Ka-fu Wong University of Hong Kong

1. Why do some activities organized by charitable organizations require a deposit upon registration of the activities, which is later refunded to the participants? Ka-fu WongUniversity of Hong Kong

2. Outline • Why do we need prior registration at all? • If no deposit is required • Who will register? • Who and how many will attend after registration? • If deposit is required, but no refund is provided • Who will register? • Who and how many will attend after registration? • If deposit is required, but deposit will be refunded upon participation • Who will register? • Who and how many will attend after registration?

3. Why do we need prior registration at all? • Organizers have to get an estimate of seats/resources needed to accommodate the participants. • If we know that there are 1000 participants, we need to prepare 1000 chairs and tea sets. • Organizers have to make sure that resources are not wasted. • More aggressive advertisement may be need if too few people are going to attend.

4. If no deposit is required, who will register? • Suppose there is no other opportunity cost in doing the registration of an activity X. • Suppose John, a typical individual, is willing to pay $A1 dollars to activity X on any other days. And, on that particular day, he could have engaged in another activity Y that has a value of $B1. John will choose to register if $A1 - $B1 >0 • Suppose Jane, another typical individual, is willing to pay $A2 dollars to activity X on any other days. And, on that particular day, she may have the chance to engage in another activity Z that has a value of $B2, with a probability p. And, $A2 - $B2 < 0. Besides these two activities, her best alternative on that day is to stay home, which has a value of zero to her. Because Jane know that she can always decide whether to go later, Jane will choose to register if (1-p)*$A2 >0.

5. If no deposit is required, who and how many will attend after registration? • Suppose among those registered, 50 are like John, and 50 others are like Jane. • 50 registrants who are like John will go to activity X because • $A1 - $B1 >0 • Suppose all other participants who are like Jane find out that the other activity, that they value at $B2, is available. Because $A2 - $B2 < 0, all the 50 other will not attend the activity X. • In this example, only 50% of the registered (only those who are like John) will attend. • If you were the organizer and you had prepared 100 tea sets for those registered, will you be disappointed?

6. If a deposit D is required but no refund will be given, who will register? • Suppose there is no other opportunity cost in doing the registration of an activity X. • Suppose John, a typical individual, is willing to pay $A1 dollars to activity X on any other days. And, on that particular day, he could have engaged in another activity Y that has a value of $B1. John will choose to register if $A1 - $B1 - D>0 • Suppose Jane, another typical individual, is willing to pay $A2 dollars to activity X on any other days. And, on that particular day, she may have the chance to engage in another activity Z that has a value of $B2, with a probability p. And, $A2 - $B2 < 0. Besides these two activities, her best alternative on that day is to stay home, which has a value of zero to her. So Jane has to decide to pay D to hedge against the risk of not able to engage in Z. Jane will choose to register if (1-p)*$A2 - D>0.

7. If deposit is required and no refund will be given, who and how many will attend after registration? The deposit is a sunk cost at the time of making decision. • Suppose among those registered, 50 are like John, and 50 others are like Jane. • 50 registrants who are like John will go to activity X because • $A1 - $B1 >0 • Suppose all other participants who are like Jane find out that the other activity, that they value at $B2, is available. Because $A2 - $B2 < 0, all the 50 other will not attend the activity X. • In this example, only 50% of the registered (only those who are like John) will attend. • If you were the organizer and you had prepared 100 tea sets for those registered, will you be disappointed?

8. If a deposit D is required but it will be refunded upon participation, who will register? • Suppose there is no other opportunity cost in doing the registration of an activity X. • Suppose John, a typical individual, is willing to pay $A1 dollars to activity X on any other days. And, on that particular day, he could have engaged in another activity Y that has a value of $B1. John will choose to register if $A1 + D - $B1 - D>0 • Suppose Jane, another typical individual, is willing to pay $A2 dollars to activity X on any other days. And, on that particular day, she may have the chance to engage in another activity Z that has a value of $B2, with a probability p. And, $A2 - $B2 < 0. Besides these two activities, her best alternative on that day is to stay home, which has a value of zero to her. So Jane has to decide to pay D to hedge against the risk of not able to engage in Z. Jane will choose to register if (1-p)*($A2 +D) - D>0.

9. If a deposit D is required but it will be refunded upon participation, who and how many will attend after registration? • Note that an amount of D may be given upon participation. • Suppose among those registered, 50 are like John, and 50 others are like Jane. • 50 registrants who are like John will go to activity X because • $A1 + D - $B1 >0 • Suppose all other participants who are like Jane find out that the other activity, that they value at $B2, is available. • If $A2 + D - $B2 < 0, all the 50 other will not attend the activity X. Hence, only 50% of the registered (only those who are like John) will attend. • If $A2 + D - $B2 > 0, all the 50 other will attend the activity X. All 100% of the registered will attend.

10. If a deposit D is required but it will be refunded upon participation, who and how many will attend after registration? • Suppose all other participants who are like Jane find out that the other activity, that they value at $B2, is available. • If $A2 + D - $B2 < 0, all the 50 other will not attend the activity X. Hence, only 50% of the registered (only those who are like John) will attend. • If $A2 + D - $B2 > 0, all the 50 other will attend the activity X. All 100% of the registered will attend. • In reality, those registered have a distribution of p and a distribution of A and B. An estimation of the participation rate requires assumptions of these distribution and the skills of integration. • In any case, by making D big enough, the organizer can make sure that all registered will participate in the activity.

11. Additional work if interested • Why do we need prior registration at all? • If no deposit is required, but a payment will be given to participants upon participation • Who will register? • Who and how many will attend after registration? • If deposit D1 is required, but an amount of D2 will be given to participants upon participation • Who will register? • Who and how many will attend after registration?

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