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# Gregor Zoettl† - page 5 / 48

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potential for the exercise of market power in the German Electricity market, in the long run, when firms investment decisions are taken into account.

The article is structured as follows: In section 2 the framework is introduced. In sections 3 and 4 we derive the benchmark cases of perfect competition and monopoly. In section 5 we analyze the case of imperfect competition, and compare them to the benchmark scenarios (section 6). In section 7 empirically analyze investment decisions in the German electricity market for all different market structures. Section 8 concludes.

# The Model

We analyze a two stage market game where firms choose cost functions under demand uncertainty and make output choices after market conditions unraveled.

Industry demand is subject to random variations. Denote by θ 0 the range of possible demand scenarios and by F (θ) the probability distribution over those demand scenarios,

with the corresponding density f(θ) = F (θ).9

# P (Q, θ) = θ

B(Q), without loss of generality we assume B(0) = 0.

Whenever P (Q, θ) > 0

the following assumptions are satisfied:

Assumption 1 Demand) . ( i ) P ( Q , θ ) i s t w i c e c o n t i n u o u s l y d i e r e n t i a b l e i n Q w i t h P q ( Q , θ ) < 0

( i i ) P q ( Q ) + P q q ( Q ) Q < 0 .

Prior to unraveling of uncertainty, firms decide on the technologies they want to install. Each unit of a technology c allows for production of one unit at marginal cost c and comes at marginal cost of investment denoted by k(c). The Technologies available for investment satisfy the following properties: +

Assumption 2 Technology) Each technology is characterized by its constant marginal cost of production denoted by c. Per unit cost of investment in technology c is denoted by k(c), which satisfies:

9Throughout the article we denote the derivative of a function g(x, y) with respect to an argument z, z = x, y, by gz(x, y), the second derivative with respect to that argument by gzz(x, y), and the cross

derivative by gxy(x, y).

10For the case of linear demand we obtain B(Q) = b Q, with b being a positive constant.

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