9 Example: Peak Load Pricing The price of a good (electricity) for time period i is given as p i The producer chooses how much to produce in each period ( x i ), and the maximal capacity of his plant ( k). The total cost of producing (x 1,…,x n ) is C(x 1,…,x n ). The cost of capacity k is D(k).
12 The Maximum Principle Optimization over time Stock – state variables Flow – control variables A.K. Dixit: Optimization in Economic Theory, Oxford University Press, 1989. Chapter 10 * * stocks of capital goods consumption, labor supply flow variable production function
13 The Maximum Principle Optimization over time Stock – state variables Flow – control variables
14 The Maximum Principle Optimization over time additively separable utility function The marginal rate of substitution between periods 1,2 is independent of the quantitiy consumed in period 0