Ka-fu Wong University of Hong Kong

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Ka-fu WongUniversity 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?
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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?

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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.

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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
  gt0
• 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 lt 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
  gt0.

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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 gt0
• Suppose all other participants who are like Jane
  find out that the other activity, that they
  value at B2, is available. Because A2 - B2 lt
  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?

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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 -
  Dgt0
• 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 lt 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 - Dgt0.

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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 gt0
• Suppose all other participants who are like Jane
  find out that the other activity, that they
  value at B2, is available. Because A2 - B2 lt
  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?

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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 - Dgt0
• 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 lt 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) - Dgt0.

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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 gt0
• 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 lt 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 gt 0, all the 50 other will
  attend the activity X. All 100 of the registered
  will attend.

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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 lt 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 gt 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.

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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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End