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.

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

Explanation / Answer

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.

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