ECON 303
Fall 2004
Exam 1
Dr. Cary Deck
This exam consists of 4 written problems worth 25 points each. Your exam should
contain 5 pages. Please write your name on the top of each page. Answer each question
as best you can. Where appropriate you must show work in order to receive full credit.
The exam is closed book. If you have any questions please raise your hand and someone
will come to you. There is no talking allowed during the exam. The use of electronic
devices other than approved calculators is prohibited. You have one hour and twenty
minutes to complete this exam. Exams will not be accepted after the end of the exam has
been announced.
Name:___________
Score:____________
Q1: The market for “Go Hogs” shirts is competitive and demand is given by P=100-Q.
Define the term choke price and calculate it for this demand curve. (2 points each)
The choke price is the price where quantity demanded falls to zero. In this case, q=0
then P=100-0=100.
If supply is given by P=10+2Q, what will be the price in this market and what quantity
will people trade? (3 points each)
Setting supply and demand equal we get 10+2Q=100-Q or 3Q=90 or Q=30. Plugging
this into supply or demand we find that the equilibrium price is 70.
Calculate the elasticity of demand at the market price. Is demand elastic or inelastic at
this price? (4 points)
Elasticity is given by dq/dp * P/Q. Rearranging demand we get that Q=100-P so dq/dp
= -1. Therefore, elasticity is -1*70/30= -2.33. Since this is less than -1, demand is
elastic.
What would happen to the price and quantity of “Go Hogs” shirts if demand were to shift
to the right? (4 points, you must sketch a graph to receive credit.)
The price and quantity would both increase. See Figure 1.4 on page 19 in text.
Give three examples of things that would shift demand for “Go Hogs” shirts to the right.
Explain. (3 points)
1) An increase in the number of buyers (as would happen if the team starts winning).
2) A price increase for a substitute (like another shirt).
3) An increase in income if the shirts are a normal good.
Suppose that one of the three things you listed comes true and that nothing happens to
supply. If you observe a price is 90 in the market and an analyst tells you that the
elasticity of demand is -4.5, find the equation for the new demand curve assuming it is
linear. (4 points)
Since nothing happened to supply, we know that if the market price is 90 then the
quantity is 40 (solve 10+2Q=90). Since elasticity = -4.5 = dq/dp * P/Q we know that
dq/dp = -4.5*40/90 = -2. Assuming a linear demand (Q=A+BP) we know that dq/dp=B.
Thus we have Q=A-2P. Using the fact that this demand curve must have the point P=90,
Q=40, it must be that 40=A-2(90) or A=220. Thus the linear demand is Q=220-2P.
Q2: The market for hog hats is characterized by D: P=250-3Q and S: P=50+2Q.
Define consumer surplus and calculate it in this market. (4 points)
Consumer surplus is the gain that buyers receive from trading. It is the area below
demand and above price. In this market, the equilibrium price is 130 and the equilibrium
quantity is 40. Therefore, CS=.5*120*40=$2400.
In order to raise money the University of Arkansas, which holds the copyright on
officially licensed apparel, is considering a $5 fee (tax) on the sale of each hog hat to pay
for improved parking on campus. What is the total amount the University will collect
from this fee (tax)? (4 points). How much of this total amount will consumers pay? (3
points) You must sketch a graph to receive full credit.
First we need to determine the equation for the new effective supply curve. The old
supply curve is P=50+2Q the tax is 5 so the effective supply is P=55+2Q. Setting this
equal to demand gives a new market quantity of 39. Since the tax is $5 per unit of 39
units the total tax collected is 5*39=195. Buyers used to pay 130, but now pay 133 (this
can be found by plugging Q=39 into the demand curve). Hence CTI=3*39=117. See
Figure 10.3 on page 415.
Would consumers as a group be willing to simply pay the University $118 more for
parking and not have the $5 fee on hog hats? Why? (4 points – Hint: consider the
welfare of buyers with the tax and with the $118 payment but no tax)
Yes. With the tax the reduction in CS is $118.5, so they would rather pay $118. They pay
$117 in tax but there is a deadweight loss too.
Suppose the student government decided that this fee was harmful to students and
lobbied the University to not impose the fee and instead place a price ceiling of $100 on
the market so that students can afford to buy hog hats. What will be the effect of this
policy? Specifically calculate the change in Consumer Surplus and Producer Surplus and
the Dead Weight Loss that would result from the price ceiling. (10 points) You must
sketch a graph to receive full credit.
With the price ceiling, the quantity traded will be 25. Originally PS = .5*80*40=1600.
Now the PS=.5*50*25=625, so PS has fallen by $975. Originally CS =
.5*120*40=2400. With the price ceiling CS= (175-100)*25+.5*(250-175)*25=$2812.5
so CS increases $412.5. The DWL is .5*(175-100)*(40-25)=$562.5. See Figure 10.7 on
page 427.
Q3: Assume that the domestic market for DVDs is competitive with demand given by
P=100-Q and domestic supply given by P=Q. If the world price is $20 and there are no
restrictions on trade how many units will this country import? (4 points) What will be
the total domestic surplus, that is CS + PS? (4 points) You must sketch a graph to
receive full credit.
At a price of 20, domestic supply is 20 and domestic demand is 80. Therefore, 80-20=60
units imported. Total Surplus = CS + PS =.5*80*80 +.5*20*20=$3400. See Figure
10.18 on page 451.
Suppose domestic producers lobby the government to place an import quota of 20 units in
the market because foreign countries do not monitor pirating of DVDs. They claim that
the world price is low because owners of the intellectual property do not receive royalties
for their work on the foreign made DVDs. Under such a policy, how many units will be
imported, what price will domestic consumers pay, and what dead weight loss will be
created? (3 points each) You must sketch a graph to receive full credit. See Figure 10.20
on page 454.
The first step is to determine the equation for the effective supply. Q in market = Q made
domestically + quota. So we have Q=P+20. Setting this equal to demand gives 100Q=Q-20 or Q=60. From demand we have P=100-60=40. So far we know that imports
= 20 and the price consumers pay = 40. To calculate DWL we need to look that the loss
for unit that are no longer bought [=.5*(40-20)*(80-60)=200] and the loss due to units
being produce at a domestic cost greater than the world price [.5*(40-20)*(40-20)=200].
Thus DWL= $400.
With the quota in place, what would happen to the price of DVDs if the price of DVD
players increased? Why (2 points). Given your answer, what would be true about the
cross price elasticity of DVDs and DVD players? (2 points)
Since DVDs and DVD players are compliments, if the price of players increases then the
demand for DVDs shifts to the left and the price of DVDs will fall. For compliments, the
cross price elasticity is negative.
Define income elasticity. (2 points) If DVDs are normal goods what would be true about
the income elasticity of DVDs? (2 points)
Income elasticity = % change in quantity demanded / % change in price. For normal
goods, income elasticity is positive.
Q4: Math Problems
Find the roots of the following equation: q2-12q+35=0. (4 points)
Using the quadratic formula, which is (-b+(b2-4ac).5)/2a, we get q=5 and q=7 as
solutions.
Sketch a graph of x2y=9 and x2y=16. (2 points each) You should have one graph with
both curves plotted on it.
NOTE: (3,0) is not on x2y=9.
Using partial derivatives find the equation for the slope of the following curves. (4 points
each)
x2y=9
dy/dx = -df/dx / df/dy = -2xy/x = -2y/x
xy+3x+2y+7
dy/dx = -df/dx / df/dy = -(y+3)/ (x+2)
Simplify the following terms. (3 points each)
(x2/y3)2(x-2/y2)-2
= (x4/y6)(x4y4) = (x8/y2)
(x2/3y3/2)/(x-1/3y1/2)
= (x2/3+1/3y3/2-1/2)= xy
If 25=5k1/2 then k equals
__25___. (3 points)
To find this answer, divide both sides by 5 and then square both sides.