Download Exam 1 Spring 2004

ECON 303
Spring 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 hog hats is competitive and demand is given by P=75-Q while
supply is given by P=15+2Q. What are the equilibrium price and quantity in this market?
(4 points)
Setting Supply and Demand equal we get 75-Q=15+2Q or Q=20. Thus P=75-20=55.
Calculate the elasticity of demand at a price of 50. (2 points). Give an economic
interpretation to your answer. (2 points) Is demand elastic, unit elastic or inelastic at this
price? (1 point)
ed=dq/dp*(P/Q). At P=50 the demand curve indicates that 50=75-Q or Q=25. To find
dq/dp we first need to write the demand curve where q is a function of p. P=75-Q so
Q=75-P and dq/dp = -1. Therefore, ed = -1*(50/25) = -2.
To enable more students to wear hog hats to games, the UA decides to give hog hat
producers a subsidy of $9 per unit. What price will consumer’s pay and how many hog
hats will they buy? (2 points each) How much will the UA spend on the subsidy? (3
points) What will be the change in producer surplus? (5 points.)
With the subsidy, the sellers can accept 9 less than on the price so still get the total
amount per unit they want. Thus, supply can be rewritten as P=15+2Q-9 or P=6+2Q.
Setting this new equation equal to demand gives 6+2Q=75-Q. So the new quantity will
be 23 and people will pay 52. Sellers will receive 52+9=61. The UA is paying $9 on
each unit and 23 units are trading so the UA will spend 9*23=$207.
The change is PS has two parts. First, the 20 units that would trade without the subsidy
each bring in an extra 61-55=$6. Second 3 additional units now trade with the subsidy.
Therefore, the change in PS=20*6 +.5*6*3=120+9=129.
Suppose that next year, the Hogs start the basketball season with 16 straight wins. Also,
suppose that new technology allows hog hats to be produced using a cheaper plastic.
What will happen to the price and quantity of hog hats? (2 points) Explain (2 points)
The demand will shift to the right as the team is winning. The supply will also shift to the
right as the price of an input has fallen. This will cause the quantity to increase but the
impact on price is indeterminate.
Q2: Because school funding is considered to be inadequate, the legislature is planning to
raise additional tax revenue. There are two proposals under consideration. The first is an
import tariff of $4 on salsa. The second is a $5 excise tax on poultry.
Demand in the salsa market is given by P=400-4Q while supply is given by P=4Q. The
price in the world market is 28. How much revenue would the $4 tariff generate? How
much dead weight loss would it cause? (4 points each)
At a price of 28 domestic quantity demanded is 28=400-4Q or Q=93. At this price the
quantity supplied is 28=4Q or Q=7. The number of imports is 93-7=86. With a $4 tariff
imported units would actually cost 28+4=32. At this price domestic quantity demanded
is 32=400-4Q or Q=92 and domestic quantity supplied is 32=4Q or Q=8. So with the
tariff imports = 92-8 = 84. The taxes collected =4*84=336. The DWL has two parts.
First 1 less unit is bought so that value is lost. Second, 1 additional unit is produced
domestically and it has a cost greater than the 28 of the world market. So
DWL=.5*4*1+.5*4*1=4.
Demand in the poultry market is given by 4P=250-Q while supply is given by P=25+Q.
How much tax revenue would the $5 tax collect? How much deadweight loss would it
cause? (4 points each)
Without the tax the market price is 55 and the market quantity is 30. With the tax, the
supply curve becomes P=25+Q+5 or P=30+Q. Solving this we find that the quantity
with the tax will be 26. The tax collection will be 5*26=130. The DWL = .5 * tax *
quantity reduction= .5*5*(30-26)=10.
By how much would the poultry tax reduce consumer surplus + producer surplus? (2
points) An alternative to the excise tax is for the buyers and sellers to simply pay the
government money. How much money would buyers and sellers as a group be willing to
pay instead of having the tax? (1 point)
The loss in CS+PS =tax collection +DWL =130+10=140. The buyers and sellers would
be willing to pay 140, what they loose if the tax goes into effect.
An economist estimated the elasticity of demand for the following products:
-1.52 for airline travel, -0.65 for poultry, and -0.120 for roasted coffee. For which good,
would an excise tax have the smallest change in the quantity traded? Why? (2 points)
Roasted coffee as it is the most inelastic.
Define cross price elasticity. (2 points) What do you think is the sign of the cross price
elasticity between chicken and beef? Based on your answer, what type of goods are beef
and chicken? (2 points)
Cross price elasticity is the % change in quantity of good x / % change in the price of
good y. The sign should be positive as the two goods are substitutes.
Q3: Define Consumer surplus (3 points).
Consumer surplus is the benefit buyers receive from trading. It is the area under demand
(value) and above price (cost).
Suppose the demand for a product is given by P=24-Q and supply is given by P=2+Q.
Calculate producer surplus and producer surplus. (2 points each)
Setting 24-Q=2+Q we find that Pe=13 and Qe=11. CS=.5*(24-13)*11=121/2=$60.5.
PS=.5*(13-2)*11=$60.5
List 3 different reasons why demand for this product might shift to the right (1 point
each)
An increase in the number of buyers.
A reduction in the price of a compliment.
An increase in income for a normal good.
List 3 different reasons why supply of this product might shift to the right (1 point each)
A technological improvement.
A reduction in the price of an input.
An increase in the number of sellers.
If a price ceiling of 18 is placed on this market, what price will consumers pay and how
many units will trade? (3 points each)
Since Pc=18>13=Pe, the price ceiling will have no impact on the market. The price will
remain 13 and the quantity will remain 11.
If a production quota of 8 units is placed on this market, what price will consumers pay,
how many units will trade, and what will be producer surplus? (2 points each)
Since Production Quota=8<Qe, this policy will limit production to 8 units. From
demand we know that consumers are willing to pay P=24-8=16 for these 8 units. PS has
two parts. The price sellers need to get to sell 8 units is $10. One part of PS is the
triangle below this price and the other part is the rectangle above this price. Producer
surplus is .5*(10-2)*8+(16-10)*8=80.
Q4: Using partial derivates, calculate the slope of the following curves. (5 points each)
f(x,y)=x2y4 +2x2+y2 at the point (1,2)
df/dx= 2xy4 +4x and df/dy is 4x2y3 +2y. The slope is –(df/dx)/(df/dy)=
- (2xy4 +4x)/(4x2y3 +2y). Plugging in (1,2) the slope is –(32+4)/(32+4) = -1.
f(x,y)=x -0.25 y0.5 at the point (16,4)
df/dx= -.25x -1.25 y0.5 and df/dy = .5x -0.25 y -0.5. The slope is –(df/dx)/(df/dy)= -(-.25x -1.25
y0.5)/(.5x -0.25 y -0.5). This reduces to (y/2x). Plugging in the point (16,4) this gives a slope
of 2.
Sketch a graph of the following equations. (3 points each) You should have a separate
graph for each equation and plot at least two points.
x2y=9
(1,9) and (3,1) are on this curve.
3x+4y=12
(0,3) and (4,0) are on this curve.
What are the slope, the x-intercept and the y-intercept of the 35=7x+10y? (2 points each)
This equation can be rewritten in slope y-int form as 35/10-7x/10=y. The slope is -7/10
and the y-int is 3.5. To find the x-int you need to plug in a y of 0 and solve for x. This
gives 35=7x or x=5.
If k=q1/3 and k=5, what is q? (3 point)
To solve for q one needs to cube both sides: k3=(q1/3)3. When raising a power to a power
you multiply the exponents, so the right hand side become q. Thus, q=53=125.