Download PUBF 303 Assignment 3

PUBF 303
Assignment 3
Due date: 16 December 2016 (time:9:45)
Please bring your homework before Friday lecture starting time(9:45).I will
solve the assignment in the lecture. If you will not come to class, send your
homework through email before 9:45 to me (zbcevik(at)ybu.edu.tr) or Songul
Kahya
1. Consider a 3 person 2 good economy where there is a private good x and a public good
g. Initially there is no public good in the economy but each unit of the public good can
be produced using 10 units of private good. That is, the cost function is C(g) = 10g.
Utility functions of the agents are as follows:
√
u1 (x1 , g) = log(g) + 2x1 , u2 (x2 , g) = log( g) + x2 , u3 (x3 , g) = log(2g) + 4x3
What is the efficient public good provision level in the economy?
2. Suppose 10 people each have the demand Q = 20 − 4P for streetlights, and 5 people
have the demand Q = 18 − 2P for streetlights.The cost of building each streetlight is 3.
If it is impossible to purchase a fractional number of streetlights, how many streetlights
are socially optimal?
3. Andrew, Beth, and Cathy live in Lindhville. Andrews demand for bike paths, a public
good, is given by Q = 12 − 2P . Beths demand is Q = 18 − P , and Cathys is Q =
8 − P/3.The marginal cost of building a bike path is M C = 21.The town gov- ernment
decides to use the following procedure for deciding how many paths to build. It asks
each resident how many paths they want, and it builds the largest number asked for by
any resident.To pay for these paths, it then taxes Andrew, Beth, and Cathy the prices
a, b, and c per path, respectively, where a + b + c = MC. (The residents know these
tax rates before stating how many paths they want.)
(a) If the taxes are set so that each resident shares the cost evenly (a = b = c), how
many paths will get built?
(b) Show that the government can achieve the social optimum by setting the correct
tax prices a, b, and c. What prices should it set?
4. Consider an economy with three types of individuals, differing only with respect to their
preferences for monuments. Individuals of the first type get a fixed benefit of 100 from
the mere existence of monuments, whatever their number. Individuals of the second and
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third type get benefits according to:
B2 = 200 + 30M − 1.5M 2
B3 = 150 + 90M − 4.5M 2
where M denotes the number of monuments in the city. Assume that there are 50 people
of each type. Monuments cost $3,600 each to build. How many monuments should be
built?
5. Taxes are compulsory, yet communities often vote to increase taxes on themselves to
pay for public goods. Under what circumstances would a voter be better off with more
government spending, even with accompanying higher local taxes? You may recall Pareto
efficiency to explain your answer.
6. The following table shows how the marginal benefit of a service varies for four consumers:
Marginal Benefit (in dollars)
Quantity
Alice
Ben
Carolyn
Don
1
1000
800
600
400
2
800
600
400
200
3
600
400
200
100
4
400
200
100
50
(a) Suppose the service is a pure private good and is sold in a competitive market with
the only buyers being the four people whose marginal benefits are shown in the
table. If the market price of the product is $400, what is the quantity demanded?
(b) Suppose the service is a pure public good with the only consumers being the four
people whose marginal benefits are shown in the table. What is the marginal social
benefit of two units of the service?
(c) If the marginal social cost of the good is $2,000, what is the efficient output assuming
that it is a pure private good?
(d) If the marginal social cost of the good is $2,000, what is the efficient output assuming
it is a pure public good?
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