Question

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?

Answer 1

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)