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Consider a utility providing water service as a natural monopoly to residents of a city. The market comprises n identical households, each of which

  

Consider a utility providing water service as a natural monopoly to residents of a city. The market comprises n identical households, each of which has an inverse demand function of p(q) = 27,500 80,000q where q is the number of megalitres (ML) of water demanded annually and p is the price per megalitre (1 ML = 1,000m3). Letting w denote total output in megalitres, inverse market demand is p(w) = 27,500 - 0.8w and the annual total cost to the utility of providing water is TC(w) = 90,625,000 + 5,000w + 0.1w 2. Thus, marginal revenue, average cost and marginal cost are, respectively, as follows: MR(w) = 27,500 1.6w; AC(w) = 90,625,000/w + 5,000 + 0.1w; and MC(w) = 5,000 + 0.2w. a. Briefly explain why water service (treatment, transmission and distribution) is a natural monopoly within the city. Determine the value of n. b. Show that the efficient price, consumption level and output level are p $9,500, q * = 0.225 and w * = 22,500, respectively. Calculate the deficit incurred by the utility if it charges p *. c. Show that the equilibrium price, consumption level and output level are p e = $17,500, q e = 0.125 and w e = 12,500, respectively, in the absence of regulation. Calculate the profit earned by the utility in equilibrium. d. The total replacement value of the utility's infrastructure is $1,000,000,000. The infrastructure is financed by shareholders whom earn a return on investment (ROI), and it requires capital replacement at a rate of $10,625,000 per annum due to physical depreciation. Depreciation and the required ROI are the only fixed costs to the utility; all other costs are variable. Determine the equilibrium rates of depreciation and ROI (in percentage terms), and decompose ROI into its required (i.e. investment opportunity cost) and economic rent components.

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