Trading cards: a small scale international trade

Yesterday I went to CW (Comic World) 32 for the sake of HKOSP gathering and IES, but I'm not going to discuss these anime today.
Many of you may have encountered with card collection series in which you have to buy cards of a series in a pack in which you don't know what cards it may contain. Interestingly you can see everyone trying to buy as many packs as they can... There's a stall selling touhou card collection (28 + 2SP) in which 4 in a pack and $10 for 1 pack. They sold more than 1000 packs in one day which is a brilliant result comparing with other goods and considering there's exceptionally smaller visitors to CW.

1)Why buyers tends to get a full set of cards? Why does SP card exist?

This one is quite easy. A full set of cards has a higher storing value (perfectionism), a full set of battling card has a higher tactic value, etc. We assume that SP card are harder to obtain so collector lacks them and wants them, sometimes we say SP card itself has a higher value.

We refer to special cards (SP cards) here. They have a higher value to people in different ways like in tactics (a useful cards), artistic (a beautiful cards or a flashy one), etc. They represents the whole set to attract customers so they exist. Their economical function will be explained later.

2)...And I see crowds staying around the stall and ask others in trading cards, trading 1 card for another. In simplified model, we assume everyone tried to obtain 1 full set. The MB decrease siginificantly at the second same card. Now when both collectors has a distinct excess card which their trading opponents lacks that card, exchanging the card increase each of their benefits so they are willing to trade.

And now what if ones does not have a card for trading? In the monetary society we are living in, transactions can be made in terms of money as well. As long as P > MB they will sell the card. (In case of P=MB, they will sell as well considering in reality storage cost > 0)

3) Trading increase the certainty of the cards and hence they actually harm the primary seller of card package. Why does the existance of market is permitted or even welcomed?

This is the main point of this passage, we will explain this by a simple international trade model.

Where's the comparative advantage?
The cost of a specified card is the average amount/expected amount of $ spent to obtain that card.
When a secondary trader forgone a card they have forgone the avg cost in obtaining the card. Since the cards in an enclosed package is uncertain, some traders would have more the amount in some of the cards, then they have a lower cost to forgone these cards (lower than the international average), then they will "export" cards.

The cost of producing different type of  cards are identical, so the concern is not "how it cost to produce that card" but it's "how much they cost so that they sell a card". Then we have the following analysis:
0)Price bounding (Terms of trade)
Upper limit of expected price > International price > average price
1)The normal cards:
The supply are rather gentle and perfectly elastic after ($P0,Q0). The demand is smaller.
Since normal cards occupies more than special card, the expected price is lower than the international price that the demand in trading is insufficient. The extreme case is that the international price is higher than equilibrium price so they can't sell normal cards.
2)The special cards
The supply are rather steep and perfectly elastic after ($P1,Q1), The demand is larger. In this case the trading is needed while quantity consumed is larger than the original equilibrium. However we buy from the primary seller instead of producing it, so we have to buy from the original seller! i.e. When secondary seller needs to buy from the primary seller. That indirectly increase their selling.

4) And finally, buyers pay more to buy cards than from the primary seller. Then why don't they but cards directly from the primary seller?
It's because market information especially information of goods are valuable. People are willing to pay more to increase their certainty in buying cards.

My first piece of econ crossover, maybe a bit messy. orz