Assume that a single electricity utility serves two 2 consumer blocks Block 1 is low consumption, Block 2 is high consumption Utility's cost function, C (y1 + y2) = F + m(y1 + y2), where F is Fixed Cost ($), m is marginal cost ($/MWh), y i (MWh) is consumption of Block i (i=1,2) Inverse Demand Functions: p i = y i + a i (i=1,2) where p i ($/MWh) is unit price of electricity for consumers of Block i Hence, Consumer Surplus ($), CS i = 0.5 y i (a i p i) = 0.5 (a i p I )^2

Total Consumer Surplus, CS = CS 1 + CS 2 Parameters: F = 2; m = 0.1; a 1 = 1.8; a 2 = 2.5

(1) Assume Block 1 is sole consuming Block, i.e., y 2 = 0. Compute lowest price, if it exists, for Block 1 such that utility breaks even, i.e., earns enough to cover cost

(2) Repeat (1) for case where Block 2 is sole consuming Block Compute Block 2's lowest price, if it exists, such that the utility breaks even

(3) Now assume that both Blocks consume (a) Allowing Block 2's price to vary, what is lowest price for Block 1, p1min , such that the utility breaks even? And in this case, what is Block 2's price? (b) In this case what are the consumer surpluses, CS 1 , CS 2 and CS? (4) If p 1 = 1.1 compute p 2 such that utility breaks even, also CS 1 , CS 2 and CS (5) Comparing results for (3) and (4), comment on the tradeoff in terms of equity and aggregate welfare as given by CS