Figure 2: Investment decision x_{i}(c) of firm i.

In order to determine total profits of firm i associated to some investment choice x_{i}(c), we first determine profits associated to some partial investment dx_{i}(c_{0}) as illustrated in figure 2. That is we determine profits generated by technology c_{0}, the amount invested in this technology is given by dx_{i}(c_{0}). Observe that such investment will only yield positive r e v e n u e s f o r d e m a n d r e a l i z a t i o n s θ > θ c 0 i . E x p e c t e d r e v e n u e s g e n e r a t e d b y d x ( c 0 ) a r e g i v by the expected markup in all those demand realizations where indeed production is at or above marginal cost c_{0 }times the amount dx(c_{0}) invested: e n

Z

c i

0

[P (Q(x, θ), θ)

c_{0}] dF (θ) ∗ dx_{i}(c_{0})

On the other hand, the cost of investment in technologies dx_{i}(c_{0}) is given by the (constant) marginal cost k(c_{0}) of investment times the amount times the amount dx(c_{0}) invested:

k(c_{0}) ∗ dx_{i}(c_{0})

In the context of electricity generation, the above analysis corresponds to determining expected profits generated by a small power plant of size dx_{i}(c_{0}) which produces at marginal cost c_{0 }and comes at a cost of investment given by k(c_{0}).

In order to obtain total profits associated to the entire investment-choice x_{i}(c), we need to sum up for all technologies, where investment took place. Suppose firm i did choose to invest into technologies c ∈ [c_{i}, c_{i}], with 0 ≤ c_{i }< c_{i}, then integration over all those

7