M.-C. CHANG

298

performance. A product with a large θ means that it gen-

erates less environmental harm, i.e., a “green” product,

where θ (0, ). A firm’s cost function is described as

c(q,

), with c(0,

) = 0, c

(q,

) > 0, c

(q,

) > 0, cq(q,

)

> 0, and cqq(q,

) 0, where the subscripts stand for par-

tial derivatives, pollution abatement costs are increas-

ingly costly, and marginal production costs are non-de-

creasing. A firm’s cost function in our model also satis-

fies the traditional hypothesis in the environmental eco-

nomics literature by Palmer et al. [6], i.e., cq

(q,

) > 0.

Polluting emissions damage the global environment

and personal health due to the ingestion of polluted air,

water, and food. We denote the social cost D(e) as the

global environmental damage, and denote the private

cost d(e) as the personal health damage. The consumers

are a continuous distribution over [0, 1]. A consumer of

type s has a maximized willingn ess to pay for the product

to be s, and each consumer purchases at most one unit of

the product at price p. Since the global environmental

damage is the same for each buyer and each non-buyer, it

does not affect our analytic result. A buyer’s net utility is

s d(e) D(e) p, while a non-buyer’s net utility is

D(e). We assume that d(0) = 0, d' (e) > 0, and d''(e) 0.

3. Game without Environmental Regulation

The game without environmental regulation is a two-

stage game. At stage 1, the firm determines the product’s

environmental performance. At stage 2, the firm sets the

price. We use backward induction to obtain a sub-game

perfect Nash equilibrium (SPNE).

sU is assigned as the marginal consumer who is indif-

ferent to buy produ cts or not. The superscript “U” sta nds

for the case of a game without environmental regulation.

sU is solved through the Eq uation (1) as follow:

1sdf sp

0. (1)

From Equation (1), we have sU = sU(p, θ), where sU

[0, 1], and from Equation (1), we obtain the relationship

between sU and p by the Implicit Function Theorem as:

1

1

U

p

sdf

0

,

. (2)

The result of Equation (2) tells us when price (p) in-

creases, it induces the critical point sU to shift to right and

it approaches 1. In other words, when price increases, it

makes the demand quantity (1 sU) decrease. Hence,

consumer behavior satisfies the demand law.

The demand function that firm faces is qU = 1 sU,

and the firm’s profit function is:

,, ,

UU

ppqpcqp

. (3)

Deriving Equation (3) with respect to parameter p and

let it be zero, we have the result in Stage 2 as:

0

UU

qU

pqs c. (4)

From Equation (1), we also obtain the relationship

between sU and θ by the Implicit Function Theorem as:

10

U

s

, (5)

where 22

011dfdfqd f

0

,

and 2

1q

qcdf

2

. The sign of U

is de-

cided by the sign of 1. When the product’s marginal

environmental damage is large enough, i.e.,

2

q

dqc f

, it induces 1 < 0 and 0

U

s

. This

implies that given one unit of emission with large health

damage to consumers, an increase in a product’s envi-

ronmental performance induces the product’s demand

quantity to increase.

We next examine the relationship between price (p)

and the product’s environmental performance (θ). The

comparative static result in Equation (4) is:

22

2

0,

for.

U

q

q

pdfqdfq

sc

dqc f

(6)

This tells us that the clearer the product is, the higher

the price will be when the product’s marginal environ-

mental damage is large enough. There are two negative

effects in a consumer’s utility: a large marginal environ-

mental damage of the product and the high price. How-

ever, the product’s marginal environmental damage can

be mitigated by increasing its environmental perform-

ance. Hence, when the product’s marginal environmental

damage is large, the consumers are willing to spend a lot

more to purchase the product with high environmental

performance. Some studies on marketing research pro-

vide various evidence to support our finding such as

Cairncross [7], and Cason and Gangadharan [8]. They

concluded that some consumers are willing to pay a

higher price on biodegradable and 3R (Reduce, Reuse

and Recycle) products. We propose this as:

Proposition 1. In a game without environmental regu-

lation, when the product’s marginal environmental da-

mage is large, the consumers are willing to pay a high

price to purchase the product with a high environmental

performance.

We solve the equilibrium solution at stage 1. Recall

the firm’s profit function in Equation (3). Derive Equa-

tion (3) with respect to parameter θ and let it be zero. We

obtain the optimal product’s environmental performance

θU that maximizes the firm’s profit. Substitute θU into

Equation (4) and Equation (3), and the equilibrium solu-

tions in the game without environmental regulation are

{θU, pU,

U, eU}.

4. Game with Environmental Regulation

We now introduce an environmental regulation into the

game. At stage 0, the regulator sets the emission standard

Open Access TEL