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1. Suppose there is a market for Pokemon trading card packets, and each packet contains a random combination of potentially valuable cards. Sellers offer packets for sale, and have X-ray machines to determine the value of the in each packet ahead of time (which buyers know about). Buyers are unaware. of the value of the packet, but know the probability is uniformly distributed between $50 and $350. Let the seller have baskets displayed with packets of ranging expected value (e.g., $50,$50−75,$50−100, ete.) A) If buyers and sellers value Pokemon trading card packets the same (i.e., at their realized market value), explain how many sales will occur. B) If buyers value Pokemon trading card packets for more than the market value of the cards, say at a premium of 20% because they get enjoyment from playing the game, up to what range basket will be sales occur? C) What is the minimum premium on the buyer's evaluation of Pokemon trading card packets to ensur sales occur from every basket (that is, up to the range of $50−350 )?

Answer :

If buyers and sellers value the packets equally, there will be sales for all baskets displayed. If buyers value the packets at a premium, sales will occur for baskets within the range where the premium makes the purchase worthwhile. To ensure sales from every basket, the minimum premium should cover the entire potential value range.

In this scenario, there is a market for Pokemon trading card packets, where sellers use X-ray machines to determine the value of the cards inside each packet. Buyers, however, are unaware of the value and only know that it is uniformly distributed between $50 and $350.

A) If buyers and sellers value the packets equally, meaning they see them as worth their market value, then there will be sales for all the baskets displayed by the sellers. This is because the buyers are willing to pay the market value for the packets, regardless of the potential value inside.

B) If buyers value the packets more than the market value, say at a premium of 20% due to the enjoyment they get from playing the game, sales will occur for the baskets within the range where the premium still makes the purchase worthwhile. For example, if a packet has a potential value range of $50-$75, buyers would be willing to pay up to 20% more, or $60-$90, for it.

C) To ensure sales occur from every basket, meaning buyers are willing to purchase packets from the entire range of $50-$350, the minimum premium on the buyer's evaluation of the packets should be enough to cover the potential value range. For example, if a packet has a potential value range of $50-$350, the minimum premium should be at least $300 (the difference between the maximum and minimum value) to ensure buyers are willing to purchase it.

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