Question

Theoretical Problem

A government employee can exert effort e ? [0,1] to produce a good. Effort has a cost ce²/2 and is unobservable. The probability that the good is produced is e and each citizen gets ?(?) utility for an arbitrary, given ? if the good is produced but 0 otherwise. One citizen is a monitor who can a cost ?m²/2 to observe whether the good was produced or not, and the monitor can successfully determine whether or not the good was produced with the probability ?. If he is successful, he pays a cost s to share the information with everyone else. If the government employee does not produce the good and the monitor informs everyone else, the government employee gets punished and has to pay ?. The timing of this game goes as follows:

• Monitor announces ?
• Government employee chooses ℯ
• Payoffs are realized

1. a) What happens to the equilibrium effort of the government employee if the arbitrary n decreases?
   17. The equilibrium increases because the equilibrium e is increasing in u
   18. The equilibrium increases because the equilibrium e is decreasing in u
   19. The equilibrium decreases because the equilibrium e is increasing in u
   20. The equilibrium decreases because the equilibrium e is decreasing in u
   21. The equilibrium decreases because the equilibrium e is decreasing in p
   22. The equilibrium decreases because the equilibrium e is increasing in p
   23. The equilibrium increases because the equilibrium e is decreasing in p
   24. The equilibrium increases because the equilibrium e is increasing in p

8. Recall that a rival good is a good that, when consumed by one person, cannot be consumed by another. An excludable good is a good that a person can be prevented from using, either through technology or by requiring a payment.

Which type of good is a common-pool resource (a fishing area is an example of a common-pool resource)?

8. 1. Rival and excludable
   2. Non-rival and non-excludable
   3. Rival and non-excludable
   4. Non-rival and excludable
9. Recall that a rival good is a good that, when consumed by one person, cannot be consumed by another. An excludable good is a good that a person can be prevented from using, either through technology or by requiring a payment.

Which type of good is a private good?

1. Rival and excludable
2. Non-rival and non-excludable
3. Rival and non-excludable
4. Non-rival and excludable

10. Recall that a rival good is a good that, cannot be consumed by another. An excludable good is a good that a person can be prevented from using, either through technology or by requiring a payment.

Now suppose that p is a function of n and u(n)=10 and p(n)=n. This set-up provides information to suggest that the good is mostly likely:

1. Rival
2. Non-rival
3. Excludable

11. In equilibrium when u(n)=10 and p(n)=n, how does the equilibrium level of m and e change as ? increases?
    1. ? increases and e decreases
    2. ? increases and e decreases
    3. ? and e both increase
    4. ? and e both decrease

Answer 1

Option d.

If the good is produced, then the citizen gets an arbitrary utility u(n) = n. Further the government employee exerts an effort with the Probability e. If the utility of the good to the individual decreases then, effort exerted by govt. employee will decrease. Therefore The equilibrium decreases because the equilibrium e is decreasing in u.

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Option c.

A common-pool resource such as a fishing area is a rival and non excludable good. It is rival because if individuals utilizes more resources for themselves it reduces the amount of resources available for others as it depletes resource base. Further it is non excludable because every person has right to use the resource by virtue and nobody can be excluded from consuming it.

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Option a.

A private good is a rival and excludable good as simultaneous consumption of good by two or more independent households is not possible. Further since private good is obtained by making payment ,therefore it excludes households which cannot afford it.

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option b.

If p is a function of n, it means that the government employee will be punished by n amount if it does not produce the good and is caught by the monitor.Also utility from the good is constant at 10, Therefore it is a non rival good.

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Option c.

If the cost of monitoring increases, then the citizen who is a monitor will be more successful in catching the govt. employee. Therefore in order to prevent being caught and paying a fine of n, the govt. employee will exert effort. So both m and e will increase.