7. Consider the problem of a monopoly supplier of water. Selling water has a con

Question

7. Consider the problem of a monopoly supplier of water. Selling water has a constant marginal cost of £5 per cubic metre. There are two types of households in the economy. The preferences of both types of households are separable in water and money. Wealthy households value cubic metres of water according to the function202, hereas low income households value water according to ul(x) = 10x1/2. Only one half of households is wealthy. Suppose that the water supplier knows the income status of each household. (a) Efficiency requires equalization of marginal utility to marginal cost. Find the efficient water supply to both types of household. (13 Marks) (b) If the monopolist can offer contracts which specify the water supply to a household and the total price charged for this supply. Find the profit-maximizing contracts offered to high and low income households. (20 Marks) (c) How would conclusions differ if the monopolist did not know the income status of each household? Would it face more constraints? Argue in words. (7 Marks)

Explanation / Answer

a) Marginal cost is given EURO 5 per cubic metre.
while the marginal utility stands at 30x1/2

so, efficiency would be :
{ 20x1/2 / 30x1/2 }* 100 = 66.6%
{ 10x1/2 / 30x1/2} * 100 = 33.3 %
therefore if the lower income household pay EURO 5 per cubic metre then wealthy household will pay EURO 10 for the same quantity of wate. this way we achive the equalization of marginal utility to marginal cost.

b) Given in the question that preferences of both types of households are seperable in terms of water and money; therefore symbolizes that wealthy people have no objections in paying till the supply of water is obstruction free.
on the other hand the lower income household has there intention to save money and hence they donot wish to spend much on water then there actuall use hence they will only pay for what they use.

So the contract made individually with the wealthy household will maximise the profit of monopolist where as the policy of contract doesn't seems to suit in the case of lower income household. Instead of making contract individually(lower income household) , here the monopolist should make contract colony wise or street wise that might get him some profit; as from the basics of economy we know huge quanty sales bring good income.

c) If the monopolist didnt knew about the income status of household the conclusion  would be diffrent as here the monopolist donot know whom to make contract with and is also not sure to rely of the utility function hence he is he would face more constraints. Being the monopolist he donot need to worry for growth but profit maximisation will be an issue.

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