Notice that for λ = 0 (the case of welfare maximization) this statement replicates theorem1 and for λ = 1 (profit maximization) it replicates theorem2. For an illustration compare figure 4.

The concept of second best solutions allows thus to cover both the case of perfect competition and the case of profit maximization. It is important to emphasize however that even for intermediate values 0 < λ < 1, the concept of second best solutions is not capable of capturing strategic interaction of firms which is the topic of the subsequent section.

# 5

# Strategic Firms – Imperfect Competition

Having reviewed the benchmark cases of welfare and profit maximization in sections 3 and 4, we now turn towards the case of imperfect competition. We derive the equilibrium of the two stage market game where firms first decide on their investment x_{i}(c) and then after having observed investment decisions and realization of demand decide on production q_{i}(x, θ). Analogously to the previous analysis we first solve for the spot market equilibria f o r g i v e n I n v e s t m e n t d e c i s i o n s x 0 i ( c ) f o r e a c h d e m a n d r e a l i z a t i o n θ .

# Since marginal cost are nondecreasing (the capacity choice problem exhibits this prop- erty by construction) and due to concavity of profits ensured by assumption 1 (ii), there

always exists a unique Cournot ment choices can be asymmetric,

equilibrium at the spot market.

# Since firms invest-

in

that

Cournot

equilibrium

for

given

demand

realiza-

t i o n θ 0 a n d g i v e n i n v e s t m e n t x 0 ( c ) fi r m s w i l l C o u r n o t e q u i l i b r i u m a t t h e s p o t m a r k e t x i ( c E Q i produce at ), for all i

different marginal cost. The = 1, . . . , n can be determined

→

by c^{EQ }

( θ ) = c E Q 1

( θ ) , . . . , c E Q n

(θ). Those are characterized by of the following well–known

# equilibrium conditions of the Cournot game:

→

c^{EQ }

(θ) =

(

∀i

"

³

c E Q i

´

:P

Ã n X j = 1

x j ( c E Q j

) , θ ! + P q

Ã n X j = 1

x j ( c E Q j

)

!

x i ( c E Q i

) = c E Q i

#)

We can now proceed analogously to the previous sections and characterize the critical

16