Measuring the effects of generic dairy advertising in a multi-market equilibrium.

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