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

Payoffs are realized

1.What is the maximization problem the government employee faces? The answer is in the format max_X((Term₁)+(Term₂))

Choose X:

qn

qn, e

qe

qm

2.What is the maximization problem the government employee faces? The answer is in the format max_X((Term₁)+(Term₂))

Choose the first term (Term₁):

q-p(e)m

qp(1-e)m

q-p(1+e)m

q-pm

q-p(1-e)m

qp(e)m

qp(1+e)m

qpm

3.What is the maximization problem the government employee faces? The answer is in the format max_X((Term₁)+(Term₂))

Choose the second term (Term₂):

q-¹/₂ce²

q¹/₂ce

q-¹/₂ce

q-ce

qCe

q-pm/c

q¹/₂ce²

qPm/c

4.What effort would the government employee choose if m=0.13, c=0.15, and p=0.9? Enter numeric value to the nearest two decimal places, rounding if necessary:

5.What is the maximization problem of the monitor? The answer is in the format max_m((Term₁) + ( -¹/₂am²) + (Term₃))

Choose the first term (Term₁):

a.u(n)(1-m)

b.u(n)e

c.u(n)s

d.u(n)(1-e)

e.u(n)m

f.u(n)(1-s)

6.What is the maximization problem of the monitor? The answer is in the format max_m((Term₁) + ( -¹/₂am²) + (Term₃))

Choose the third term (Term₃):

a.ms(1-e)

b.s¹/₂ce²

c.ms(e)

d.-ms(e)

e.-¹/₂ce²

f.¹/₂ce²

g.-ms(1-e)

h.-s¹/₂ce²

7.What happens to the equilibrium effort of the government employee if the arbitrary n decreases?

a.The equilibrium increases because the equilibrium e is increasing in p

b.The equilibrium increases because the equilibrium e is decreasing in p

c.The equilibrium decreases because the equilibrium e is increasing in p

d.The equilibrium decreases because the equilibrium e is decreasing in p

e.The equilibrium decreases because the equilibrium e is decreasing in u

f.The equilibrium decreases because the equilibrium e is increasing in u

g.The equilibrium increases because the equilibrium e is decreasing in u

h.The equilibrium increases because the equilibrium e is increasing in u

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 exampleof a common-pool resource)?

a.Rival and excludable

b.Non-rival and non-excludable

c.Rival and non-excludable

d.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?

a.Rival and excludable

b.Non-rival and non-excludable

c.Rival and non-excludable

d.Non-rival and excludable

10.Recall that a rival good is a good that, cannot be consumed byanother. 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:

a.Rival

b.Non-rival

c.Excludable

11.In equilibrium when u(n)=10 and p(n)=n, how does the equilibrium level of m and e change as increases?

a. increases and e decreases

b. increases and e decreases

c. and e both increase

d. and e both decrease

12.Now consider how the equilibrium changes as n changes, and specifically compute m¹(n) and e¹(n).

What is the numerator of e¹(n) when completely simplified?

a.(c - 2ns)²

b.10c+2sc²c

c.20nc²-20scn²+sc³

d.(c+2ns)²

e.20nc² - 20scn² - sc³

f.10c - 2s²c

g.(c² + 2nsc)²

h.(c² - 2nsc)²

13.Now consider how the equilibrium changes as n changes, and specifically compute m¹(n) and e¹(n).

What is the denominator of e¹(n) when completely simplified?

a.10c-2s²c

b.(c-2ns)²

c.(c²+2nsc)²

d.(c² -2nsc)²

e.20nc² - 20scn² + sc³

f.20nc² - 20scn² - sc³

14.Now consider how the equilibrium changes as n changes, and specifically compute m¹(n) and e¹(n).

What is the numerator of m¹(n) when completely simplified?

a.(c+2ns)²

b.(c²-2ns)²

c.10c - 2s²c

d.(c -2ns)²

e.10c + 2s²c

f.20 ns² - 20scn² + sc³

g.20 nc² - 20scn² - sc³

h.(c² + 2nsc)²

15.Now consider how the equilibrium changes as n changes, and specifically compute m¹(n) and e¹(n).

What is the denominator of m¹(n) when completely simplified?

a.(c² + 2nsc)²

b.10c + 2s²c

c.20 nc² - 20scn² - sc³

d.10c - 2s²c

e.(c - 2nsc)²

f.20nc² - 20scn² - sc³

g.(c² - 2nsc)²