A water company owns water pipes that burst often due to poor maintenance. The company can invest GHS m in the maintenance of the pipes. More maintenance means less water loss through bursts and fewer compensation payments to residents due to flooding of their properties. Assume that the value of lost water is 1/m so that more maintenance reduces the amount of loss. Assume that the value of damage to properties where the pipes are routed is 3/m , so that more maintenance decreases the amount of damage to properties. (i.) What is the socially optimal level of maintenance, m? What is the associated value of lost water and property damage? (Note: Minimize the total cost function) ( ii). What level of m is chosen when pipes that burst run through land owned by the government (the company pays nothing for damages even though there is still some damage associated with pipe bursts)? What is the new value for property damage? What is the deadweight loss?

A water company owns water pipes that burst often due to poor maintenance. The company can invest GHS m in the maintenance of the pipes. More maintenance means less water loss through bursts and fewer compensation payments to residents due to flooding of their properties. Assume that the value of lost water is 1/m so that more maintenance reduces the amount of loss. Assume that the value of damage to properties where the pipes are routed is 3/m , so that more maintenance decreases the amount of damage to properties. (i.) What is the socially optimal level of maintenance, m? What is the associated value of lost water and property damage? (Note: Minimize the total cost function) ( ii). What level of m is chosen when pipes that burst run through land owned by the government (the company pays nothing for damages even though there is still some damage associated with pipe bursts)? What is the new value for property damage? What is the deadweight loss?

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter2: Mathematics For Microeconomics

Section: Chapter Questions

Problem 2.16P

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