Assignment

1. Robinson Crusoe and his friend, Mr. Friday, live on an island. There is a central bank on the island called RBC, Royal Bank of Crusoe. There is also a commercial bank called FBI, the Fifth Bank on the Island. The RBC issues 1 dollar of fiat money (M0) and sets the reserve ratio for the FBI to be 50%.

(1) Suppose the FBI only keeps the required amount of reserves, what is the total amount of money (M1) on the island? Hint: this will be the maximum amount of money given the reserve ratio.

(2) If we write down the balance sheet of the FBI, we can get the following:

Assuming both Robinson and Mr. Friday own the same amount of deposits. Where M0 represents the initial amount of fiat money and M1 represents the total amount of money in the economy, which is the result from last question. You do not need to know the accounting knowledge but can check that now FBI just meets the requirement of the reserves ratio. However, in this case the total amount of fiat money hold by the FBI is merely M0. In other words, if both Robinson and Mr. Friday want to withdraw their money from the FBI before the payment of the loans, the FBI can not afford it and will declare bankruptcy because there is no enough fiat money in FBI's safe. Every day, Robinson tosses a coin and withdraws his deposit if it turns out to be a face. Fortunately, they will never withdraw together and if Robinson withdraws, Mr. Friday will never withdraw before all loans are clear.

So will the FBI declares bankruptcy? Why?

(3) Now instead suppose Mr. Friday will observe Robinson's behavior and thus once Robinson withdraws his deposit from the FBI Mr. Friday will follow. So now what is the probability that the FBI will declare bankruptcy? Hint: Robinson still tosses his coin every day. (This phenomenon is called Bank Run, which occurs in a fractional reserve banking system when a large number of customers withdraw their deposits at the same time because they believe that the financial institution is, or might become, insolvent)

(4) Knowing the fact that both individuals may withdraw together, the FBI decides not to lend anymore and keeps a reserve ratio of 100%. What is the total amount of money on the island now?

2. The economy is under a recession due to a demand shock and thus the short run equilibrium output is lower than the long run natural rate of output. The government and the Fed are planning to intervene. Briefly discuss the advantages and disadvantages of the following plans using the loanable fund model and the ADAS model:

(1) The federal government builds more roads and other public transportations

(2) The Fed decreases the reserve ratio for commercial banks

3. For each of the following examples of "money", briefly discuss whether it satisfies the 3 criteria. If it does, judge whether it is a kind of fiat money.

a. In the mobile game, Pokemon Go, players can earn "pokecoin" via winning battles and use those coins to buy items from the shop inside the game.

b. "Credit cards" are widely used nowadays. People can use credit card to pay for goods they desired and pay back to the credit card company later.

c. McDonald's recently issues "coupons" that can be used when ordering. The coupon has no expiration date and is transferable. One can get a free large drink after purchasing a Big Mac using this coupon.

d. "Tokens" are widely used in many casinos in Las Vegas. Inside each casino, the token issued by the casino can be used to make all kinds of payments (including tips) and it is transferable as well. When leaving, one can exchange tokens into cash or keep a record so that he can use remaining tokens next time.