1 - Benchmarking with DEA, SFA and R PDF

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Benchmarking with DEA, SFA and R...

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Network and Infrastructure Regulation Problem Set 1 Natural Monopolies October 20, 2015

Exercise 1: Natural Monopoly Show that the following proposition holds: If the production of a single good shows falling average costs in the whole relevant region (the region of demand quantity), a natural monopoly exists.

Exercise 2: Natural Monopoly Assume a cost function with decreasing average cost up to Q∗ and increasing average costs for q > Q∗. 1. Construct the average cost function if two firms share the market equally. 2. In which area is one firm the least cost solution? 3. In which area is the natural monopoly unsustainable? What might happen?

Exercise 3: Subadditivity in single product firms The cost function of a firm is given by C = 1 + q ² Demand is given by D = 10 − 5.571q 1. Check for economies of scale 2. When should a second firm enter the market? (Assume that the market is shared equally) 3. What happens if demand shift outwards?

Exercise 4: Economies of scale Show graphically that decreasing average cost are not a necessary condition for a natural monopoly in the single product case!

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Exercise 5: Economies of scale The cost function of the Public AG is given by C(q) = 4q 3 − 25q 2 + 75q + 112, where q is expressed in 10,000 units. 1. Draw a graph (independent of the function above) including a function of average costs and a function of marginal costs with economies of scale within the interval (0,m) 2. Does the function mentioned above exhibit economies of scale and if this is the case, in which interval?

Exercise 6: Subadditivity of multi-product cost functions A multi-product firm is producing the goods q1 and q 2 and faces the following cost function: C = q1 + q2 + (q1 ∗ q2 )1/3 . Is this multi-product cost-function subadditive?

Exercise 7: Economies of scope Given the two cost functions 1. C(q1 ; q2 ) = F + 10q1 + 20q2 with F > 0 and 2. C(q1 ; q2 ) = (q1 + q2 )1/2 Do the two cost functions exhibit economies of scope?

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