Quality Difference between Two Products

Quality difference may be the result of, for example, asymmetric product R&D investments. We define

θ = α

₁

α

₂ as the degree of quality differentiation. For

θ > 1

, product 1 has an absolute advantage in demand; for

θ < 1

, firm 2 has an absolute advantage in demand, because

α

₂

> α

₁; and

θ = 1

implies no quality difference between the products.

Recall that Assumption 4.2 make restriction on parameters

α

_i

β

_j

− α

_j

γ > 0

. That is,

γ

β α α β γ

α

2 2

<

1

<

2 1 . Effect of quality differential will be examined by complement and substitute products and degree of cross effect is also considered here.

Complement Products

As the quality had improved, equilibrium profit of the manufacturer is higher (see Figure 56-Figure 61). This higher profit is attributed to the increase of margin and quantity. Due to the nature of complement products, more of product1 being bought would result in more of product2 also being bought. Hence, all members contained in the channel can be benefited.

According to our results, quality differentiation makes no effect on choice of strategic

0 5 10 15 20 25 30

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Quantity

Degree of Cross Effect

Q2RS (QQQ) Q2RS (QPP) Q2RS (QPQ) Q2RS (PPP) QW2RS (PQQ) Q2RS (PPQ)

62

variable.

Figure 56 Manufactures' profit with quality differential (complement products;

γ² β₁β₂

= 0 . 3 )

Figure 57 Retailer's profit with quality differential (complement products;

γ² β₁β₂

= 0 . 3 )

0 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000

Manufacturers' Profit

θ

πRSM1 (QQQ) πRSM1 (QPP) πRSM1 (QPQ) πRSM1 (PPP) πRSM1 (PQQ) πRSM1 (PPQ) πRSM2 (QQQ) πRSM2 (QPP) πRSM2 (QPQ) πRSM2 (PPP) πRSM2 (PQQ) πRSM2 (PPQ)

0 5000 10000 15000 20000 25000 30000 35000 40000 45000 50000

0.5480.6180.6880.7580.8280.8980.9681.0381.1081.1781.2481.3181.3881.4581.5281.5981.6681.7381.8081.824

Retailer's Profit

θ

πRSR (QQQ) πRSR (QPP) πRSR (QPQ) πRSR (PPP) πRSR (PQQ) πRSR (PPQ)

63

Figure 58 Manufacturers' profit with quality differential (complement products;

γ² β₁β₂

= 0 . 6 )

Figure 59 Retailer's profit with quality differential (complement products;

γ² β₁β₂

= 0 . 6 )

0 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000

Manufacturers' Profit

θ

πRSM1 (QQQ) πRSM1 (QPP) πRSM1 (QPQ) πRSM1 (PPP) πRSM1 (PQQ) πRSM1 (PPQ) πRSM2 (QQQ) πRSM2 (QPP) πRSM2 (QPQ) πRSM2 (PPP) πRSM2 (PQQ) πRSM2 (PPQ)

0 10000 20000 30000 40000 50000 60000

0.7760.8040.832 0.86 0.8880.9160.9440.972 1 1.0281.0561.0841.112 1.14 1.1681.1961.2241.252 1.28 1.29

Retailer's Profit

θ

πRSR (QQQ) πRSR (QPP) πRSR (QPQ) πRSR (PPP) πRSR (PQQ) πRSR (PPQ)

64

Figure 60 Manufacturers' profit with quality differential (complement products;

γ² β₁β₂

= 0 . 9 )

Figure 61 Retailer's profit with quality differential (complement products;

γ² β₁β₂

= 0 . 9 )

0 10000 20000 30000 40000 50000 60000 70000

Manufacturers' Profit

θ

πRSM1 (QQQ) πRSM1 (QPP) πRSM1 (QPQ) πRSM1 (PPP) πRSM1 (PQQ) πRSM1 (PPQ) πRSM2 (QQQ) πRSM2 (QPP) πRSM2 (QPQ) πRSM2 (PPP) πRSM2 (PQQ) πRSM2 (PPQ)

0 20000 40000 60000 80000 100000 120000 140000 160000 180000 200000

Retailer's Profit

θ

πRSR (QQQ) πRSR (QPP) πRSR (QPQ) πRSR (PPP) πRSR (PQQ) πRSR (PPQ)

65

Substitute Products

For the case of substitute products, as the quality had improved, equilibrium profit of the manufacturer and retailer are higher (see Figure 62-Figure 67). This higher profit is attributed to the increase of margin and quantity.

However, for substitute products, more of product1 being bought would result in less of product2 being bought. Where high-quality product possesses a higher profit, it hurts the low-quality manufacturer. According to our results, quality differentiation makes no effect on choice of strategic variable.

Figure 62 Manufacturers' profit with quality differential (substitute products;

γ² β₁β₂

= 0 . 3 )

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000

Manufacturer2's Profit

θ

πRSM1 (QQQ) πRSM1 (QPP) πRSM1 (QPQ) πRSM1 (PPP) πRSM1 (PQQ) πRSM1 (PPQ) πRSM2 (QQQ) πRSM2 (QPP) πRSM2 (QPQ) πRSM2 (PPP) πRSM2 (PQQ) πRSM2 (PPQ)

66

Figure 63 Retailer's profit with quality differential (substitute products;

γ² β₁β₂

= 0 . 3 )

Figure 64 Manufacturers' profit with quality differential (substitute products;

γ² β₁β₂

= 0 . 6 )

5000 10000 15000 20000 25000 30000

Retailer's Profit

θ

πRSR (QQQ) πRSR (QPP) πRSR (QPQ) πRSR (PPP) πRSR (PQQ) πRSR (PPQ)

0 500 1000 1500 2000 2500 3000 3500 4000

Manufacturers' Profit

θ

πRSM1 (QQQ) πRSM1 (QPP) πRSM1 (QPQ) πRSM1 (PPP) πRSM1 (PQQ) πRSM1 (PPQ) πRSM2 (QQQ) πRSM2 (QPP) πRSM2 (QPQ) πRSM2 (PPP) πRSM2 (PQQ) πRSM2 (PPQ)

67

Figure 65 Retailer's profit with quality differential (substitute products;

γ² β₁β₂

= 0 . 6 )

Figure 66 Manufacturers' profit with quality differential (substitute products;

γ² β₁β₂

= 0 . 9 )

0 2000 4000 6000 8000 10000 12000 14000 16000 18000

Retailer's Profit

θ

πRSR (QQQ) πRSR (QPP) πRSR (QPQ) πRSR (PPP) πRSR (PQQ) πRSR (PPQ)

0 200 400 600 800 1000 1200 1400 1600 1800 2000

Manufacturers' Profit

θ

πRSM1 (QQQ) πRSM1 (QPP) πRSM1 (QPQ) πRSM1 (PPP) πRSM1 (PQQ) πRSM1 (PPQ) πRSM2 (QQQ) πRSM2 (QPP) πRSM2 (QPQ) πRSM2 (PPP) πRSM2 (PQQ) πRSM2 (PPQ)

68

Figure 67 Retailer's profit with quality differential (substitute products;

γ² β₁β₂

= 0 . 9 )

7000 8000 9000 10000 11000 12000 13000 14000

Retailer's Profit

θ

πRSR (QQQ) πRSR (QPP) πRSR (QPQ) πRSR (PPP) πRSR (PQQ) πRSR (PPQ)

69

6 SUMMARY AND CONCLUSIONS

This research is aimed to provide a precise understanding of price and quantity competition models when differentiated products made by different manufacturer and sold them through a common retailer. We especially focus on the channel structure as Retailer-Stackelberg game mentioned in Choi’s paper (1991).

We perform our results in numerical example. In Section 5.1 we analyzed the choices of strategic variable with different channel structure. It was shown that retailer always benefit from being a Stackelberg leader and, whatever the strategic variable retailer chooses, it makes no influence on the equilibrium outcomes. When the degree of cross effect is relatively low, channel structure plays an important role on the equilibrium outcomes. As the degree of cross effect grows, choices of strategic variable by the manufacturers become more critical. With regard to the manufacturers, to set quantity as their strategic variable is a dominant strategy when they produce complement goods. There is no dominant strategy when products are substitutes, but the manufacturers are more likely to set quantity. From retailer point of view, manufacturers fall into price competition would be always preferred.

How the degree of cross effect works upon RS game is analyzed in Section 5.2.1. We found that when retailer possesses a Stackelberg leadership, no matter how large the degree of cross effect is and what strategies the manufacturers play, retailer margin of the two products remain constant. That is, retail price of each product is depends on the wholesale price.

Unsurprisingly, manufacturers compete in price result in more quantity demand. Thus retailer always prefers its manufacturer compete in price. For the case of manufacturers, their best strategies are base on the cross-effect of the products. When products are complement and the cross-effect is relatively low, the dominant strategy of manufacturers is to set quantity. As the cross-effect increases, setting quantity is still a best strategy, but the best outcome occurred when both of them set price. That is the so-called “Prisoner’s Dilemma”. When products are substitute, there is no more dominant strategy, but they are more likely to set quantity.

Quality differential is considered in Section 5.2.2. According to our results, as the quality

70

of product had improved, equilibrium profit of the manufacturer is higher and this higher profit is attributed to the increase of margin and quantity. When products are complements, thanks to the complementary nature, all members contained in the channel can be benefited by product improvement. On the other hand, manufacturer which produces high-quality product and the retailer possess higher profit, but it hurts the low-quality manufacturer. Moreover, quality differentiation makes no effect on choice of strategic variables.

Two manufacturers and only one dominant retailer are considered as members in this research. Hackner (2000) had shown that the results developed in Singh and Vives (1984) are sensitive to the duopoly assumption. Besides, researchers have already probed into the interactions between two retailers and two manufacturers. Furthermore, capacity restriction is not considered in the article. There is space for extension which contains more channel members in the models to help understand a more realistic market.

71

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簡 歷

 

姓名：麥豪傑

籍貫：廣東省台山縣

生日：民國七十三年八月二十六日

學歷：民國九十八年七月國立交通大學運輸科技與管理學系碩士班畢業

民國九十六年七月國立交通大學運輸科技與管理學系學士班畢業

電郵信箱：[email protected]

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