Assignment on Elasticity of Demand and Consumer Surplus

General Instructions of Elasticity of Demand and Consumer Surplu

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NOTE:

Before attempting to complete the Unit 5 Assignment, it is strongly recommended that you complete the TWO Learning Activities associated with this Assignment. The links to the Learning Activities are found within the course by selecting “Content”, then on “Unit 5”, then on “Assignment”, and then on “Unit 5 Assignment.” The links appear within the paragraph entitled “Learning Activity.”

In this Assignment, you will calculate the Price Elasticity of Demand, demonstrate a firm understanding of consumer choices based on differing marginal utilities, consumer surplus, and how the buying choice and amount of consumer surplus changes based on various pricing schemes

In this Assignment, you will be assessed on the following outcome:

BU224-5: Examine how the concept of utility affects purchasing decisions by individuals and consumer surplus.

Questions

1. The accompanying table shows the price and monthly demand for barrels of gosum berries in Gondwanaland

Price of gosum berries per barrel Native Demand for gosum berries per month

$100 0

$90 100

$80 200

$70 300

$60 400

$50 500

$40 600

$30 700

$20 800

$10 900

$0 1000

Using the midpoint method (show your work), calculate the price elasticity of demand when the price of a barrel of gosum berries rises from $10 to $20. What kind of elasticity is this value that you computed for the price elasticity of demand and what does it mean for how demand will change based on a change in price within this price range? (10 points)

Price elasticity of demand represent how consumer would respond to the changes made in prices of the offered product. In this case, price of each barrel for gosum berries is increased from $10 to $20. Considering this change, price elasticity of demand is calculated below:

Price Elasticity of Demand =  (percentage  Change in Quantity (Q))/(percentage Change in Price (P) )

% change in Q = Demand for gosum berrirs at $20 - Demand for gosum berrirs at $ 10

= 800 - 900  =  - 100

 % change in Q =  (Demand for gosum berrirs at $ 10 +  Demand for gosum berrirs at $20)/2

% change in Q =(900 + 800 )/( 2)

% change in Q =  1700/2  = 850

% change in Q =  (- 100)/850  =  - 0.1176 

% change in Q = - 11.76 

% change in P = $ 20 - $ 10  = $ 10

% change in P =  ($ 10 + $ 20)/2

% change in P =  ($ 30)/2  = 15

=  ($10 )/($15 )    = 0.666667 

= 0.666667 * 100

 = 66.66 

Price Elasticity of Demand =  (percentage  Change in Quantity (Q))/(percentage Change in Price (P) )

Price Elasticity of Demand =  (-  11 .76 )/(66.66  )

Price Elasticity of Demand = - 0.176

According to the calculation, price elasticity of demand value is not positive and the overall value is less than 1 which indicate totally inelastic demand. The value represents that with the increase in prices buyer’s demand for berries does not present a high level of change. 

Using the midpoint method (show your work), calculate the price elasticity of demand when the price of a barrel of gosum berries rises from $70 to $80. What kind of elasticity is this value that you computed for the price elasticity of demand and what does it mean for how demand will change based on a change in price within this price range? (10 points)

According to the given scenario, the price of gosum berries is inclined to $80 from $70 (per barrel) as a result of which demand for gosum berries will also change. How much price change will influence demand for berries shows elasticity or inelasticity of demand. Price elasticity of demand value will be calculated by dividing up the percentage of change in quantity by percentage of change in prices.   

Price Elasticity of Demand =  (percentage  Change in Quantity (Q))/(percentage Change in Price (P) )

% change in Q= Demand for gosum berrirs at $ 80 - Demand for gosum berrirs at $ 70

= 200 - 300 = - 100

 % change in Q=  (Demand for gosum berrirs at $ 70 +  Demand for gosum berrirs at $ 80)/2

Percentage Change in Q=( 300 + 200)/2

Percentage  Change in Q =  500/2  = 250

Percentage Change in Q =  (- 100)/250  =  - 0.4 

Percentage Change in Q = - 40 

Percentage Change in P = $ 80 - $ 70 = $ 10

Percentage Change in P =  ($ 70 + $ 80)/2

Percentage Change in P =  ($ 150)/2  = 75

 =  ($ 10 )/($ 75 )    = 0.1333 

= 0.1333 * 100

= 13.33 

Price Elasticity of Demand =  (percentage  Change in Quantity (Q))/(percentage Change in Price (P) )

Price Elasticity of Demand =  (-  40 )/(13.33  )

Price Elasticity of Demand =  - 3.00

Using the midpoint method price elasticity of demand is calculated for gosum berries when prices were increased from $70 to $80. According to the calculated value, price elasticity of demand (PED) is negative (-3). The calculated value represents that demand for berries will fall in response to the increase in prices from $70 to $80

Notice that the estimates from (a) and (b) above are different. Why do price elasticity of demand estimates change along the demand curve? (10 points)

In the above estimation, price elasticity of demand values was different for (a) and (b). In these estimations, values are different because of the percentage of change in both scenarios. For instance, in scenario (a) the percentage of change in quantity was -11. 76 but for scenario (b) percentage of change is calculated as -40 even change in quantity seems -100 only (200 – 300 = -100, and 800- 900 = -100). Moreover, values are different because of changes in price as well as other consumer market factors. For instance, changes in consumer market tastes and perceived maximum satisfaction level of consumers are the also key factors other than prices that cause to bring changes in the consumer demand. Excluding this, changes in consumer purchasing power also cause for the shift in the demand curve. 

2. Matilda is downloading music and videos from an online site. She is currently buying three music downloads that cost $3 each and two video downloads that also cost $3 each. The table below indicates what she reports as the marginal utility of the last music download and the last video download in this combination of purchases.

Quantity Price per Download MU per download

Music downloads 3 $3 60

Video downloads 2 $3 45

As an assignment for her Microeconomics course, Matilda used the marginal utilities that she gave to her 3rd music download and her 2nd video download to complete the Experiment Tally Sheet below. Her available budget was $19.00.

Downloads of mu (score) from

1 to 100 Price of each

$3.00

Money spent on

Downloads of mu (score) from 1 to 100 Price of each

$3.00

Money spent on

Total Money

Total Budget 

music mu mu/$ music Videos Mu mu/$ videos Spent Remaining

1st 20 6.6 $3.00 1st 22.5 7.5 $3.00 $6.00 $13.00

2nd 40 13.3 $3 2nd 45 15 $3.00 $12.00 $7.00

3rd 60 20 $3.00 3rd $15.00 $4.00

4th 4th

Total money spent on music $9.00 Total money spent on videos $6.00 $15.00 $4.00

A consumer maximizes utility when the last dollar spent on any good generates the same satisfaction as the last dollar spent on every other good. Is Matilda maximizing her utility? Explain your answer. (3 points

Marginal utility is calculated by using marginal utility per dollar formula. 

Marginal Utility per dollar for Music

Mu of last $ = Price ×  ( mu score)/(mu/$)

Mu f last $ = 20  ×  ( 60 )/($ 3)

= 400

Marginal Utility per dollar for Videos 

Mu of last $ = Price  ×  ( mu score)/(mu/$)

Mu of last $ = 15  ×  ( 45 )/($ 3)

= 225

The values of marginal utility for music and video regarding the last dollar spent on every good is not the same. Thus Matilda is not maximizing her utility. However, marginal utility is diminishing because of the extra utilization of one product (music). 

Should Matilda consume one more video download, to move her closer to her optimum utility? Explain your answer. (3 points)

According to the concept of maximization of utility, marginal utility per dollar for each product should be equal for maximum utility. However, in the above scenario, Matilda’s utility for both product is not the same as she was not maximizing her utility. Considering this, Matilda should not consume 1 more video as it would reduce her maximum utility. Moreover, she would have only $4 after downloading one more video.

Should Matilda consume one less music download and one more video download, to move her closer to her optimum utility? Explain your answer. (3 points)

Matilda should not add one more video while reducing one music item as it will not bring the required change in optimum utility of Matilda. According to the results of calculation, while creating equality she would reduce her maximum utility level as well as budget to purchase videos and music. Thus, calculations suggest that the price of each product of music and the price of each product of video cannot be made equal by reducing music products and increasing videos. 

Should Matilda consume one more music download, to move her closer to her optimum utility? Explain your answer. (3 points)

In accordance with the shared information, Matilda had a budget of $19 in which she planned to get 3 music downloads and two videos downloads. Although her optimum utility is accomplished. Matilda cannot add one music as it does not fulfil her optimum utility. Moreover, she cannot download one more video while reducing one music download as she after this she would have $4. While if she just plans to add one more music in downloads while keeping video downloads to 2 only, then she can move her closer to her optimum utility. Adding one more music would decrease her marginal utility per dollar to 15 and thus she would have equal marginal utility for both products (music and videos) on her last dollar. Although, after downloading one more music she cannot reach the level of maximum utility because she would have $1 left behind from budget after this. 

3. Bradon and his family often rent movies from the new internet movie streaming service, Xanadu. The table below shows Brandon’s demand schedule for eight movie rentals that Brandon’s family is interested in watching

Number of internet movie rentals Willingness to pay each rental

1st $7

2nd $6

3rd $5

4th $4

5th $3

6th $2

7th $1

8th $0

a. If the price of each movie rental from Xanadu is $3, how many movie rentals will Brandon buy and how much consumer surplus does Brandon receive? Explain your answer. (5 points)

In case the price of movie rental from Xanadu is $3 then the surplus on 5 movies would be calculated as: 

Amount of forking out 5 movies = Rental Movies  ×  Price for Rent

= 5  ×  $ 3

= 1

= Total Possible rental - Amount of forking out 5 movies 

To reach the total surplus total possible rental is required to be calculated. 

Total possible rental is calculated as: 

Total Possible Rental = 7 + 6 +  5 + 4 + 3 = $ 25

Now calculating surplus of 5 movies at $3 each: 

Surplus of 5 movies = $ 25 - $ 15 

Surplus of 5 movies = $ 10 

Thus, total surplus earned by Brandon will be around $10 on 5 movies as the total amount of forking out 5 movies a night is $15 that is subtracted from $25 which is a total possible rental of 5 movies (based on willingness). 

b. If the price of each movie rental from Xanadu is $5, how many movie rentals will Brandon buy and how much consumer surplus does Brandon receive? Explain your answer. (5 points)

In this scenario, the price of each movie rental from Xanadu is around $5. Considering this, Brandon can rent only 3 movies which will have a surplus lower than the calculated surplus for 5 movies at price $3. 

To calculate total surplus, firstly amount of forking out 3 movies is calculated. 

Amount of forking out 3 movies  = Rental Movies  ×  Price for Rent

= 3 ×$5

= $ 15

= Total Possible rental (willingness)  -Amount of forking out 3 movies 

Calculating total possible rental of 3 movies (based on willingness) 

Total Possible Rental = 7 + 6 +  5 = $  18

The formula used to calculate surplus is presented below:

Surplus of 3 movies  = $ 18 - $ 15 

Surplus of 3 movies  = $  3  

Thus, Brandon will earn total surplus around $3 on rent of 3 movies at $5 each. 

c. If the Xanadu online service offers as many movie rentals as the customer wants to download, all for a one-time fee of $25.00, how many movie rentals will Brandon download and how much consumer surplus will Brandon receive? Explain your answer. (5 points)

Brandon is not interested to spend even a single dollar on the rent of 8th movie so total surplus will be calculated while considering 7 movies only. Thus the total surplus would be as:

Total Possible (willingness)Rental = 7 + 6 +  5 + 4 + 3 + 2 + 1 = $ 28

Surplus = $ 28 - $ 25

= 3

According to the calculation, if he plans to purchase online services offer to get unlimited movies rentals at $25 then overall surplus would be limited to 3 only. However, in this situation, he would be able to enjoy all the movies at night in $25 only. Moreover, the calculated surplus in the previous scenario (3 movies in $5 each) was also $3 but in that case, Brandon could enjoy only 3 movies. However, in this situation surplus is again $3 but Brandon can enjoy a total of 7 movies at night to reach his maximum utility and satisfaction limits. Considering this, Brandon should buy online services at $25 price to enjoy unlimited movies with a surplus of $3. 

If the Xanadu online service offers as many movie rentals as the customer wants to download, all for a one-time fee of $35.00, how many movie rentals will Brandon download and how much consumer surplus will Brandon receive? Explain your answer. (5 points)

Brandon is willing to watch only 7 movies. In case he is given an offer of pay $35 fee of a yearly subscription to download unlimited movies the total surplus would as: 

Total Possible (willingness)  Rental = 7 + 6 +  5 + 4 + 3 + 2 + 1

= $ 28

Now calculating surplus for $35 yearly fee of subscription. 

 Surplus=Total possible rental (willingness)-Yearly Subscription Fee

Surplus = $  28 - $ 35 

 = - 7

Considering this calculated value of (-7) it is clear that Brandon will not have a surplus as value is negative. In fact, if he decides to subscribe for the yearly offer he would have a deficit of $7. Based on this calculation it is clear that purchasing online services at $35 is not an attractive offer for Brandon as by purchasing this offer package he would have a loss of $7. Brandon would spend extra $7 even after the fulfilment of his utility for movies. 

e. If the Xanadu’s market research showed that Brandon’s demand represented what most of Xanadu’s customers wanted, what would be the most that Xanadu could charge as a one-time fee for all the downloads that the customer wanted? (4 points)

Xanadu is interested to provide movies on rent to the targeted audience. Xanadu can offer movies in a package with some limitations about downloading. However, to make this package an attractive package for targeted audience Xanadu should have to set optimal prices for this package. According to the given scenario, Xanadu wants to charge as a one-time fee only in a month or year to enable consumers to download unlimited movies in the selected time duration. Considering these requirements and specifications, Xanadu should select a one-time fee of $28 for this package as consumers are only willing to spend $28 for 7 movies at night. In case, Xanadu sets prices higher than $28 then he would not be able to get the attraction of consumers as without this package they can already enjoy 7 movies in $28. Excluding this, to make this offer successful and get the attraction of maximum consumers Xanadu should set the price lower than $28 for unlimited movies download offer.

4. Newspaper vending machines are designed so that once you have paid for one paper; you have access to all the papers in the machine and could take multiple papers at a time. However, other vending machines dispense only one item (the item you bought). You do not have access to all the goods (sodas, candy, snacks, etc.) at one time. Using the concept of marginal utility, explain why these vending machines differ? (6 points)

There is no marginal utility or real value for a product when you purchase it for the very first time. Even for the second time purchase, we cannot determine the marginal utility of the product. While purchasing the first newspaper buyer already achieved all that was required to be achieved. However, when you purchase candy and enjoy the taste of it then you would like to purchase for the second and third time also. Thus the marginal utility of this candy can be calculated. However, with the purchase of each unit (candy) level of satisfaction and utility will reduce. Each time a new candy will give utility less than the first candy and each previously taken candy. Thus, considering the concept of marginal utility for candies these candy vending machines are different.   

References of Elasticity of Demand and Consumer Surplus:

Unit 5 Assignment: Elasticity of Demand and Consumer Surplus Possible Points Points Earned

Overall Writing: 8  

The used correct file name in uploading assignment document. 1  

Demonstrated concerted effort to utilize material from the textbook and/or seminars to answer questions. 3  

Correctly formatted paper in 6th edition. Includes in-text citations and listed at least one reference. 3  

Used standard English with few or no grammatical errors. 1  

Individual Questions: 64  

1.a. Correctly calculated price elasticity of demand ($10-$20), and thoroughly explained the meaning of the value calculated. 10  

1.b. Correctly calculated price elasticity of demand ($70-$80), and thoroughly explained the meaning of the value calculated. 10  

1.c. Correctly explained why these Dpe estimates changed at various prices? 10  

2.a. Correctly determined and explained if the utility was maximized at 3rd music and 2nd video. 3  

2.b. Correctly determined and explained if the utility was maximized at 3rd music and 3rd video. 3  

2.c. Correctly determined and explained if the utility was maximized at 2nd music and 3rd video. 3  

2.d. Correctly determined and explained if the utility was maximized at 4th music and 2nd video. 3  

3.a. Correctly computed Brandon's total movie rentals and Consumer Surplus at $3/rental. 5  

3.b. Correctly computed Brandon's total movie rentals and Consumer Surplus at $5/rental. 5  

3.c. Correctly computed Brandon's total movie rentals and Consumer Surplus at a one-time $25 fee. 5  

3.d. Correctly computed Brandon's total movie rentals and Consumer Surplus at a one-time $35 fee. 5  

3.e. Correctly determined Xanadu's maximum one-time fee. 4  

4. Correctly explained how Marginal Utility determines how newspaper and snack vending machines differ. 6  

Fewer points deducted for late submission  

Total Points 80