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The Diamond and Dybvig model is an economic theory that explains how banks function and why they sometimes face financial crises. Here's an explanation that's simplified for kids around the age of 12:

Imagine you have a piggy bank where you save your money. When you put money into your piggy bank, you trust that it will be safe and you can get it back whenever you want. Banks work in a similar way. People deposit their money into banks, and the banks keep it safe for them.

Now, let's say you and your friend both have piggy banks at the same bank. Sometimes, you may need your money to buy something, but your friend doesn't need his money yet. In the Diamond and Dybvig model, this is called a "bank run." A bank run happens when many people suddenly want to take their money out of the bank at the same time because they're worried the bank might not be able to give it back to them.

The Diamond and Dybvig model explains that banks face challenges during a bank run. They need to have enough money on hand to give back to all the people who want to withdraw their money. But the problem is, banks usually lend out a large portion of the money they receive as loans to other people. So if everyone wants their money back at once, the bank might not have enough cash available.

To prevent this, banks keep a small portion of the deposited money as reserves. Think of it like the bank's emergency fund. The rest of the money is lent out to people who need it, like when your friend borrows some money from the bank to buy a bike. Banks make money by charging interest on these loans.

However, the Diamond and Dybvig model also suggests that banks face a dilemma. If they keep too much money in reserves, they won't be able to make many loans and earn much profit. But if they keep too little, they might run into trouble during a bank run.

So, to summarize, the Diamond and Dybvig model explains how banks store people's money and lend it to others. It also shows how banks try to balance the need to have enough money on hand to give back to depositors while still making loans and earning profits.

Diamond and Dybvig Model: \begin{equation} V = \max\{W, R\cdot D\} \end{equation}

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