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Homework 8
1.
Suppose that the demand for broccoli is given by:
Q
D
 1000  5P where Q is the quantity per
year measured in hundreds of bushel and P is price in dollars per hundred bushels.
The long run
supply curve for broccoli is given by: Q
S
= 4P  80.
a)
Show that the equilibrium quantity here is Q = 400.
At this output what is the
equilibrium price?
How much in total is spent on broccoli?
What is the consumer
surplus at this equilibrium?
What is the producer surplus at this equilibrium?
b)
How much in total consumer and producer surplus would be lost if Q = 300 instead of
400?
c)
Show the allocation of the loss of total consumer and producer surplus between suppliers
and demanders described in part b depends on the price at which broccoli is sold.
How
would the loss be shared if P = 140?
What if P = 95?
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What would the total loss of consumer and producer surplus be if Q = 450 rather than Q
= 400?
Show that the size of this total loss also is independent at of the price at which
the broccoli is sold. Graph your results.
2.
Suppose that the current market price of VCR's is $300, the average consumer has disposable
income of $30,000 and the price of laser disk players ( a substitute for VCR's) is $500.
Under
these conditions the annual US demand for VCR's is 5 million per year.
Statistical studies have
shown that for this product the own price elasticity of demand is
e
Q,P
= 1.3
, the income elasticity
of demand is
e
Q,I
=1.7
and the cross price elasticity of demand is
e
Q,P'
= .8
where P' is the price of
laser disk players.
Use this information to predict the annual number of VCR's sold under the
following conditions:
a)
Increasing competition from Korea causes VCR prices to fall to $270 with I and P'
unchanged.
b)
Income and tax reductions raise average disposable income to $31,500 with P and P'
unchanged.
c)
Technical improvements in laser disk players cause their price to fall to $400 with P and I
unchanged.
d)
All of the events above simultaneously.
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View Full Document 3. Consider a market composed of 8 buyers and 8 sellers.
Each of the 8 sellers has one unit of the
good to sell and each of the buyers wants to buy exactly one unit of the good. The reservation
prices of the buyers and the costs of production of each of the suppliers are given in the following
table;
Buyer
Reservation Price
Seller
Cost of
1 Unit
Alice
10
Alex
2
Blanche
9
Bob
3
Cary
8
Charles
4
Donna
7
David
5
Edwina
6
Edgar
6
Fanny
5
Fred
7
Georgia
4
Glenn
8
Harriet
3
Howard
9
a)
Assume that both buyers and sellers are perfectly competitive. What is the market
clearing price? What is the total surplus associated with the market clearing price and
quantity?
b)
Match each buyer with a seller such that each can gain by trading with the other (for
example a buyer with a reservation value of 4 can be matched with a seller with a cost of
3 and each could gain by trading with the other). What would be the total surplus
generated by this matching of every buyer and seller?
Compare your answer with (a).
c)
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This note was uploaded on 02/10/2010 for the course IEOR 3600 taught by Professor Chudnovsky during the Winter '09 term at Columbia.
 Winter '09
 chudnovsky

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