homework_assignmentPF2008_II_answers

homework_assignmentPF2008_II_answers - ISM Public finance...

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Unformatted text preview: ISM Public finance 2008 Homework assignment #2 Answers 1 20 points The supply of newspapers is perfectly elastic at a price of $0.75. Sketch the supply and demand graph below and calculate the equilibrium number of newspapers demanded by consumers in this market assuming the quantity demanded is given by the function: 
 
 
 
 
 QD
=
864,000
–
512,000P
 
 Suppose that a 20 percent tax is imposed on newspapers, causing the after-tax price to increase to $0.9. Show the effect of this tax in your graph (label the new supply line S’) and calculate the excess burden resulting from the tax. Calculate the price elasticity of demand coefficient at the initial equilibrium point using the formula εD = |(ΔQD/ΔP)(P/QD)| and use this value to verify that the excess burden can also be calculated using the formula EB = ½εD(PQ)t 
 
 Please
note,
that
you
can
get
the
same
result
by
moving
demand
curve,
however
 you
can’t
move
both
the
curves
together.
 
 
 
 
 
 
 
 2.

 20
points
 
 a)
 Knowing
 the
 formula
 of
 excess
 burden
 S=1/2Pxgxt2xε
 you
 can
 conclude
 that
 if
 elasticity
increases,
deadweight
loss
increases.
The
result
might
seem
ambiguos
if
 we
do
not
know
relative
elasticities
of
supply
and
demand,
but
if
consumers
bear
all
 the
 tax
 burden,
 it
 is
 obvious,
 that
 supply
 is
 perfectly
 elastic,
 thus
 lim
 1/η→0.
 Therefore,
 we
 have
 no
 ambiguity
 in
 this:
 DWL
 increases
 as
 demand
 elasticity
 is
 increasing.
 
 b)
Simple:
equate
demand
and
supply.
You
will
get:
 215 1075 Pe = ;Qe = − 15
 5 +δ 5 +δ 
 c)
If
new
quantity
tax
is
implemented
on
producers,
we
will
get
two
prices:
one
for
 producers
and
another
one
for
consumers.

 € 
 Qd=200­δP;
Qs=5(P­3)­15
 
 Equilibrium:
 
 200­δP=5(P­3)­15;

 
 230 5 * 230 P= ;Q = − 30 
 5 +δ 5 +δ 
 Consumers
 pay:
 PC=230/(5+δ);
 Producers
 receive:
 PP=(230/(5+δ))­3.
 Burden
 sharing
 depends
 on
 δ.
 If
 δ
 is
 high
 (demand
 is
 elastic),
 final
 price
 goes
 down,
 as
 € elasticity
 lowers
 denominator.
 Thus,
 higher
 δ
 lowers
 consumers
 tax
 burden
 and
 increases
producers
burden.
 
 5 * 230 d)
Qe= − 30 = 113, 75 ;
revenue:
113,75*3=341,25;
DWL=527;

 5+3 DWL =1,54,
thus
DWL
is
higher
than
tax
revenue
in
our
case.
 Tax revenue 
 € e)
 Since
 DWL=1/2Pxgxt2xε,
 it
 will
 increase
 geometrically,
 however
 tax
 revenue
 raised
will
increase
only
aritmetically.
Thus
if
t
will
increase,
this
ratio
will
increase
 € even
more.
 
 
 
 
 
 
 
 
 
 
 3.

 
 30
points
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 For the L types, this is 
 
 
 
 
 
 
 pL √ √ y − xL + (1 − pL ) y √ √ = 0.8 20 − 3 + 0.2 20 = 4.19. For the E types, this is pE √ √ y − xE + (1 − pE ) y √ √ = 0.4 20 − 2 + 0.6 20 = 4.38. 
 (b) Suppose there exists one insurance company that charges actuarially fair prices for coverage levels bE and bL . It can tell whether each customer spent their lives exercising. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 (i) What is the price of insurance coverage for each plan in terms of requested coverage levels bL and bE ? Suppose that type i ∈ {E, L} buys coverage bi . Then actuarially fair price means that price mi is set such that the insurance company makes no profits: pi (mi bi − bi ) + (1 − pi )(mi bi ) = 0. (1) What (1) means is that in the bad “state,” the insurance company gets the price of coverage but has to pay for the drug benefits. In the good “state,” the insurance company gets only the price of coverage. These are the firms expected profits, which must be zero by the definition of actuarially far. Then (1) implies that price is mi = pi . (ii) How much insurance does each type of elderly person buy? Show your work. Next, let’s set up the expected utility maximization problems for each type. max pi · u(y + bi − pi bi − xi ) + (1 − pi ) · u(y − pi bi ) bi 2 (2) 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 4.

 30
points
 
 This
was
derived
in
our
lectures.
See
lecture
notes.
 ...
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This note was uploaded on 12/02/2009 for the course ECONOMICS PF taught by Professor Leika during the Spring '09 term at Cambridge.

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