Suppose the estimated demand function for a public water utility (for which ther

Question

Suppose the estimated demand function for a public water utility (for which there is no substitute) is given by: w = 7510P where w is the number of units per period and P is the price per unit. The price per unit is $2.00 (set by the utility’s oversight board). The typical (average) consumer spends 0.5% of his or her income on water and his or her income elasticity of demand for water is 0.2. The local municipality, whose objective is to maximize societal economic welfare (the sum of consumer and producer surplus), currently runs the utility. Due to maintenance problems in the system, the water system is constrained at 50,000 units of water per period. Suppose there are 1000 identical consumers and suppose the marginal cost per unit of water is $2.00 and there is a fixed cost of $10,000 per period.

a) What is the optimal price the utility will charge and how much water will be used?

b) What is the marginal value of capacity? Explain.

c) The municipality is considering selling the utility to a profit maximizing firm. Given the circumstances in b), what is the optimal price the firm will set and how much water will be consumed?

d) Consider the outcomes under maximizing societal economic welfare and the optimal private outcome (maximizing profits). Find the total impact on welfare of privatization broken down by the impact on both the supply and the demand side, including transfers and deadweight loss (DWL). Provide a graphical analysis and calculation of actual value. Show the relevant areas within the graph for your calculations.

e) If the firm were able to perfectly price discriminate, what would the outcome be and what is the economic welfare outcome?

Explanation / Answer

a.The utility will charge price =Marginal cost . This will maximize the total welfare . Therefore price will be $2 and quantity supplied will be (75-10*2) = 55
b.

The marginal value of capacity generally define as the value of the business by producing one more extra unit of goods.

Now, here the equation is

W = 75-10p

and price = $2.00

So, W = 75-10*2

W = 75-20

W = 55

So 55 units of capacity occur her

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