We can thus easily compare the case of imperfect competition to the monopoly outcome:
imply that the marginal cost function under imperfect competition will be chosen such that strictly more output is produced at each given marginal cost c than in the case of monopoly. ( i . e . x ∗ E Q ( c ) > x ∗ M ( c ) ∀ c ∈ [ c ∗ , c ∗ ] ) . T h i s i s i l l u s t r a t e d i n fi g u r e 4 . F i n a l l y n o t i c e t could replicate firms’ total capacity choice x∗ under imperfect competition by a “second best” scenario (as analyzed in the peak load pricing literature) by the appropriate choice h a t w e o f λ . F o r t h e c a s e o f n fi r m s , λ = 1 n w o u l d y i e l d t h e s a m e t o t a l c a p a c i t y c h o i n–firm equilibrium. However, for technologies below the capacity bound. In equilibrium firms invest strictly more into low marginal cost technologies than predicted by the λ = approximation. Thus, even though the approximation would yield the same total capacity, under imperfect competition firms invest relatively more in low marginal cost technologies c e a s t h e 1 n
This is nicely illustrated in figure 7 when comparing equilibrium investment
for the case of n = 2 and n = 4 firms (i.e.
c o r r e s p o n d i n g λ – S o l u t i o n s ( i . e . X ∗ λ =
a n d X ∗ λ =
X ). ∗ E Q
( n = 2 ) a n d X ∗ E Q
(n = 4)) with the
When it comes to compare the case of imperfect competition to the first best outcome, clear cut solutions are obtained only for the total capacity choice. Recall that the critical demand realizations for the First Best case and the case of imperfect competition coincide at the upper bound c∗ (i.e. θEQ(c∗) = θF B(c∗). We can thus conclude that total capacity invested under imperfect competition is strictly below total capacity in the First Best solu- tion. For interior technologies below the capacity bound, however, this may turn around, since the locus of the critical demand realization is above the benchmark case at each tech- nology c. In the following lemma we provide a condition under which firms invest more in low marginal cost technologies under imperfect competition than in the First Best solution.
Lemma 6 Over–investment in low marginal cost technologies) In the case of imperfect competition firms invest more in efficient technologies (close to c∗) than in
the first best case if and only if kcc(c∗) >
2(n 1) n2
f (c∗ ).
Proof see appendix 8.
As we can see, for n = 2 firms we will never observe overinvestment in low marginal cost technologies under imperfect competition. For n ≥ 3 firms, however, if the set of technologies available on the market is sufficiently convex, overinvestment in low marginal cost technologies occurs.24
24In the subsequent section 7 we apply our theoretical framework to the case of investment choice in