ECON7030 competitive equilibrium price
competitive equilibrium price
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ECON7030
Problem Set 1: Answer all questions (25 Marks)
1. (4 marks) A market has supply () = ඥ and demand () = ଽ
√
(a) (2 marks) Find the competitive equilibrium price and quantity.
(b) (2 marks) Draw the supply and demand curves and label the area that represents
producer surplus. You do not need to calculate it.
2. (4 marks) Mary has the following preferences over the alternatives {, , , }:
≿= {(, ), (, ), (, ), (, ), (, ), (, ), (, ), (, ), (, ), (, )}
(a) (2 marks) Argue either that these preferences are complete or that they are not. State
which one you are arguing for and give an argument.
(b) (2marks) Argue either that these preferences are transitive or that they are not. State
which one you are arguing for and give an argument.
3. (4 marks) Consider a set of alternatives and a person that is indifferent between all
alternatives. Argue either that these preferences are complete and transitive or that they
are not. You must state which case your will argue and give an argument for it.
4. (7 marks) Mark has faced the following choice sets (left column) and revealed the following
choice sets (middle column):
() Reveals
{, , } {, , }
{, , } {, }
{, , } {, , }
{, } {, }
{, } {}
(a) (2.5 marks) What do these choices reveal (assuming the preferences are complete and
transitive)? Fill out the 3rd column to show what they reveal.
(b) (2.5 marks) Do these choices satisfy the weak axiom? Argue for or against and give an
argument.
(c) (2 marks) Argue either (i) there is a utility representation of these preferences over
{, , , , } or (i) these is no utility representation for these preferences.
5. (6 marks) Consider the following utility functions over bundles of two goods (, ) where
denotes the quantity of the first good and denotes the quantity of the second and each
can take on any non-negative real number. For each pair of utility functions, determine if
they represent the same preferences. You must give an argument in favour or against them
representing the same preferences:
(a) (2 marks) (, ) = + ଶ and (, ) = √ +
(b) (2 marks) (, ) = + and (, ) = ଶ + ( + 2) − 1
(c) (2 marks) (, ) = and (, ) = ଶ