22][EP.sub.2] + [[alpha].sub.21]([Et.sub.1] + EM) +
[[alpha].sub.22]([Et.sub.2] + EM)
(17) [EW.sub.1] = [EP.sub.1]
(18) [EW.sub.2] = [EP.sub.2]
(19) [EW.sub.1] = [gamma][EW.sub.2]
(20) EW = [v.sub.1]([EM.sub.1] + [EW.sub.1]) + [v.sub.2]([EM.sub.2]
+ [EW.sub.2]) - EM
(21) [EW.sub.f] = [[omega].sub.f]EW - [[omega].sub.t1][Et.sub.1] -
[[omega].sub.t2][Et.sub.2]
(22) EM = [s.sub.1][EM.sub.1] + [s.sub.2][EM.sub.2]
where [[epsilon].sub.f] is the elasticity of supply of milk with
respect to the farm price; [[eta].sub.ij] is the elasticity of demand
for product i with respect to the price of product j; [[alpha].sub.ij]
is the elasticity of demand for product i with respect to advertising
expenditure for product j; [gamma] ([equivalent to][W.sub.2]/[W.sub.1])
is the ratio of milk prices for fluid products and manufactured
products; [v.sub.v] ([equivalent to]([W.sub.i][M.sub.i])/(WM)) is the
share of milk revenue from product i; [omega]f([equivalent to]
W/[W.sub.f]) is the ratio of the blend price to the net farm price;
[[omega].sub.ti] ([equivalent to] [t.sub.i]/[W.sub.f]) is the ratio of
the per unit check-off for product i to the farm price; [s.sub.i] is the
share of milk allocated to product i, where the shares sum to one.
Equations (13) and (14) follow from an assumption of constant returns to
scale technology in dairy product manufacturing.
The model can be expressed equivalently in matrix form as
(23) RY = Z
where R is a matrix of model parameters, Y a column vector of
endogenous, proportional changes in prices and quantities relative to an
initial equilibrium, and Z a column vector of zeros, the proportional
changes in the per unit check-offs, advertising elasticities of demand,
and the ratio of the per unit check-offs to farm price as follows:
(24) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
(25) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII],
and
(26) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
The model defines proportional changes in equilibrium dairy prices
and quantities in response to exogenous changes in the advertising
check-offs:
(27) Y = [R.sup.-1]Z.
The change in producer surplus created by advertising can be
measured in terms of the changes in prices and quantities from solutions
of the model, as follows
(28) [DELTA]PS = [W.sub.f0][M.sub.0] [[EW.sub.f]][1 + 0.5EM]
where subscript 0 indicates initial price and quantity, and
[EW.sub.f] and EM are the appropriate elements of the vector on the
right-hand side of equation (27). (2)
Comparative Statics
Dividing equation (27) by [Et.sub.1] yields the elasticities of
dairy-sector prices and quantities with respect to the per unit
check-off for advertising product 1 as follows:
(29) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
(30) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
(31) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
(32) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
(33) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
(34) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
(35) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
where [DELTA] = {1 + [v.sub.1]([gamma] - 1)}[epsilon]
[[omega].sub.f]{1 - [s.sub.1]([[alpha].sub.11] + [[alpha].sub.12]) -
[s.sub.2]([[alpha].sub.21] + [[alpha].sub.22])} -
[s.sub.1]([gamma][[eta].sub.11] + [[eta].sub.12]) [s.sub.2] x
([gamma][[eta].sub.21] + [[eta].sub.22] + (v.sub.1] -
[s.sub.1])[[epsilon].sub.f][[omega].sub.f][([gamma][[eta].sub.11] +
[[eta].sub.12]).]. (1 - [[alpha].sub.21] - [[alpha].sub.22]) -
([gamma][[eta].sub.21] + [[eta].sub.22])(1 - [[alpha].sub.11] -
[[alpha].sub.12])]. Note that we suppress the elasticities of retail
prices and quantities, since [EX.sub.i]/[Et.sub.1] =
[EM.sub.i]/[Et.sub.1] and [EP.sub.i]/[Et.sub.1] = [EW.sub.i]/[Et.sub.1]
under our maintained assumption of constant returns technology.
Equations (29)-(35) define the marginal effects of a change in
producer-funded advertising for product 1.
Optimal Advertising Expenditure for Dairy Products
The comparative statics in equations (29)-(35) can be used to
develop a rule for allocating dairy advertising expenditure funded by
per unit check-off. Following Alston, Freebairn, and James 2001 we
define the optimal per unit check-off for advertising for each dairy
product as that which maximizes producer surplus:
(36) PS = TR - TVC = [W.sub.f] M- TVC(M) = (W - [t.sub.1] -
[t.sub.2])M - TVC(M)
where PS is the net producer surplus for dairy farmers, TR is the
total milk revenue, and TVC is the total variable cost of producing
milk. The first-order condition for the optimal per unit check-off for
fluid milk advertising is
(37) [partial derivative]W/[partial derivative][t.sub.1] = 1. (3)
Noting that W is the processor price of milk, equation (37)
indicates that producers should continue to increase the check-off as
long as the vertical shift in derived aggregate demand is large enough
to raise the equilibrium processor price by the change in the check-off,
leaving the net farm price no lower than without the check-off. (Note
from equation (10) that [partial derivative]W/[[partial
derivative].sub.t1] = 1 implies that [partial
derivative][W.sub.f]/[partial derivative][t.sub.1] = 0.) This
first-order condition can be restated in proportional change form:
(38) EW/[Et.sub.1] = [t.sup.*.sub.1]/W
or
(39) [t.sup.*.sub.1] = EW/[Et.sub.1] W.
It follows that optimal advertising expenditure is
(40) [A.sup.*.sub.1] = EW/[Et.sub.1]WM.
Equations (39) and (40) show that the optimal per unit check-off,
and thus optimal advertising expenditure, is proportional to the
elasticity of the blend price with respect to the check-off.
Substituting equation (33) into (39) and (40) yields the optimal per
unit check-off and advertising expenditure:
(41) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
and
(42) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
The presence of cross-price and cross-advertising elasticities, as
well as the own-price elasticity for manufactured milk ([[eta].sub.22]),
in equations (41) and (42) make it clear that optimal advertising
depends on the direct effect of advertising on demand in each market, as
well as the links between the two markets. However, most of the
empirical literature on the economics of generic advertising for dairy
ignores the market for non-advertised dairy products. An exception is
Wohlgenant and Clary (1994), who allow for linkages across dairy product
markets by estimating the effects of advertising on the (inverse)
derived demand for farm milk. In another exception, Kaiser and Schmit
(2003) model the supply link (i.e., fluid milk and cheese processors
competing for the same input), but assume cross-price and
cross-advertising elasticities are zero. In this case, the optimal
check-off and advertising expenditure can be viewed as a special case of
equations (41) and (42). (4) The rest of the literature considers yet a
more restricted model in which prices and quantities in markets for
non-advertised dairy products are assumed exogenous, thereby eliminating
all spillover and feedback effects within the dairy sector.
Numerical Simulation of the Effects of Generic Dairy Advertising
We now turn to numerical simulation to quantify the effects of
generic dairy advertising in the U.S. dairy sector and to demonstrate
the role of horizontal markets. We model the markets for three products
(fluid milk, cheese, and other dairy products) produced from milk and
potentially related in demand. To simulate the model, we draw parameter
values from the literature where available, and use data on the 2005
U.S. dairy market. We consider a range of possible values for the
cross-advertising elasticities of demand ([[alpha].sub.ij], i [not equal
to] j), as no published estimates exist.
Parameter Values and Data Used for Simulations
Base values of demand elasticities used in our simulations are
reported in table 1. Published estimates of demand and supply
elasticities vary as a result of different levels of aggregation across
time, products, and geography, as well as different econometric
specifications. Estimates of the own-price elasticity of U.S. retail
demand for fluid milk range from -0.882 to -0.0431 (Heien and Wessels
1988; Huang 1993; Kaiser 1999; Schmit and Kaiser 2002; Chouinard et al.
2005). Estimates of the own-price elasticity of U.S. retail demand for
cheese range from -0.773 to -0.146 (Heien and Wessels 1988; Huang 1993;
Kaiser 1999; Schmit and Kaiser 2002; Chouinard et al. 2005). Estimates
of the own-price elasticity of U.S. demand for butter range from -0.410
to -0.2428 (Huang 1993; Chouinard et al. 2005). Estimates of own-price
elasticities of demand exist for frozen products (Huang 1993, -0.0784;
Chouinard et al. 2005, -0.803) and yogurt (Chouinard et al. 2005,
-0.773). Based on the published estimates, we choose own-price
elasticities that fall in the range of the published estimates: -0.2 for
fluid milk, -0.5 for cheese, and -0.6 for other dairy products.
Evidence on the sign and magnitude of cross-price elasticities is
mixed (Heien and Wessels 1988; Huang 1993; Chouinard et al. 2005). We
proceed under the assumption that dairy products are likely to be
substitutes at the level of aggregation relevant for national generic
commodity advertising. This assertion is supported by many of the
published estimates, and also by the recent 3-A-Day[TM] dairy
advertising campaign that encourages consumers to consume three servings
of milk, cheese or yogurt a day (DMI 2006). As base values in our
simulation analysis, we assume the cross-price elasticities between
fluid milk and cheese are 0.02, and the cross-price elasticities between
other dairy products and cheese and other products and fluid milk are
zero.
Estimates of the U.S. own-advertising elasticity of demand for
fluid milk range from 0.014 (Liu et al. 1990) to 0.057 (Kaiser 1999).
Estimates of the own-advertising elasticity of demand for cheese range
from 0.015 (Kaiser 1999) to 0.039 (Kaiser and Schmit 2003). We choose
0.036 as the own-advertising elasticity of demand for fluid milk, 0.027
as the own-advertising elasticity of demand for cheese, and 0.02 as the
own-advertising elasticity of demand for other dairy products.
None of the research listed above estimates cross-advertising
elasticities. Basmann 1956 showed that for a weakly separable group of n
products, the advertising elasticities must satisfy
[[summation].sup.n.sub.i=1] [B.sub.i][[alpha].sub.ij] = 0, j = 1, ... n,
where [B.sub.i] is the retail (consumer) expenditure share for the
[i.sup.th] product. Intuitively, Basmann's adding up condition
states that if advertising is effective at increasing demand for the
advertised product, it must also decrease demand for some other
products. Thus advertising has potentially important direct effects on
demand for non-advertised products (e.g., Alston, Freebairn, and James
2001; Kinnucan and Myrland 2002; Kinnucan and Miao 2000). In the case of
dairy advertising, under our maintained hypothesis that dairy products
are substitutes, advertising for one product decreases demand for other
dairy products. In our base scenario, we impute the cross-advertising
elasticities under the assumption that cheese and fluid milk comprise a
separable group of dairy products. This scenario sets an upper bound on
the magnitude of the cross-advertising elasticities for fluid milk and
cheese. We also simulate the model under the assumption that the
cross-advertising elasticities between cheese and fluid milk are zero.
In all scenarios, the cross-advertising elasticities between other dairy
products and fluid milk and cheese are assumed to be zero.
Estimates of the elasticity of the U.S. milk supply range between
0.22 and 2.53, depending on the relevant time horizon and econometric
specification (Chavas and Klemme 1986, short-run elasticity of 0.22,
long-run elasticity of 1.17; Cox and Chavas 2001, 0.37; Helmberger and
Chen 1994, 0.583; Chen, Courtney, and Schmitz 1976, 2.53). We use 1.0 as
the value of the elasticity of supply for milk over a one-year time
horizon.
Shares and price ratios used in the model are calculated from data
from the U.S. Departments of Agricultural and Labor, reflecting prices
and quantities in U.S. dairy markets in 2005 (table 2). The processor
prices for milk in fluid milk ([W.sub.1]) and cheese ([W.sub.2]) are
weighted averages of FMMO Class 1 and Class III prices, respectively.
The blend price (W) is the weighted average FMMO uniform price, and the
net producer price ([W.sub.f]) is calculated as the blend price less the
check-off of $0.15. The processor price of milk in other dairy products
([W.sub.3]) is imputed from FMMO data. We calculate product-specific
check-offs based on the 2003 Dairy Management Inc. annual report (DMI
2003). The DMI annual report shows that a total of 68% DMI revenue was
used for "marketing," which we take to mean generic
advertising: 23% of the DMI budget was used for fluid milk marketing,
35% for cheese marketing, 3% for dairy ingredient marketing, and 7% for
school marketing. We allocate the 7% for school marketing to the other
three categories based on each category's share of the DMI
marketing budget, and multiply the result by the full check-off
($.15/cwt) to calculate the product-specific check-off rates.
Simulation Scenarios
In order to quantify the importance of cross-market linkages in
measuring the effects of dairy advertising, we simulate 40% increases in
the check-offs for fluid milk and for cheese. In each case, we measure
the market effects under four parameter scenarios:
1. Base scenario with horizontal supply and demand linkages: the
cross-advertising elasticities between fluid milk and cheese are imputed
using Basmann's adding-up condition, assuming fluid milk and cheese
are a separable group, and all other model parameters reflect likely
values (tables 1 and 2).
2. A restricted model assuming no horizontal demand linkages (i.e.,
all cross-price and cross-advertising elasticities of demand are zero),
but allowing for horizontal supply linkages (i.e., dairy product markets
are integrated through their common use of raw milk).
3. A restricted model assuming no horizontal demand or supply
linkages.
4. A restricted model assuming no cross-advertising effects (i.e.,
all cross-advertising elasticities of demand are zero), but allowing for
cross-price effects in demand and horizontal supply linkages.
Comparing scenario 1, where the model includes all the cross-market
effects, with scenarios 2, 3 and 4, where some of the cross-market
linkages are suppressed, provides a measure of the direction and
magnitude of estimated effects of different cross-market linkages on the
estimated returns from generic advertising.
Simulated Effects of 40% Increases in Check-Offs for Dairy
Advertising
Table 3 shows the effects of a 40% increase in the per unit
check-off for fluid milk advertising under scenarios 1-4. Under all
scenarios, fluid milk advertising increases the price and quantity of
milk used in fluid products, as well as the price and quantity of fluid
milk products. (5) When dairy product markets are linked through supply
and demand (scenario 1), fluid milk advertising reduces both supply and
demand for cheese, and reduces supply for other dairy products, causing
reduced consumption of these products and reduced quantities of milk
used in these products. We also find fluid milk advertising causes
higher prices for milk in cheese and other dairy products. Because of
the spillover and feedback effects of fluid milk advertising, the
increase in milk production (M) is less than the increase in milk used
in fluid products ([M.sub.1]). The 40% increase in advertising for fluid
milk increases producer surplus by $31 million in scenario 1.
In contrast, in scenario 2 (all cross-price and cross-advertising
elasticities of demand equal zero), demand for cheese and for other
dairy products is not affected by fluid milk advertising. Advertising
for fluid milk affects the markets for other dairy products only through
the supply of milk; advertising raises the price paid for milk by all
processors. Accordingly, the price increases are larger and reductions
in the quantities smaller in the market for cheese in scenario 2 than in
scenario 1. The cross-price and cross-advertising elasticities of demand
have important effects on the ability of fluid milk advertising to raise
the farm price of milk. When there are no demand linkages across dairy
product markets, fluid milk advertising is 2.6 times as effective at
raising the farm price of milk (a 0.301% increase compared to a 0.116%
increase), and the net producer gain is 2.6 times as large ($80 million
compared to $31 million).
In Scenario 3, both the supply and demand linkages across product
markets are eliminated, so that prices and quantities in markets for
cheese and other dairy products are exogenous. Thus, even though fluid
milk advertising raises the price of milk in fluid uses, the price of
milk in cheese and other products is assumed unaffected. Compared to
scenario 1, fluid milk advertising is 3.2 times more effective at
increasing the farm-price of milk (a 0.375% increase compared to a
0.116% increase) and producer surplus ($99 million versus $31 million),
when there are no cross-market effects.
Under our maintained hypothesis that cheese and fluid milk are
substitutes, fluid milk advertising is more effective when the
cross-advertising elasticities are smaller. Thus, fluid milk advertising
is more effective in scenario 4 than in scenario 1. However, comparison
of scenarios 3 and 4 suggests that horizontal market linkages are
important even when cross-advertising effects are zero. The change in
producer surplus from fluid milk advertising in scenario 3, $99 million,
is 22% higher than the change in producer surplus with in scenario 4,
$81 million.
Table 4 tells an analogous story for generic cheese advertising,
with two notable differences. In scenario 1, the increase in cheese
advertising makes producers worse off. This result is driven by two
factors. First, the relatively large cross-advertising elasticity of
demand for fluid milk with respect to cheese advertising causes such a
large decrease in demand for fluid milk so as to decrease the total
consumption of milk. Second, because the initial price of milk in cheese
is low relative to the price of milk in fluid products and other dairy
products (table 2), cheese advertising effectively increases the share
of milk sold to its lowest-value use, causing the net producer price to
fall even though the price of milk in each product rises. Thus, milk
marketing order regulation, which raises the price of milk in fluid
products relative to that in manufactured dairy products, undermines the
effectiveness of advertising for manufactured dairy products.
Also notable in the cheese advertising case is that the horizontal
supply linkages increase the effectiveness of cheese advertising, which
can be seen by comparing scenarios 2 and 3 in table 4. Note that the
horizontal supply linkages across product markets have two related
effects. First, the advertising-induced increase in the price of milk
reduces consumption of the non-advertised products. Second, the demand
response in the non-advertised markets increases the elasticity of
(residual) supply of milk facing the advertised market. In the case of
cheese advertising, the increased sale of milk in cheese outweighs the
reduced consumption of fluid milk and other dairy products in response
to the advertising-induced rise in the price of milk. This contrasts
with the fluid milk advertising case, where the horizontal supply
linkages reduce the effectiveness of fluid milk advertising; the reduced
consumption of cheese and other dairy products outweigh the increased
sales of fluid milk. The difference is caused in part by the relatively
inelastic demand for fluid milk; the higher milk price caused by cheese
advertising has a relatively small effect on fluid milk consumption.
Further, relatively inelastic demand for fluid milk results in a
relatively inelastic supply of milk facing the cheese market, so that
the advertising-induced increase in cheese demand results in a
relatively large increase in the price of milk in cheese. The larger
market share of milk in cheese also contributes to the difference, as
the positive effects of cheese advertising in the cheese market outweigh
the negative effects of cheese advertising in the (relatively small)
fluid milk market.
The change in producer surplus from cheese advertising assuming no
cross-market effects, $54 million, is 11% lower than the change in
producer surplus with no cross advertising elasticities, $61 million
(scenario 4). Again, analyses that ignore the cross-market effects
misstate the returns to advertising, even when cross-advertising effects
are negligible.
Optimal Advertising Expenditure of Dairy products
In table 5 we report the optimal check-offs and advertising
expenditures for each product for each of the four scenarios, using
equations (39) and (40). The results mirror those of the simulations
reported in tables 3 and 4 and discussed above. Optimal advertising
expenditure for fluid milk under the assumption that no horizontal
relationships exist between dairy product markets ($316 million in
scenario 3) is between 18% (compared to $268 million in scenarios 2 and
4) and 118% (compared to $145 million in scenario 1) greater than
optimal expenditure under the more general models. In the case of cheese
advertising, optimal expenditure assuming no horizontal linkages is
larger or smaller than optimal expenditure under the more general
models, depending on the magnitude of the cross-advertising elasticities
and other model parameters. Optimal cheese advertising expenditure is
zero in scenario 1.
[FIGURE 1a OMITTED]
Figures 1a-d illustrate the sensitivity of optimal advertising for
fluid milk to key model parameters. In each figure, the vertical axis
measures EW/[Et.sub.1], to which the optimal check-off and advertising
expenditure for fluid milk are proportional. (6) Figure la shows that
EW/[Et.sub.1] is increasing in the cross-advertising elasticity of
demand for cheese with respect to fluid milk advertising
([[alpha].sub.21]), and may be negative for large, negative values of
[[alpha].sub.21]. (7) Figures 1b and 1c show that EW/[Et.sub.1] is also
increasing in the elasticity of demand for fluid milk with respect to
the price of cheese ([[eta].sub.12]) and in the elasticity of demand for
cheese with respect to the price of fluid milk ([[eta].sub.21]). Under
our assumption that cheese and fluid milk are substitutes, the
advertising-induced rise in the price of fluid milk increases the demand
for cheese, and the rise in the price of cheese induced by fluid milk
advertising feeds back to increase the demand for fluid milk. These
feedback effects increase as [[eta].sub.12] and [[eta].sub.21] increase.
Figure 1d shows that EW/[Et.sub.1] is increasing in the own-price
elasticity of demand for cheese. As demand for cheese becomes less
elastic, the (residual) supply of milk facing the advertised market
becomes less elastic, and the advertising-induced shift in demand for
fluid milk has a larger effect on the price of milk.
[FIGURE 1b OMITTED]
[FIGURE 1c OMITTED]
[FIGURE 1d OMITTED]
Conclusion
This article provides theoretical and empirical evidence that
producer-funded generic advertising for dairy products has important
spillover and feedback effects that influence the return to advertising
and optimal advertising expenditure. We draw on the concept, highlighted
recently in this journal by Alston, Freebairn, and James (2001), that
commodity advertising increases demand for the advertised product at the
expense of producers of substitute commodities. We extend this idea to
the case of the dairy sector, where dairy farmers produce a single
commodity that is used in multiple products, some of which are related
in demand. We show that in this setting, the spillover effects of
product-specific advertising are internalized and should be considered
to accurately measure the returns to advertising.
A multitude of empirical research has assessed the economic effects
of dairy advertising in the United States. With few exceptions, this
literature has considered only the partial equilibrium effects of
advertising in the advertised market. Our multimarket equilibrium
displacement model of the dairy sector makes explicit the implications
for dairy advertising of horizontal linkages across dairy markets.
Cross-price and cross-advertising elasticities of demand cause shifts in
demand for non-advertised dairy products, and feedback effects in the
advertised market. Moreover, dairy product markets are linked through
the common use of milk, so that an advertising-induced increase in
demand for milk in one product raises the price of milk in all products.
Numerical simulations of our model suggest that the extant
literature does not accurately measure the returns to dairy advertising.
In our simulations we find that analyses of fluid milk advertising that
ignore cross-market effects overstate returns to dairy farmers by at
least 22% and by as much as 219%. Further, we find that generic cheese
advertising in the presence of cross-market effects may actually reduce
producer welfare, a result driven in part by milk marketing order
regulation that raises the price of milk in fluid products and reduces
the price of milk in cheese and other manufactured dairy products. In
this case, analyses that ignore cross-market effects misstate not only
the magnitude, but the direction of the effects of generic advertising.
[Received June 2006; accepted February 2007.]
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(1) Kaiser and Schmit (2003) consider the incidence of generic
promotion on fluid milk and cheese processors, noting that all dairy
processors compete for milk. However, they do not address the
implications for dairy-farmer welfare, or for farmer-funded advertising.
(2) Our measure of the change in producer surplus assumes that
supply and demand are linear in the region of interest.
(3) The first-order condition for the optimal per unit check-off is
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
Under the maintained hypothesis of perfectly competitive markets,
[W.sub.f](= W - [t.sub.1] - [t.sub.2]) = MC, so that [partial
derivative]PS/[partial derivative][t.sub.1] = ([partial
derivative]W/[partial derivative][t.sub.1] - 1)M = 0. Then, assuming a
strictly positive quantity of milk at the optimum, we have [partial
derivative]W/[partial derivative][t.sub.1] = 1.
(4) Kaiser and Schmit consider the effects of advertising for fluid
milk on cheese processors, and of advertising for cheese on fluid milk
processors. However, they do not make the important link back to dairy
farmers, or discuss the implications for the effectiveness of
advertising funded by farmers. That is, they do not find or calculate
the appropriate, restricted versions of equations (41) and (42).
(5) Under our assumption of constant returns technology in dairy
product manufacturing, the percentage changes in retail quantities and
prices of dairy products are equal to the percentage changes in,
respectively, the prices and quantities of milk used in those products.
Thus we report results only farm prices and quantities to conserve
space.
(6) All model parameters are held constant at the values used in
scenario 1, as reported in tables 1 and 2.
(7) EW/[Et.sub.1] < 0 implies that the optimal check-off and
advertising expenditure for fluid milk are zero.
Joseph V. Balagtas is assistant professor, Department of
Agricultural Economics, Purdue University. Sounghun Kim is research
associate, Agricultural Industry and Agribusiness Research Center. Korea
Rural Economic Institute, Seoul, Korea.
Senior authorship is not assigned. This research was supported by
the Purdue University Agricultural Experiment Station. Partial funding
was provided by National Milk Producers Federation. The authors thank
the editor, Wally Thurman, and two anonymous referees for many
constructive comments.
Table 1. Demand Elasticities Used in Base Scenario
Elasticity with Respect to
Price of ([[eta].sub.ij]): (a)
Other Dairy
Demand for: Fluid Milk Cheese Products
Fluid milk -0.20 0.02 0.00
Cheese 0.02 -0.50 0.00
Other dairy products 0.00 0.00 -0.60
Elasticity with Respect to
Advertising Expenditure for
([[alpha.sub.ij]): (b)
Other Dairy
Demand for: Fluid Milk Cheese Products
Fluid milk 0.036 -0.055 0.0
Cheese -0.018 0.027 0.0
Other dairy products 0.0 0.0 0.020
(a) Price elasticities reflect published estimates. Cross-price
elasticities between other dairy products and fluid milk or
cheese are assumed to be zero.
(b) Own-advertising elasticities reflect published estimates
Cross-advertising elasticities between fluid milk and cheese are
imputed from Bassmann's adding up condition, assuming fluid milk
and cheese are separable. Cross-advertising elasticities between
other dairy products and fluid milk or cheese are assumed to be zero.
Table 2. 2005 U.S. Dairy Market Statistics Used in Simulations
Units
Prices
Farm price of milk ([W.sub.f]) $/cwt 14.92
Blend price (W) $/cwt 15.07
Processor price of milk in fluid milk $/cwt 17.13
([W.sub.1])
Processor price of milk in cheese $/cwt 13.97
([W.sub.2])
Processor price of milk in other $/cwt 14.35
products ([W.sub.3])
Retail price of fluid milk ([P.sub.1]) $/gallon 3.19
Retail price of cheese ([P.sub.2]) $/lb. 4.13
Retail price of other dairy products $/lb. 1.13
([P.sub.3])
Per unit check-off
Check-off for fluid milk advertising [cents]/cwt 3.85
([t.sub.1])
Check-off for cheese advertising [cents]/cwt 5.85
([t.sub.2])
Check-off for other dairy products
advertising ([t.sub.3]) [cents]/cwt 0.50
Quantities
Farm supply of milk (M) mil. lbs. 176,989
per year
Farm milk sold for fluid milk mil. lbs. 54,724
([M.sub.1]) per year
Farm milk sold for cheese ([M.sub.2]) mil. lbs. 66,504
per year
Farm milk sold for other dairy products mil. lbs. 55,761
([M.sub.3]) per year
Retail supply of fluid milk ([X.sub.1]) mil. lbs. 54,543
per year
Retail supply of cheese ([X.sub.2]) mil. lbs. 10,349
per year
Retail supply of other diary products mil. lbs. 18,635
([X.sub.3]) per year
Note: All prices and quantities are from data in U.S. Department of
Agriculture (USDA-NASS Agricultural Statistics 2005 and Federal Milk
Marketing Order Statistics) and U.S. Department of Labor. [W.sub.1]
and [W.sub.2] are weighted averages of FMMO Class I and Class III
prices, respectively. W is the weighted average FMMO uniform price,
and [W.sub.f] is calculated as the blend price less the check-off of
$0.15. [W.sub.3] is imputed from FMMO data. [P.sub.i] is from the
U.S. Department of Labor, Bureau of Labor Statistics. Quantities are
from data in USDA-NASS Agricultural Statistics 2005 in U.S.
Department of Agriculture, and [t.sub.i] is based on the 2003 Dairy
Management Inc. (DMI) annual report.
Table 3. Market Effects of a 40% Increase in the Per Unit Check-off
for Fluid Milk Advertising
1. Horizontal 2. No
Demand and Horizontal
Supply Demand
Linkages (a) Linkages (b)
% Level % Level
Change Change Change Change
Prices (cents per cwt)
Net farm price 0.116 1.7 0.301 4.5
of milk ([W.sub.f])
Blend price (W) 0.218 3.3 0.401 6.0
Processor price 0.117 2.0 0.294 5.0
of milk in
fluid milk ([W.sub.1])
Processor price of 0.144 2.0 0.360 5.0
milk in cheese ([W.sub.2])
Processor price 0.140 2.0 0.350 5.0
of milk in other
products ([W.sub.3])
Quantities (million lbs. per year)
Farm supply of milk (M) 0.116 205.7 0.301 533.3
Farm milk sold 1.417 775.6 1.392 761.8
for fluid milk ([M.sub.1])
Farm milk sold
for cheese ([M.sub.2]) -0.789 -524.4 -0.172 -114.2
Farm milk sold -0.082 -45.5 -0.204 -113.8
for other dairy
products ([M.sub.3])
Producer surplus 31 80
(mil. dollars per year)
3. No Horizontal 4. No
Demand Cross-
or Supply Advertising
Linkages (c) Effects (d)
% Level % Level
Change Change Change Change
Prices (cents per cwt)
Net farm price 0.375 5.6 0.305 4.5
of milk ([W.sub.f])
Blend price (W) 0.474 7.1 0.405 6.1
Processor price 1.199 20.5 0.296 5.1
of milk in
fluid milk ([W.sub.1])
Processor price of 0.0 0.0 0.362 5.1
milk in cheese ([W.sub.2])
Processor price 0.0 0.0 0.353 5.1
of milk in other
products ([W.sub.3])
Quantities (million lbs. per year)
Farm supply of milk (M) 0.375 664.2 0.305 539.0
Farm milk sold 1.214 664.2 1.400 765.6
for fluid milk ([M.sub.1])
Farm milk sold
for cheese ([M.sub.2]) 0.0 0.0 -0.167 -111.3
Farm milk sold 0.0 0.0 -0.206 -114.8
for other dairy
products ([M.sub.3])
Producer surplus 99 81
(mil. dollars per year)
Note: To conserve space, we do not report results for retail prices
and quantities. Under our assumption of