Download Midterm Review Answers

Midterm Review Answers
Homework Assignment 5 Answers
1.
Max enjoys windsurfing (W) and snorkeling. He obtains the following total utility
from each of these sports:
Half-hours
MUW
MUW
MUS
(per month)
TUW
MUW
PW
PW′
TUS
MUS
PS
1
2
3
4
5
6
7
8
9
60
110
150
180
200
206
211
215
218
60
50
40
30
20
6
5
4
3
6
5
4
3
2
.6
.5
.4
.3
12
10
8
6
4
1.2
2
.8
.6
20
38
53
64
70
75
79
82
84
20
18
15
11
6
5
4
3
2
4
3.6
3
2.2
1.2
1
.8
.6
.4
(a)
Calculate Max’s marginal utility from windsurfing and from snorkeling. (You may
add this information to the above table with columns for the MU for windsurfing
and the MU for snorkeling.
(b)
If Max has $35 to spend, and equipment for windsurfing rents for $10 per half-hour,
while snorkeling equipment rents for $5 per half-hour, how long will Max choose to
windsurf?
3 units or 1 ½ hrs.
Snorkeling?
1 unit or ½ hour
Why? When all income is spent… (compare columns 4 and 8)
MUS = MUW
PS
PW
(c)
and Total Utility is maximized. TU = 170 utils.
What is Max’s budget constraint? Explain verbally and write the equation for his
budget constraint below.
B = I = PWQW + PSQS
(d)
Now, suppose Max’s sister gives him $20 to send on his leisure pursuits, so he now
has $55 to spend. How long will Max windsurf?
4 units or 2 hours
Snorkeling?
3 units or 1 ½ hours
When all of the income is spent… (compare columns 4 and 8)
MUS = MUW
PS
PW
(e)
$3(5) = $10(3) + $5 (1)
and Total Utility is maximized. TU = 233 utils.
If Max has $55 to spend and the rent on windsurfing equipment is cut to $5 per halfhour, how will Max now spend his time windsurfing?
6 units or 3 hours
Snorkeling? 5 units or 2 ½ hours.
Additional Problem 1 Answers: Utility Analysis
Assume that Maxi Mizer is trying to decide which combination of ice cream cones, Good
A, and magazines, Good B, she should purchase with her limited income of $20. Maxi’s
preferences for ice cream and magazines, Goods A and B, are given in the table below.
Further assume that the prices of ice cream cones and magazines, Goods A and B, are $2
and $4 respectively.
Unit of
Good
Marginal
Utility of Ice
Cream Cones
(Good A)
20
16
14
12
10
8
6
1
2
3
4
5
6
7
a)
MUA
PA
10
8
7
6
5
4
3
Price of
B=4 B=2
(2) (6)
(4) (7)
(8)
(9)
Marginal
Utility of
Magazines
(Good B)
MUB
PB
B=$
4
MUB'
PB'
B=
$2
48
40
36
32
24
12
8
12
10
9
8
6
3
2
(1)
(2)
(3)
(4)
24
20
18
16
12
6
4
(1)
(2)
(3)
(4)
(5)
(9)
How many ice cream cones and magazines will Maxi purchase? ___2A, 4B___
Why?
MUA
PA
b)
Purchase
Order
=
MUB
PB
Maximum Total Utility = 192
Total Expenditures =
2x $2 =
4x $4 =
$4
$16
$20
Now assume that the price of magazines falls to $2. How many ice cream cones
and magazines will Maxi purchase now? __________
4A, 6B
MUA
PA
=
MUB
PB'
Maximum Total Utility = 254
Total Expenditures =
4x $2 =
6x $2 =
$8
$12
$20
c)
On the basis of the information determined so far, determine the demand curve for
magazines. Provide a graph of the demand for magazines.
PB = $4
PB' = $2
PB
QB = 4
QB' = 6
$4
$2
DB
0
4
QB
6
Does the demand for magazines follow the “law of demand”? ____Yes___ (Yes;No)
Give reasons to explain the “law of demand” and explain them briefly.
d)
1)
Diminishing Marginal Utility
2)
Income Effect
3)
Substitution Effect
Compute the price elasticity of demand for the price change for magazines
indicated in part (b). Interpret this elasticity coefficient and provide the formula
for calculations for this price elasticity.
P1 = $4
P2 = $2
Q1 = 4
Q2 = 6
Q2 – Q1
Q2 + Q1
2
P2 – P1
P2 + P1
2
=
6-4
5
-2
3
= 2  3 = -6
5
-2
10
Demand Inelastic
A 1%  P  .6%  QD + vice versa
= -3
5
=
-.60
Additional Problem #3: Consumer and Producer Surplus (Note: This is listed on
the course website as part of Homework #3 Answers).
Now consider the market for pizza. Suppose that the market demand for pizza is given by
the equation P = 40 – 4QD, and the market supply for pizza is given by the equation P = 10 +
2QS, where QD = quantity demanded, QS = quantity supplied, P = price consumers pay (per
pizza) and the price producers receive (per pizza).
(1)
Graph the supply and demand schedules for pizza and indicate the equilibrium price
and quantity. (Your answer must contain your complete algebraic solution).
Calculate the consumer surplus and producer surplus and identify these areas in the
graph below.(Be sure to label the axes and functions, and number your intercepts.)
P
40
S
CS
PE = $20
PS
10
0
D
QE = 5
10
Equilibrium Price:
Q
$20
Equilibrium Quantity:
5
(Show your complete algebraic solution for the equilibrium price and
quantity in the space below.)
In Equilibrium:
S=D
40 – 4Q = 10 + 2Q
30 = 6Q
5 = QE
PE = 40 – 4 (5) = $20 for demand
and
PE = 10 + 2 (5) = $20 for supply
Consumer Surplus at Equilibrium:
$50
(Show all work.)
$25
(Show all work.)
CS = ½ (20 x 5) = $50
Producer Surplus at Equilibrium:
PS = ½ (10 X 5) = $25
Handout 2:
Market Analysis (Answer Key)
The table below gives the individual demands’ of Lisa and Chuck for movies:
Price / movie
$7
6
5
4
3
2
Quantity of movies demanded / mo.
Lisa
Chuck
1
0
2
0
3
0
4
1
5
2
6
3
a) Calculate the market demand for movies assuming that only Lisa and Chuck have
individual demands for movies. Explain this market demand.
Price / movie
$7
6
5
4
3
2
Sum of individual demand curves

Market QD
1
2
3
5
7
9
b) Graph the market demand for movies found in (a). Does this market demand follow
the “law of demand.”? Explain and offer reasons for this law.
P
Yes, it follows “law of demand.”
Inverse relationship between P and Q .
Reasons for law:
a) Income effect
b) Substitution effect
c) Diminishing Marginal Utility
d) Simple reasoning:
Buy more at lower prices.
SM
7
6
5
4
3
2
1
0
DM
1 2 3 4 5 6 7 8 9
Q (mov/mo)
c) Calculate the price elasticity of demand for movies given your market demand in (a)
for each price change. Is demand elastic, unit elastic, inelastic? Explain in detail.
(Show all your work and give the complete elasticity formula).
%QD
Q2 - Q1
EP = ——— = ————— /
%P
Q2 + Q1
———
2
Price / movie
$7
6
5
4
3
2
P2 - P1
—————
P2 + P1
———
2
Market QD
1
2
3
5
7
9
EP
- 4.33
- 2.20
- 2.25
- 1.17
- .625
2-1
——
1.5
1
6.5
6.5
EP = ——— = —— x —— = —— = - 4.33
6-7
1.5
-1
- 1.5
——
6.5
3-2
——
2.5
1
5.5
5.5
EP = ——— = —— x —— = —— = - 2.20
5-6
2.5
-1
- 2.5
——
5.5
5-3
——
4
2
4.5
9
EP = ——— = —— x —— = —— = - 2.25
4-5
4
-1
-4
——
4.5
Elastic
7-5
——
6
2
3.5
7
EP = ——— = —— x —— = —— = - 1.17
3-4
6
-1
-6
——
3.5
Elastic
9-7
——
8
2
2.5
5
EP = ——— = —— x —— = —— = - .625
2-3
8
-1
-8
——
2.5
d)
Inelastic
Now, assume that 7 movies are offered per month. (1) Determine the market
price for each movie. Explain your reasoning. (2) If Chuck’s demand for movies
increases, as shown below, calculate the new market price for movies if 7 movies
are offered per month.
(1)
Price / movie
Quantity of movies demanded/mo
Chuck
$7
6
5
4
3
2
0
0
1
3
4
6
If the quantity of movies offered / mo is 7 then $3 / mo will be the market
price.
At $3 / mo QD = QS. Lisa will see 5 movies and Chuck will see 2 movies.
Price / movie
New Market QD
$7
6
5
4
3
2
1
2
4
7
9
12
(2)
If 7 movies are offered/mo. the market price will be $4/movie, Lisa will
see 4 movies and Chuck will see 3 movies.
What factor or factors could have increased Chuck’s demand for movies?
Chuck’s demand could have increased due to:
a) Increase his income (asssumig movies are superior/normal)
b) Decrease price of complements
c) Increase price of substitutes
d) Increase tastes and preferences
e) Expectation of future price increase
f) Expectation of future income decrease (assuming movies are
superior/normal)
Additional Problem 3 Answers :
Market Analysis
Consider the market for bus service. First draw a graph depicting market equilibrium for
bus service. Then, for each of the events given below, analyze what effects each event
will have on the market equilibrium for bus service, i.e. effect on equilibrium price,
equilibrium quantity, demand or quantity demanded, supply or quantity supplied. You
must draw separate graphs for each of the following events. Remember to label all axes,
functions, and equilibrium points in your graphs precisely.
a) Bus drivers go on strike in order to pressure their employers for wage increases.
Bus Service
S′
P
S

PE′
S decreases →
Temporary shortage (AB) →
Increase PE
Decrease QE
Decrease in QD from B to C
C

PE
A

B
D
0
QE ′ QE
Q
Decrease in “Supply” from S to S′
Decrease in “Quantity Demanded” from B to C
Bus drivers go on strike: Supply decreases to S’: Fewer drivers,
fewer buses.
b) The number of parking spaces decreases due to new land use planning requirements.
Bus Service
P

S

PE′
PE
0
C
A
QE
B

D
QE ′
D increases →
Temporary shortage (AB) →
Increase PE
Increase QE
Increase in QS from A to C
D′
Q
Increase in “Demand” from D to D′
Increase in “Quantity Supplied” from A to C
Decrease in parking spaces: Increase in demand for bus service.
c) Employers with 100 or more employers offer subsidized bus passes to their
employees.
Bus Service
P

S

PE′
C
PE
A
0
B

D
QE
D increases →
Temporary shortage (AB) →
Increase PE
Increase QE
Increase in QS from A to C
D′
QE ′
Q
Increase in “Demand” from D to D′
Increase in “Quantity Supplied” from A to C
Subsidies make it less expensive to ride the bus so demand for bus
service increases.
d) Two thousand miles of Metrolink and commuter rail service are opened.
Bus Service
P

S

PE
PE′
A
B
C

D′
0
QE ′ QE
D decreases →
Temporary surplus (AB) →
Decrease PE →
Decrease QE
Decrease in QS from B to C
D
Q
Decrease in “Demand” from D to D′
Decrease in “Quantity Supplied” from B to C
As Metrolink service increases it is likely that some bus customers
will switch to the train thereby causing a decrease in Demand for
bus service.
e) Congestion on the freeways increases with no plants to fund construction of new
freeway lanes.
Bus Service
P

S

PE′
PE
0
C
A
QE
B

D
QE ′
DB increases →
Temporary shortage(AB) →
Increase PE
Increase QE
Increase in QS from A to C
D′
Q
Increase in “Demand” from D to D′
Increase in “Quantity Supplied” from A to C
More people may take the bus given increased congestion on the
freeways with no funds to increase freeway lanes. Increase in
demand for bus service may result.
Additional Problem 2:
Elasticity (Answer Key)
For each of the elasticity cases given below, verbally explain what the elasticity
coefficient means, and offer an interpretation of the elasticity coefficient.
(a)
The income elasticity of movies is 3.41.
EI = 3.41
Elastic; superior / normal good.
A 1% increase in I  3.41% increase in QD + vice versa.
(b)
The price elasticity of tobacco is -0.61.
EP = -0.61
Inelastic; demand
A 1% increase in P  .61% decrease in QD + vice versa.
(c)
The cross price elasticity of popcorn with respect to the price of soft drinks is
2.38.
EP,SD = 2.38
Elastic; substitutes
A 1% increase PPopcorn  2.38% increase in QD Soft Drinks + vice versa.
or
A 1% increase in PSoft Drinks  2.38% increase in QD Popcorn + vice versa.
(d)
The price elasticity of rail service is 0.89.
EP = 0.89
Inelastic; supply
A 1% increase in PRail  0.89% increase in QS
(e)
Rail
+ vice versa.
The income elasticity of dental services is 1.00.
EI = 1.00
Unit elastic; superior / normal
A 1% increase I  1% increase in QD dental service + vice versa.
Additional Problem #1 Answers: Consumer and Producer Surplus
The graph below shows the demand and supply of rental housing for Microtown.
$/month
1200
1200
1000
S
800
600
400
200
D
0
1
2
3
4
5
6
Quantity
(thousands/month)
a)
What is the equilibrium rent/month? __$600________; the total
rent/month at the equilibrium quantity of rental units?
__$1,800,000______; the consumer surplus? ____$900,000____; the
producer surplus? ___$900,000____.
b)
What is the quantity of apartments that will be rented if a price
ceiling is set at $800? ___3,000__. What is the quantity of apartments
that will be rented if a price ceiling is set at $400? _2,000__. What is
the consumer surplus given this price ceiling? ____$400,000___; the
producer surplus?
___$400,000__;
the dead weight loss?
____$200,000____; the search cost for rental? __$800,000___.
Note: This problem may also be constructed with algebraic expressions for demand and
supply as follows:
Demand: P = 1200 – 200Q
Supply: P = 200Q
Additional Problem #2 Answers: Consumer and Producer Surplus
The graph below shows the market for anti-freeze. The government imposes a sales tax
on sellers of T.
$/gallon
60
12002
00 50
S+T
S
40
30
20
10
D
0
1
2
3
4
5
6
Quantity
(thousands of gallons)
a)
What is the equilibrium price/gallon without the tax?
___$30_______; the equilibrium quantity without the tax? __3,000
gallons____.
b)
What is the tax per gallon? ___$20________. How much revenue will
the sales tax raise? __$40,000_____.
c)
The tax decreases consumption by? __1,000 gallons__.
d)
What is the consumer surplus before the tax? ___$45,000___; after
the tax? ___$20,000____. What is the producer surplus before the
tax? __$45,000__; after the tax? __$20,000__. What is the dead
weight loss associated with the tax? _____$10,000_____.
Note: This problem may also be constructed with algebraic expressions for demand and
supply as follows:
Demand: P = 60 – 10Q
Supply: P = 10Q
Supply + Tax:
P = 20 + 10
Handout 1 :
Production Possibilities (Answer Key)
A certain economy only produces two goods, calculators (C) and tea (T). To
manufacture these goods, it has three kinds of resources: (1) a fixed quantity of capital,
useful only in producing calculators; (2) a fixed quantity of land, useful only in
producing tea; and (3) a fixed quantity of labor of 100 men (M) capable of working in
either occupation. The table below indicates the amounts of calculators and tea that can
be produced when varying amounts of labor work with the specialized resources,
calculators and tea.
Number of
men
0
10
20
30
40
50
60
70
80
90
100
Daily
production
of calculators
0
40
105
200
300
390
450
500
550
580
600
M
10
10
10
10
10
10
10
10
10
10
C
Number of
men
40
65
95
100
90
60
50
50
30
20
0
10
20
30
40
50
60
70
80
90
100
Daily production
of tea
M
0
5
12
20
28
36
43
49
54
58
60
1. Draw this economy’s production-possibility curve. (Be careful to label axes. Use of
graph paper will enable your graph to be more accurate.)
PPF
600
Calculators (Y)
500
400
300
200
100
0
0
5
12
20
28
36
43
49
54
58
60
Tea (X)
2. According to the table above, diminishing returns first appear in the production of
calculators when the total number of men employed rises to :
Between 40 and 50 men.
Explain what causes this diminishing returns phenomenon briefly.
As additional units of the variable input, labor, are combined with the fixed input,
capital (in respect to calculator production) eventually ever-decreasing increases
in output (of calculators) will result. (The fixed input is crowed out by additions
of the variable input.)
3. What is the opportunity cost of producing 200 calculators instead of 40?
9 units of tea.
Explain the concept of opportunity cost briefly.
In this example, if more calculators are produced the units of tea production
foregone, given the available labor, resources, represent the opportunity costs.
4. Assume that the production possibility curve above exists in 1985. Assume further
that the following (separate) events took place between 1985 and 2000. Other things
being equal, explain carefully how the production possibility curve would be altered.
a) The use of robotics technology is introduced into computer industry.
b) A strain of virus destroys a large percentage of tea plants worldwide.
c) Improved harvesting methods are employed in the tea industry.
d) Population growth continues at current positive rates over this period.
a)
Calculators
b)

Calculators

Tea
Tea
c)
d)
Calculators
Calculators


Tea
Tea