need economic major to modify the answer in 3 hour

(a) Common property: internet

(b) A club good: private park.

(c) A public good: defense

(d) good that is a public good when there are only few consumers, but becomes congested with too many consumers: air

Question 2.

(a) Yes, they will have a trade. Because when there is no trade, Albert can only consume x1 and Betty can only consume x2, for the utility function, in this situation, their utility will be 0. So trade can help them to increase their utility.

(b)

(c) MRS12=Ux1/Ux2=x2/x1

x1^2=x2^2

Hence, when equilibrium,

X1=X2=200

So, A consumes (200x1,200x2) B consumes (200x1,200x2)

(d) Yes, because B cannot store the nuts, so in the winter, she will have nothing and her utility will be 0. So she needs to trade with A.

Question 3.

(a) To compute the contract curve, apply the Samuelson rule:

MRSA +MRSB =dUA/dg/(dUA/dXA)+ dUB/dg/(dUB/dXB)=1

XA/2g + 2XB/g =1

By the feasibility constraint, xA + xB + g = wA + wB=3

XA+XB=3-g

XA+4XB=2g

The Kolm triangle is composed with the two functions above.

And the endowment point is (4-2g,g-1)

(b) The contract curve is 1/2XA+XB=1

(c) To compute the Nash equilibrium, let sA and sB denote the consumers' contributions to the public good, so that g = sA + sB. Then

UA=(2-SA)^2*(SA+SB)

dUA /dSA=(2-SA)*(2-3SA-2SB)=0

For UB, it is similar.

UB=(1-SB)(SA+SB)^2

(SA+SB)(2-SA-3SB)=0

SB=4/7 SA=2/7

The total amount of public good provided is therefore sA+Sb=6/7

(d) The Nash equilibrium allocation in the Kolm triangle is

XA= 6/7 XB=6/7 g=6/7

It is efficient.

(e) If B’s utility function is the same as A.

XA+XB=2g

XA+XB=3-g

XA+XB=3/2+g/2

SA=SB=2/5

g=4/5

So there will not be equilibrium when A and B has the equal utility function. B can act as he has the same utility function as A, since the public goods take higher percentage in his function.

Question 4.

(a) E(valuation)=0*1/3*1/3+1*2/3*2/3+2(1/3*2/3*1/2)=2/3

It is efficient to provide the public good.

(b)

2/9*1(1-2/3)+4/9*1*(1-1/3)>=1/9*0*(1-0)+2/9*q*(1-0)

q<=5/3

So setting q = 5/3 is the best we can do.

(c) That is, the probability of outcome (vA = 0; vB = 1) where the inefficiency occurs

(ie.2/9) times the probability that the good is not provided in this case (i.e 1 - q)

times the value that provision would create (i.e. 0 + 1- 2/3). How big of a loss is

that? To answer this, compute the expected overall value created by e_cient public

good provision

1/9*0+2/9(1-2/3)+2/9(1-2/3)+4/9(2-2/3)=20/27

(d)

2/9*1(1-2/3)+4/9*1*(1-k)>=1/9*0*(1-0)+2/9*1*(1-0)

k<=2/3

So setting k =2/3 is the best we can do.

(e)No, because in this condition, nobody will want to buy the public good because they may get loss in this process. In this condition, there will be a free ride problem.