ECOn 302 Homework Problems

1. (14
points) Suppose a public referendum is being held on whether or not to
levy a tax on cigarettes. Currently, the
supply of cigarettes is given by Qs = -900 + 200P. You estimate the demand for cigarettes to be
Qd = 1200 – 50P.

You are asked to evaluate the likely effects of a
tax on cigarettes equal to $2 per pack of cigarettes. Specifically, you are to file a report which
predicts by how much this will reduce the amount of cigarettes sold. You are also asked to estimate the proportion
of the tax that will be paid by the cigarette companies (sellers), and the
proportion of the tax that will be paid by the smokers (consumers) of
cigarettes.

To do this, you will first need to calculate the
current price and quantity of cigarettes sold.

a) (2 points) What is the equilibrium price and
quantity of cigarettes?

Next you know from your economics class that you
will need to know the price elasticity of demand and the price elasticity of
supply of cigarettes. (Note: for parts b-e, please leave your answers in the
form of a fraction.)

b) (2 points) What is the price elasticity of
demand for cigarettes at the equilibrium price?
c) (2 points) What is the price elasticity of
supply of cigarettes at the equilibrium price?
Using your answers to b) and c), you are now able
to determine what proportion of the tax will be paid by buyers, and what
proportion of the tax will be paid by sellers.

d) (2 points) What proportion of the tax will be
paid by sellers?

e) (2
points) What price will buyers pay after the tax is imposed?
f) (2
points) What quantity of cigarettes will be sold after the tax?

g) (2 points) the deadweight loss that results from
the tax
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Suppose you have
$800 to spend on either concert tickets or CDs. Concert tickets cost $50 each,
and CDs cost $20 each. Let T = the number of Concert Tickets, and C = the
number of CDs.
a) Write the equation of the consumer’s budget
constraint.
b)Using a graph,
illustrate the budget constraint faced by this consumer. Be sure to label your
graph carefully indicating the appropriate values on the axes. Please put the
number of concert tickets (T) on the vertical axis and the number of CDs (C) on
the horizontal axis. What is the value of the marginal rate of transformation
between concert tickets and CDs?

3) Suppose hamburger is an inferior
good.Using a graph , illustrate what happens in the market for hamburger if
consumer’s income rises. Be sure to label your graph carefully and accurately ,
and clearly indicate what happens to the equilibrium price and quantity of
hamburger.

.gif”>4)– Suppose a
consumer’s preferences are represented by the utility functionsU(X,Y) = x*y
Therefore – MU x = Y -MU y = X

Also suppose the consumer has $120 to spend ( M=
$120) Py=1, and that they spend all of their money on goods X and Y. Also,
assumer the consumer maximizes their utitlity subject to theit budget
constraint. Completely the following table