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

2. 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. 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. 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 $A 1 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 $B 1. John will choose to register if $A 1 - $B 1 >0 Suppose Jane, another typical individual, is willing to pay $A 2 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 $B 2, with a probability p. And, $A 2 - $B 2 0.

5. 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 $A 1 - $B 1 >0 Suppose all other participants who are like Jane find out that the other activity, that they value at $B 2, is available. Because $A 2 - $B 2 < 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. 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 $A 1 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 $B 1. John will choose to register if $A 1 - $B 1 - D>0 Suppose Jane, another typical individual, is willing to pay $A 2 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 $B 2, with a probability p. And, $A 2 - $B 2 0.

7. 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 $A 1 - $B 1 >0 Suppose all other participants who are like Jane find out that the other activity, that they value at $B 2, is available. Because $A 2 - $B 2 < 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. 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 $A 1 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 $B 1. John will choose to register if $A 1 + D - $B 1 - D>0 Suppose Jane, another typical individual, is willing to pay $A 2 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 $B 2, with a probability p. And, $A 2 - $B 2 0.

9. 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 $A 1 + D - $B 1 >0 Suppose all other participants who are like Jane find out that the other activity, that they value at $B 2, is available. If $A 2 + D - $B 2 < 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 $A 2 + D - $B 2 > 0, all the 50 other will attend the activity X. All 100% of the registered will attend.

10. 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 $B 2, is available. If $A 2 + D - $B 2 < 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 $A 2 + D - $B 2 > 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. 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 D 1 is required, but an amount of D 2 will be given to participants upon participation Who will register? Who and how many will attend after registration?

12. 12 End