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Social Science Clinic => Economics => Macroeconomics => Topic started by: kms5229 on Nov 23, 2022

Title: Determining How Much of a Public Good to SupplyJack and Jill both own businesses on a deserted road ...
Post by: kms5229 on Nov 23, 2022

Determining How Much of a Public Good to Supply

Jack and Jill both own businesses on a deserted road and both need a security guard. Once a security guard is hired, the guard will be able to protect both businesses despite who hires the security guard. The table shows the price Jack and Jill are willing to pay for each hour of protection.

Quantity (hours of protection)	Jill's willingness to pay (dollars per hour)	Jack's willingness to pay (dollars per hour)
1	76​	74​
2	74​	72​
3	72​	70​
4	70​	68​
5	68​	66​

Suppose the security guard has a constant marginal cost of $138 dollars an hour. What is the optimal number of hours of security guard services?
◦ 1 hours
◦ 4 hours
◦ 0 hours
◦ 3 hours

Title: Determining How Much of a Public Good to SupplyJack and Jill both own businesses on a deserted road ...
Post by: koswald on Nov 23, 2022

4 hours

To find the total demand for security guard services, a public good, add the individual demand curves vertically; that is, add the price each consumer is willing to pay for each quantity of the public good.

Quantity (hours of protection)	Jill's willingness to pay (dollars per hour)	Jack's willingness to pay (dollars per hour)	Total demand
1	76​	74​	76+74=150
2	74​	72​	74+72=146
3	72​	70​	72+70=142
4	70​	68​	70+68=138
5	68​	66​	68+66=134

The optimal quantity is where supply meets demand.
In this example, supply is constant at $138, so the optimal quantity is 4 hours of protection.