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

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U.S. Department of Agriculture, National Agricultural Statistics Service. 2005. USDA-NASS Agricultural Statistics 2005. Available at www.usda.gov/nass/pubs/agr05/acro05.htm, accessed June 2006.

U.S. Department of Labor, Bureau of Labor Statics. Consumer Price Index-Average Price Database. Available at data.bls.gov/PDQ/outside.jsp?survey=ap, accessed June 2006.

Wohlgenant, M.K., and C.R. Clary. 1994. "Development and Measurement of Farm-to-Retail Price Linkage for Evaluating Dairy Advertising Effectiveness." The Journal of Agricultural Economics Research 44(4):18-27.

(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