# Rsm455 | Economics homework help

Assignment 3

Q1. A group of 12 consumers are considering whether to connect to a new social network. Consumer 1 has an intrinsic value of \$1 for hooking up to the network, consumer 2 has an intrinsic value of \$2, consumer 3 has an intrinsic value of \$3, and so on up to consumer 12. Each consumer’s willingness-to-pay (WTP) to connect to the network depends on the total number of persons who are connected to it. The exact relationship is described as follows: for each i, consumer i’s willingness-to-pay to connect to the network is i times the total number of persons connected. Thus if 5 people are connected to the network, consumer 1’s willingness-to-pay is \$5, consumer 2’s willingness-to-pay is \$10 and so on.

1. (3 points) Assume that for any given number of person in the      social network, consumer with the highest willingness-to-pay will sign up      first. Use a table to show the      relationship among the total number of person in the network, the marginal      consumer who joins the network, and the willingness-to-pay for the      marginal consumer. The table should      have three columns: (i) Total no. of consumers in the network, (ii) The      intrinsic value of the marginal consumer, (iii) Willingness-to-pay of the      marginal consumer.
2. (5 points) Suppose the network has decided to subsidize      consumers 1 and 2 (i.e., the consumer with intrinsic value = 1, and      consumer with intrinsic value = 2) to      join the network for free, and then set the price at \$35. Assume that a consumer will not sign up for the network unless      his/her willingness-to-pay will be higher than the price he/she pays, as      soon as he/she signs up. What will      be the total number of consumers who will sign up the network?

[Hint: Create a table similar to part (a), and use it to help you answer the question.]

1. (5 points) Suppose the network has decided to subsidize      consumers 11 and 12 (i.e., the consumer with intrinsic value = 11, and      consumer with intrinsic value = 12) to join the network for free, and then      set the price at \$35. Assume that a      consumer will not sign up for      the network unless his/her willingness-to-pay will be higher than the      price he/she pays, as soon as he/she signs up. What will be the total number of      consumers who will sign up the network?

[Hint: Create a table similar to part (a), and use it to help you answer the question.]

1. (5 points) Suppose the network has decided to subsidize      consumers 5 and 6 (i.e., the consumer with intrinsic value = 5, and      consumer with intrinsic value = 6) to join the network for free, and then      set the price at \$35. Assume that a      consumer will not sign up for      the network unless his/her willingness-to-pay will be higher than the      price he/she pays, as soon as he/she signs up. What will be the total number of      consumers who will sign up the network?

[Hint: Create a table similar to part (a), and use it to help you answer the question.]

Q2. The Customer Information Management Center at Cheung Kong Graduate School of Business in Beijing is organizing its inaugural conference in Marketing. The main purpose of this conference is to present cutting-edge research topics and methodologies to research communities within China so that Chinese academics can learn about what marketing science can bring to the practice of marketing. It also serves as a forum to generate discussions on research issues related to emerging markets and learn about the potential for the application of marketing science in China. The conference provides a platform for professional networking and exchange of ideas, learning and knowledge.

Conference attendees will include both academicians and industry practitioners. If someone would like to present his/her research in the conference, he/she needs to submit a research paper to the conference by a deadline, and the conference committee will select a subset of the submissions for presentation. In order to attend the conference, attendees must register. The registration fees are:

i. Presenters \$0 (covered by the conference)

ii. Academic participants \$250 (register before May 1, 2012)

\$300 (register after May 1, 2012)

iii. Industry participants \$400 (register before May 1, 2012)

\$500 (register after May 1, 2012)

Note that Industry participants are the people who work for companies.

Explain the following in details:

(a) Why does the conference charge the industry participants more than academic participants? (3 points)

(b) Why is the registration fee lower for early registration? (3 points)

(c) Why does the conference decide NOT to charge presenters anything? (6 points)

Q3. (Road Pricing) Suppose that the government would like to discourage certain percentage of private drivers from using their cars. Assume the following.

(i) Currently, there are 1000 drivers. They all drive round-trip each day.

(ii) Average driving time per one-way trip as a function of the number of drivers is given in Table 1.

(iii) The distribution of monthly income for the current drivers is given in Table 2.

(iv) The opportunity costs of driving per hour = 50% hourly salary during work.

(v) Each driver in Table 2 works 160 hours per month.

(vi) Choice of transport mode is only based on time and cost.

(vii) Gas price and public transportation fare are ignored.

(viii) Drivers only care about traveling time when deciding whether to drive.

(ix) All drivers currently (i.e., before the congestion tax is imposed) save 10 minutes one-way by driving instead of taking public transportation.

(x) If 25% of drivers stop driving, they will use subway. But that will cause more congestion in subway and the travel time in subway will increase by 3 minutes.

Table 1. Number of drivers and average driving time.

Number of drivers

Average driving time per one-way trip   (minutes)

250

15

300

15

500

20

750

30

950

40

1000

45

Table 2. Income distribution of the drivers.

Monthly income (\$)

Percentage of the current drivers (%)

< 1,000

10

1,000 – 1,999

15

2,000 – 2,999

25

3,000 – 3,999

25

4,000 – 4,999

15

5,000 – 7,000

10

1. Given the above information, if the government wants to use      congestion tax to achieve its goal of discouraging 25% of drivers, what is      the level of congestion tax (assume that the government can only set one      congestion tax level for all drivers)? Explain your answer carefully (5 points)
2. Given the level of congestion tax that you set in part (a), how      much benefits per day would the income group of \$5,000-\$7,000 receive      after the tax is imposed? Explain      your answer carefully. (5 points)
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