Answer to Question #307358 in Microeconomics for smarta

Question

Demonstrate how if a public good is to be provided in some fixed amount or not provided at all, then a necessary and sufficient condition for provision to be Pareto efficient is that the sum of the willingnesses to pay (the reservation prices) exceeds the cost of the public good

Answer 1

Pareto efficient is achieved when the resources and goods allocated achieve their maximum efficiency and that no change can be made without making someone worse off. Reservation prices enforced implies that the type pf good or service are only accessible to those who pay the reservation prices. Moreover, for a resource or good to be provided efficiently with people paying reservation prices, then it means the reservation prices must exceed the cost of producing the good or service to enable financing of the good or resource.

A good example is when the cost of watching cinemas is 5 dollars (reservation prices), this needs to be paid by viewers who want to watch. Then a total of 150 people pays the price bringing it to a total of 750 dollars. The cost of producing the film or maintaining the cinema halls must be less than 750 dollars per night for the cinema to continue operating. If it is more than 750 dollars, then people will not watch the cinemas that night, which will have violated the Pareto efficient.

This is because a certain amount of service, in this case a cinema was provided where all the customers provided reservation prices for a service, which they did not receive. Pareto efficient states that reservation prices must exceed cost of production for all the customers to receive maximum service, which was not the case.