Download Answer Key to Exam 1

ECON 303
Spring 2005
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 “HOGS” ties is competitive and demand is given by P=210-Q. If
supply is given by P=2Q, what will be the price in this market and what quantity will
people trade? (3 points each)
To find equilibrium set 210-Q=2Q. Solving this gives 210=3Q or Q=70, so 70 units will
trade and the price will be 210-70=140.
Suppose that a fraternity requires all of its pledges to wear a new pair of “HOGS” ties
every day. Draw a graph of this situation indicating what will happen to the market price
and quantity. (5 points)
This will cause demand to shift to the right resulting in a higher price and a higher
quantity. See figure on page 35.
Define producer surplus. (2 points).
Producer surplus is the gains from trade received by sellers. It is the difference between
what sellers are paid (the price) and their costs (the supply curve) for the units sold.
What will happen to producer surplus when the fraternity mandates that its pledges must
wear “HOGS” ties? Explain (2 points)
Since sellers will sell more units at a higher price the producer surplus will increase.
List three things that might shift the supply curve for “HOGS” ties to the left. (1 point
each)
1) an increase in the price of an input
2) a decrease in the number of sellers
3) a deterioration in technology
Suppose that the independent students feel that the price of “HOGS” ties is too high and
petition the university to institute an effective price ceiling in this market. What does it
mean for a price ceiling to be effective? (2 points). How would such a policy impact
consumers, producers, and society? (5 points) Assume that the fraternity no longer
requires pledges to wear “HOGS” ties.
For the price ceiling to be effective, it must be that it prevents prices from going as high
as they would without the policy. That is Pc <Pe. Holding the prices low will hurt
suppliers. The consumers who still buy will be better off, but some consumers will no
longer be able to find units and they will be worse off. Since fewer units will trade there
will be a dead weight loss meaning society is worse off.
Q2: The market for Valentine’s Day chocolate in heart shaped boxes is characterized by
D: P = 500-2Q and S: P = 50+3Q. To raise money for a battered women’s shelter, the
city is planning to impose an excise tax of $20 on boxes of chocolate. How much tax
will be collected, and how will this tax be split among the consumers and producers? (12
points).
Without the tax, the market price is such that 500-2Q=50+3Q. This gives 450=5Q or
Q=90. Thus P=320. With the excise tax the effective supply would be P=50+3Q+20.
Thus the quantity with the tax would be where 500-2Q=70+3Q or 430=5Q or Q=86.
The price consumers are paying is P=500-2(86)= 328. Sellers are receiving 32820=308. The total tax collected is 20*86=1720. Consumer tax incidence is (328320)*86=688 and producer tax incidence is (320-308)*86 =1032 which is equal to 1720688 as CTI + PTI = total taxes.
What do you think would true about the cross price elasticity of Valentine’s Day cards
and boxes of chocolate? What do you think would be true about the income elasticity of
Valentine’s Day cards? Explain (2 points each)
I would guess that these are substitutes so the cross price elasticity would be positive. (If
you think they are compliments than you should have said the cross price elasticity is
negative). I would think the income elasticity would be positive but small. As you earn
more you might get a nicer card, but I would not think you would buy more cards.
Calculate the elasticity of demand for boxes of chocolate at the original equilibrium price.
(2 points) Is demand elastic or inelastic at this price? (2 points)
Elasticity of demand is dQ/dP * P/Q. From Demand we know that Q= 250-P/2 so dQ/dP
= -1/2. Since P= 320 and Q=90, elasticity of demand is (-1/2)*(320/90)= -1.77. Demand
is elastic at this point as this number is less than -1.
Speaking of elasticity, studies have found that teens have an elastic demand for
cigarettes, while adults have an inelastic demand. Using this information, draw a
diagram to show how an excise tax on tobacco would impact each group. (5 points)
When demand is inelastic, as with
adults, an excise tax is not going to have
much impact on behavior (quantity of
cigarettes bought). But for teens, who
do have an elastic demand, the excise
tax will greatly reduce the number of
cigarettes bought.
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 $30 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 the world price of 30 people want to buy Qd=70 units (30=100-Q) and people want to
sell Qs=30 units (30=Q). The number of imports will be 72-30=40. The choke price is
100, so CS = .5* (100-30)*70 = $2450. Producer surplus is .5*(30-0)*30=$450.
Therefore, total surplus is $2900. See figure on page 451.
Suppose domestic producers lobby the government to place a tariff of $10 on imported
units 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 new graph to receive full credit.
With the tariff, domestic consumers would have to pay $40 to import units (the world
price of 30 plus the tariff of 10). At this price they would want to buy 60 units. Domestic
sellers would be willing to supply 40 units, so now 60-40 =20 units would need to be
imported. Dead weight loss will have two parts. One part is .5*10*(40-30)=$50. The
second part is .5*10*(70-60)=$50. So total DWL = $100. See figure on page 453.
In this case, dead weight loss has two parts. Explain why each part represents a loss to
society (2 points each)
One part [the .5*10*(40-30)] is due to the fact that units 31 through 40 are being
produced domestically at a cost greater than the world price. Paying a higher costs than
had to be paid reduces the gains from trade. The second part is due to the fact that wit
the tariff units 61 through 71 no longer trade and thus those gains from trade are not
realized.
How would this impact the market for movies on VCR tapes? (2 points)
Since VCR tapes and DVDs are substitutes for each other, an increase in the price of
DVDs would lead to an increase in the demand for VCR tapes resulting in a higher
quantity of tapes trading at a higher price.
Q4: Math Problems
Find the roots of the following equation: q2-11q+28=0. (4 points)
Using the quadratic equation the roots are {–(-11)+[(-11)2-4(1)(28] 1/2}/(2*1)
= {11+(121-112)1/2}/2 = (11+3)/2. Thus the roots are 4 and 7.
Sketch a graph of xy=9 and xy=16. (2 points each) You should have one graph with both
curves plotted on it.
See figure on page 93. That figure is for (xy)1/2, so the curve for (xy)1/2=3 is the same as
xy=9 and the curve for (xy)1/2=4 is the same as xy=16
Using partial derivatives find the equation for the slope of the following curves.
(4 points each)
x2y3=1000
dy/dx = - (df/dx)/(df/dy) = - (2xy3)/(3x2y2) = - 2y / 3x
xy2+3x2+2y=7
dy/dx = - (df/dx)/(df/dy) = -(y2+6x)/(2xy+2)
Simplify (x0.3y1.4)/(x1.3y-0.6)
(3 points)
(x0.3y1.4)/(x1.3y-0.6) = x0.3y1.4x -1.3y0.6 = x0.3 - 1.3 y1.4+0.6 = x-1y2 = y2/x.
Find the equation for the line that contains the points (0,10) and (5,0). (3 points)
The slope of this line is (10-0)/(0-5) so the slope is -2. Using the point slope formula for
a line we can write y-10 = -2(x-0) or y = -2x+10.
What is the slope of the line 20=2x+4y? (3 points)
Rewriting the line in slope y-int form gives y = -0.5x+5. So the slope is -0.5.