Pam is in charge of putting on the NYE fireworks show. The show can either be...

Pam is in charge of putting on the NYE fireworks show. The show can either be anywhere from 10 - 20 minutes long. There are 4 neighborhoods in your city that each offer different views of the firework show, and thus each have a different marginal benefit from additional minutes of the show as shown in the table below:

Show Length in Minutes	Marginal Benefit of Neighborhood A	Marginal Benefit of Neighborhood B	Marginal Benefit of Neighborhood C	Marginal Benefit of Neighborhood D
10	$34	$22	$20	$10
11	$32	$21	$18	$9
12	$30	$20	$16	$8
13	$28	$19	$14	$7
14	$26	$18	$12	$6
15	$24	$17	$10	$5
16	$22	$16	$8	$4
17	$20	$15	$6	$3
18	$18	$14	$4	$2
19	$16	$13	$2	$1
20	$14	$12	$0	$0

If each additional minute of the show costs $44, what is the optimal length of the show in minutes?

Since each additional minute of the show costs $44, each of the 4 neighborhoods is required to contribute $11 in taxes for each additional minute. Each neighborhood gets a vote on the maximum number of minutes they want the show to run based on this cost. What is the maximum length of the show that 3 of the 4 neighborhoods would accept?

Expert Solution

The marginal benefits of all the four neighborhoods has to be considered together.

The criteria to be used is MB = MC

In other words, the duration where the marginal cost of an additional minute equals the marginal benefits, for all neighborhoods combined:

At 17 minutes duration: MB = $44 (20 + 15 + 6 + 3)

and MC = $44

Thus, the optimal length is 17 minutes

---

The table shows that neighborhood D would not like to pay more than $10 for any show duration.

Now, 3 out of 4 neighborhoods should be ready to contribute $11

Looking at their marginal WTP, it is observed that:

At a show duration of 14 minutes, at least 3 neighborhoods (A, B and C) are willing to pay $11, or more.

Hence, now the optimal length is 14 minutes

(Note: since neighborhood D will not pay $11, but only $6, there will be a shortfall, which A, B and C will have to bear. However, the price they pay will be much less than their maximum willingness to pay)

Rahul Sunny answered 2 years ago

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