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
(per month) / TUW / MUW / MUW
PW / MUW
PW′ / TUS / MUS / MUS
PS
1 / 60 / 60 / 6 / 12 / 20 / 20 / 4
2 / 110 / 50 / 5 / 10 / 38 / 18 / 3.6
3 / 150 / 40 / 4 / 8 / 53 / 15 / 3
4 / 180 / 30 / 3 / 6 / 64 / 11 / 2.2
5 / 200 / 20 / 2 / 4 / 70 / 6 / 1.2
6 / 206 / 6 / .6 / 1.2 / 75 / 5 / 1
7 / 211 / 5 / .5 / 2 / 79 / 4 / .8
8 / 215 / 4 / .4 / .8 / 82 / 3 / .6
9 / 218 / 3 / .3 / .6 / 84 / 2 / .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 and Total Utility is maximized. TU = 170 utils.

PS PW

B = I = PWQW + PSQS $3(5) = $10(3) + $5 (1)

(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 and Total Utility is maximized. TU = 233 utils.

PS PW

(e) If Max has $55 to spend and the rent on windsurfing equipment is cut to $5 per half-hour, 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) / MUA
PA / Purchase Order
Price of
B=4 B=2 / Marginal Utility of Magazines (Good B) / MUB
PB / B=$4 / MUB'
PB' / B=$2
1 / 20 / 10 / (2) / (6) / 48 / 12 / (1) / 24 / (1)
2 / 16 / 8 / (4) / (7) / 40 / 10 / (2) / 20 / (2)
3 / 14 / 7 / (8) / 36 / 9 / (3) / 18 / (3)
4 / 12 / 6 / (9) / 32 / 8 / (4) / 16 / (4)
5 / 10 / 5 / 24 / 6 / 12 / (5)
6 / 8 / 4 / 12 / 3 / 6 / (9)
7 / 6 / 3 / 8 / 2 / 4

a) How many ice cream cones and magazines will Maxi purchase? ___2A, 4B___

Why?

Maximum Total Utility = 192

Total Expenditures =

b) Now assume that the price of magazines falls to $2. How many ice cream cones and magazines will Maxi purchase now? ______

4A, 6B

Maximum Total Utility = 254

Total Expenditures =

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 QB = 4

PB' = $2 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.

1) Diminishing Marginal Utility

2) Income Effect

3) Substitution Effect

d) 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 Q1 = 4

P2 = $2 Q2 = 6

Q2 – Q1
Q2 + Q1
2 / = / 6-4
5 / = / 2 / · / 3 / = / -6 / = / -3 / = / -.60
P2 – P1 / -2 / 5 / -2 / 10 / 5
P2 + P1
2 / 3

Demand Inelastic

A 1% ê P è .6% é QD + vice versa

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.)

40 S

PE = $20

PS 10 D

0 QE = 5 10 Q

Equilibrium Price: $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.)

CS = ½ (20 x 5) = $50

Producer Surplus at Equilibrium: $25 (Show all work.)

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:

Quantity of movies demanded / mo.
Price / movie / Lisa / Chuck
$7 / 1 / 0
6 / 2 / 0
5 / 3 / 0
4 / 4 / 1
3 / 5 / 2
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.

Sum of individual demand curves

Price / movie / Market QD
$7 / 1
6 / 2
5 / 3
4 / 5
3 / 7
2 / 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.

Yes, it follows “law of demand.” SM

Inverse relationship between P and Q . 7

Reasons for law: 6

a) Income effect 5

b) Substitution effect 4

c) Diminishing Marginal Utility 3

d) Simple reasoning: 2 DM

Buy more at lower prices. 1

0 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).

%DQD Q2 - Q1 P2 - P1

EP = ——— = ————— / —————

%DP Q2 + Q1 P2 + P1

——— ———

2 2

Price / movie / Market QD / EP
$7 / 1
6 / 2 / - 4.33
5 / 3 / - 2.20
4 / 5 / - 2.25
3 / 7 / - 1.17
2 / 9 / - .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 Elastic

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

7 - 5

——

6 2 3.5 7

EP = ——— = —— x —— = —— = - 1.17 Elastic

3 - 4 6 - 1 - 6

——

3.5

9 - 7

——

8 2 2.5 5

EP = ——— = —— x —— = —— = - .625 Inelastic

2 - 3 8 - 1 - 8

——

2.5

d) 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.

Quantity of movies demanded/mo
Price / movie / Chuck
$7 / 0
6 / 0
5 / 1
4 / 3
3 / 4
2 / 6

(1) 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 / 1
6 / 2
5 / 4
4 / 7
3 / 9
2 / 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

P S′

PE′ C S decreases →

è Temporary shortage (AB) → PE A B Increase PE

ç Decrease QE

D Decrease in QD from B to C

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

è S D increases →

è Temporary shortage (AB) →

PE′ C Increase PE

Increase QE

PE A B Increase in QS from A to C

è D′

0 QE QE′ 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

è S D increases →

è Temporary shortage (AB) →

PE′ C Increase PE

Increase QE

PE A B Increase in QS from A to C

è D′

0 QE 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

ç S D decreases →

è Temporary surplus (AB) →

PE A B Decrease PE →

Decrease QE

PE′ C Decrease in QS from B to C

ç D

D′

0 QE′ QE 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

è S DB increases →

è Temporary shortage(AB) →

PE′ C Increase PE

Increase QE

PE A B Increase in QS from A to C

è D′

0 QE QE′ 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 è 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 è .61% decrease in QD + vice versa.

EP,SD = 2.38

Elastic; substitutes

A 1% increase PPopcorn è 2.38% increase in QD Soft Drinks + vice versa.

A 1% increase in PSoft Drinks è 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 è 0.89% increase in QS Rail + vice versa.

(e) The income elasticity of dental services is 1.00.

EI = 1.00

Unit elastic; superior / normal

A 1% increase I è 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

800

600

200 D

Quantity

0 1 2 3 4 5 6 (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____.