Cooperative (co-op) advertising is attracting more and more attention. This paper analyzes co-op advertising behavior based on a dual-brand model with a single manufacturer and a single retailer, and some interesting conclusions are achieved. Firstly, the firm in the supply chain advertises both brands, and the difference of advertising expenditure is not very large in equilibrium. Secondly, the retailer's advertising and the manufacturer's participation ratios depend on both the retailer's and the manufacturer's marginal profits. Thirdly, the stimulating effect increases the advertising investment while the competition effect decreases it, but they have no effect on the manufacturer's participation ratio. Fourthly, co-op advertising is more sensitive to the manufacturer's marginal profits than those of the retailer. Lastly, total advertising investment and profit are greater under cooperative decision than under Stackelberg decision.

Taking cooperative advertising as an example, the industrial firm becomes more dependent on its cooperative partners [

In practice, the manufacturer with co-op advertising contributes at least 50% of the advertising expenditure. Berger [

Berger [

Karray and Zaccour [

In summary, most of existent papers used single-manufacturer single-retailer single-brand or single-manufacturer dual-retailers single-brand model, and few of them considered the situation that the supply chain supplies dual/multiple substitute brands. But it is common for one manufacturer to produce two or more substitute brands simultaneously. (Procter & Gamble produces several kinds of shampoos, such as Rejoice, Head & Shoulders, Pantene, and Sassoon.) Stimulated by this phenomenon, this paper employs a dual-brand model with a single manufacturer and a single retailer to study co-op advertising and reaches some interesting conclusions. (It is easy to be expended to multiple-brand case). Assuming that the manufacturer supplies two substitute. (The substitute relationship of the two brands is reflected by the competition effect of co-op advertising, which means that the increase in advertising of one brand decreases the sales of the other brand) brands and launches co-op advertising with the retailer and co-op advertising has both the stimulating effect and the competition effect, (the stimulating effect means that co-op advertising increases the sale of the advertised brand, while the competition effect the implies advertising decreases the sale of the substitute brand) this study obtains the following conclusions. Firstly, co-op advertising promotes both the profit of the manufacturer and the profit of the retailer, but the gap between the advertising expenditure of different brands is smaller than a certain amount. Secondly, marginal profits of the manufacturer are more than half of the marginal profits of the retailer, or else the manufacturer has no incentive to share any advertising expenditure with its retailer. Besides, the stimulating effect promotes advertising while the competition effect inhibits it. Co-op advertising increases with the marginal profits of the manufacturer and the retailer, but it is more sensitive to the manufacturer’s marginal profit than the retailer’s. More interestingly, the participation ratio of the manufacturer has nothing to do with those effects of advertising. Finally, profits of both participants are higher in the cooperative situation than in the Stackelberg case.

The rest of this paper proceeds as follows. The basic model and assumptions are presented in the next section. The model is analyzed in Section

Assume that there are one manufacturer and one retailer in the supply chain, and they supply two substitute brands, denoted to brand

The manufacturer solves the following problem:

We have the following assumptions:

Assumption (i) means that the stimulating effect is stronger than the competition effect and the advertising impacts on the two brands are difference. Assumption (ii) illustrates that the marginal profits different of the manufacturer (retailer) should not be too large. Combining assumptions (i) and (ii) yields assumption (iii). Furthermore,

Many firms supply products without advertising, which means that it is not essential for firms in the supply chain to launch co-op advertising for both brands. Indeed, we reach Proposition

If the sale of brand 2 (or 1) is more than zero even without advertising, advertising expenditure for brand 1 (or 2) should be no more than

When

Proposition

The profit functions of the manufacturer and the retailer are concave.

See the appendix.

Proposition

In the Stackelberg situation, the manufacturer acts as the leader and the retailer acts as the follower. The two firms in the supply chain play a two-stage Stackelberg game. The manufacturer decides its participation ratio in the first stage. Then, given the participation ratio, the retailer decides its best advertising expenditure in the second stage. To get the Stackelberg equilibrium solution, backward induction method is introduced, which means that we should solve the reaction function of the retailer in the second stage first. So solving function (

(i) The theoretical condition for the manufacturer to participate in co-op advertising is

See the appendix.

We call

(i)

See the appendix.

Proposition

Given the best participation ratio

(i)

See the appendix.

Comparing with Proposition

By Propositions

Consider the following

Following the proof of Proposition

The proof of Proposition

Proposition

Total profits of the manufacturer and the retailer are denoted as

The profits of the manufacturer and the retailer under different conditions satisfy the following relationships:

See the appendix.

Advertising increases the profits of both the manufacturer and the retailer. So if the firms in the supply chain have no cash flow constraint, they always advertise for all their brands. We can find evidence in the reality. For example, Procter & Gamble always advertises all of its shampoo brands, such as Rejoice, Head & Shoulders, Pantene, and Sassoon, and all detergent brands, such as Tide, Lenor, and Ariel, at the same time.

Many researches [

And the maximization problem for the supply chain under the cooperation situation is

The total profit of the manufacturer and the retailer under the Stackelberg situation is presented as follows:

See the appendix.

Proposition

Advertising has strong spillover effect, and firms in the supply chain cannot acquire all the profits brought by advertising. So, more and more supply chain firms choose co-op advertising to improve sales. Stimulated by these phenomena, this paper employs a single-manufacturer single-retailer two-brand model to address co-op advertising. Different from other studies, this paper considers the phenomenon that the supply chain supplies two substitute brands simultaneously. Besides, this paper separates advertising effects into stimulating effect and competition effect.

This paper achieves several interesting conclusions. Firstly, if the supply chain firms supply two (or multiple) substitute brands, the difference of total expenditure between the two (or multiple) brands should not be too large. Secondly, cooperative (co-op) advertising increases the total supply chain profits and advertising expenditure. More interestingly, although both the stimulating effect and the competition effect affect the retailer’s advertising decision, they have no effect on the manufacturer’s participation ratio decision. The manufacturer’ marginal profit as well as the retailer’s marginal profit affects both the manufacturer’s and the retailer’s behavior. Moreover, the manufacturer’s marginal profit has more effect on the supply chain decision than the retailer’s. The stimulating effect increases co-op advertising while the competition effect decreases co-op advertising.

Next, the study can extend to multiple brands or considers the effect of capital market, such as debt financing behavior, which will also complicate the analysis. These are our further studies.

The first- and second-order optimal conditions of (

If

From (

We have the following:

For

Proof of Proposition

If

This work was supported by the National Social Science Foundation of China (11BGL034) and the Soft Science Foundation of Guangdong Province of China (2012B070300046). Sincere thanks are offered to the anonymous reviewers for their helpful suggestions.