The price is established by Cournot compet it ion conditional on 8+ and s+. Each of the n firms in the indust ry is assumed to be identical, and to simplify the model each is assumed to have zero cost. The profit Ti of firm i then is 丌i=P(X)xi where Ti is the out put of firm i, X=fl ci, P(X)is the inverse demand function obt ained from X(s+, 0+, y)and (s+, 0+, y). The equilibrium price ,(s+, 0+) (s+,.+) so the price reveals the informat ion the firms have. From(1) information that the ex ternality is more serious(higher 0f) reduces demand, and the firms respond with lower prices. Despite the lower price, demand is lower the higher is 0+. The marginal valuation (s+,0+)6(s+,+,yf(s+,.+) which is strict ly increasing in 6+ and in st for a > l, so regulation decreases the demand x(s+,0+)0X(s+,O 0+) (s+,O+ 0(1-as+)-(1-s+)+m Thich is positive if 1 S+)0+IN which will be assumed to be the case when n is small. I1 That some consumer who purchases. The ext ernality 0+X(s+, 0+) could exceed 0; 1. e, the externality could be quite serious The profit f(s+, 0+) of firm i is NyP(0+)2 r(s+,0+) (1 N((1-as+)-(1-s+)0+nN)2 (7+1)2(1-a8+)b extent (n) to which consumers internalize the externality / (n)a in i. Similarly, the The price in(2)is decreasing in 0+, n, a,8+, and n and increasi Ing in 0+ or a>l, the compet it iveness The proport ion of mers who purchase is increasing in i and limy,a Profit is decreasing in the st andard only if a>l. The increases in CAFE st andards three aut makers to the producers of smaller, higher fuel economy vehidles. from the big during the 1970s and 1980s shift ed considerable market share and profitsThe price is established by Cournot competition conditional on θ+ and s+. Each of the n firms in the industry is assumed to be identical, and to simplify the model each is assumed to have zero cost. The profit πi of firm i then is πi = P(X)xi, where xi is the output of firm i, X = Σn i=1xi, P(X) is the inverse demand function obtained from X(s+, θ+, y) and v∗(s+, θ+, y). The equilibrium price y∗(s+, θ+) is y∗(s+, θ+) = 1 n + 1 ￾ vˆ(1 − αs+) − (1 − s+)θ+ηN
, (2) so the price reveals the information the firms have. From (1) information that the ex￾ternality is more serious (higher θ+) reduces demand, and the firms respond with lower prices. Despite the lower price, demand is lower the higher is θ+. The marginal valuation v∗(s+, θ+) ≡ v∗(s+, θ+, y∗(s+, θ+)) is v∗(s+, θ+) = vˆ n + 1 + n(1 − s+)θ+ηN (n + 1)(1 − αs+) , (3) which is strictly increasing in θ+ and in s+ for α > 1, so regulation decreases the demand for the product. Demand X(s+, θ+) ≡ X(s+, θ+, y∗(s+, θ+)) is X(s+, θ+) = n n + 1 N (1 − αs+)ˆv ￾ vˆ(1 − αs+) − (1 − s+)θ+ηN
, (4) which is positive if ˆv> (1−s+)θ+ηN (1−αs+) , which will be assumed to be the case when η is small.11 That is, there is some consumer who purchases. The externality θ+X(s+, θ+), however, could exceed ˆv; i.e., the externality could be quite serious. The profit π∗ i (s+, θ+) of firm i is π∗ i (s+, θ+) = Ny∗(θ+)2 (1 − αs+)ˆv = N(ˆv(1 − αs+) − (1 − s+)θ+ηN)2 (n + 1)2(1 − αs+)ˆv . (5) The price in (2) is decreasing in θ+, η, α, s+, and n and increasing in ˆv. Similarly, the profit is decreasing in θ+, s+ for α>1, the competitiveness (n) of the industry, and the extent (η) to which consumers internalize the externality.12 11 The proportion of consumers who purchase is increasing in ˆv and limvˆ→∞ v∗ vˆ = 1 n+1 . 12 Profit is decreasing in the standard only if α>1. The increases in CAFE standards during the 1970s and 1980s shifted considerable market share and profits from the big three automakers to the producers of smaller, higher fuel economy vehicles. 13