Introduction to the Reserve Ratio

Introduction to the Reserve Ratio The reserve ratio is the fraction of total deposits that a bank keeps on hand as reserves (i.e. cash in the vault). Technically, the reserve ratio can also take the form of a required reserve ratio, or the fraction of deposits that a bank is required to keep on hand as reserves, or an excess reserve ratio, the fraction of total deposits that a bank chooses to keep as reserves above and beyond what it is required to hold. Now that weve explored the conceptual definition, lets look at a question related to the reserve ratio. Suppose the required reserve ratio is 0.2. If an extra $20 billion in reserves is injected into the banking system through an open market purchase of bonds, by how much can demand deposits increase? Would your answer be different if the required reserve ratio was 0.1? First, well examine what the required reserve ratio is. What Is the Reserve Ratio? The reserve ratio is the percentage of depositors bank balances that the banks have on hand. So if a bank has $10 million in deposits, and $1.5 million of those are currently in the bank, then the bank has a reserve ratio of 15%. In most countries, banks are required to keep a minimum percentage of deposits on hand, known as the required reserve ratio.This required reserve ratio is put in place to ensure that banks do not run out of cash on hand to meet the demand for withdrawals. What do the banks do with the money they dont keep on hand? They loan it out to other customers! Knowing this, we can figure out what happens when the money supply increases. When the Federal Reserve buys bonds on the open market, it buys those bonds from investors, increasing the amount of cash those investors hold. They can now do one of two things with the money: Put it in the bank.Use it to make a purchase (such as a consumer good, or a financial investment like a stock or bond) Its possible they could decide to put the money under their mattress or burn it, but generally, the money will either be spent or put into the bank. If every investor who sold a bond put her money in the bank, bank balances would initially increase by $20 billion dollars. Its likely that some of them will spend the money. When they spend the money, theyre essentially transferring the money to someone else. That someone else will now either put the money in the bank or spend it. Eventually, all of that 20 billion dollars will be put into the bank. So bank balances rise by $20 billion. If the reserve ratio is 20%, then the banks are required to keep $4 billion on hand. The other $16 billion they can loan out. What happens to that $16 billion the banks make in loans? Well, it is either put back into banks, or it is spent. But as before, eventually, the money has to find its way back to a bank. So bank balances rise by an additional $16 billion. Since the reserve ratio is 20%, the bank must hold onto $3.2 billion (20% of $16 billion). That leaves $12.8 billion available to be loaned out. Note that the $12.8 billion is 80% of $16 billion, and $16 billion is 80% of $20 billion. In the first period of the cycle, the bank could loan out 80% of $20 billion, in the second period of the cycle, the bank could loan out 80% of 80% of $20 billion, and so on. Thus the amount of money the bank can loan out in some period ​n of the cycle is given by: $20 billion * (80%)n where n represents what period we are in. To think of the problem more generally, we need to define a few variables: Variables Let A be the amount of money injected into the system (in our case, $20 billion dollars)Let r be the required reserve ratio (in our case 20%).Let T be the total amount the bank loans outAs above, n will represent the period we are in. So the amount the bank can lend out in any period is given by: A*(1-r)n This implies that the total amount the bank loans out is: T A*(1-r)1 A*(1-r)2 A*(1-r)3 ... for every period to infinity. Obviously, we cannot directly calculate the amount the bank loans out each period and sum them all together, as there are an infinite number of terms. However, from mathematics we know the following relationship holds for an infinite series: x1 x2 x3 x4 ... x / (1-x) Notice that in our equation each term is multiplied by A. If we pull that out as a common factor we have: T A[(1-r)1 (1-r)2 (1-r)3 ...] Notice that the terms in the square brackets are identical to our infinite series of x terms, with (1-r) replacing x. If we replace x with (1-r), then the series equals (1-r)/(1 - (1 - r)), which simplifies to 1/r - 1. So the total amount the bank loans out is: T A*(1/r - 1) So if A 20 billion and r 20%, then the total amount the bank loans out is: T $20 billion * (1/0.2 - 1) $80 billion. Recall that all the money that is loaned out is eventually put back into the bank. If we want to know how much total deposits go up, we also need to include the original $20 billion that was deposited in the bank. So the total increase is $100 billion dollars. We can represent the total increase in deposits (D) by the formula: D A T But since T A*(1/r - 1), we have after substitution: D A A*(1/r - 1) A*(1/r). So after all this complexity, we are left with the simple formula D A*(1/r). If our required reserve ratio were instead 0.1, total deposits would go up by $200 billion (D $20b * (1/0.1). With the simple formula D A*(1/r) we can quickly and easily determine what effect an open-market sale of bonds will have on the money supply.

The Death of Balder in Norse Mythology

The Death of Balder in Norse Mythology Odin, the king of the Norse gods, often sat upon Hildskialf, the throne of the Aesir gods, with his companions, the two ravens, Hugin (Thought) and Munin (Memory), whispering in his ears. From this position, he could look out on all of the nine worlds. Sometimes his wife Frigg would sit there, too, but she was the only other god who was so privileged. Frigg was the second and favorite wife of Odin, whose daughter she may also have been. She was the only Aesir as clever and knowledgeable about the future as Odin, although her foreknowledge did not depress her as it did her husband. Frigg had her own palace, which was known as Fensalir, where she sat spinning clouds to float above Midgard. Fensalir also served as the afterlife home for married couples who wished to be together. It was a counterpart to the famous home of valiant warriors, Valhalla, where Odin spent much of his time - drinking (he is said to have stopped eating when he heard about the inevitable doom of Ragnarok) with his feasting and fighting companions and the Valkyries. Balder the Handsome The most handsome of the gods was born to Frigg and Odin. He was named Balder (also known as Baldur or Baldr). He was a god of truth and light. Balder was also knowledgeable in healing herbs and runes, which made him a favorite among the people of Midgard. Balder lived in a palace named Breidablik with his wife Nanna (n.b. there is also a Mesopotamian goddess of this name), a vegetation goddess. It was believed that no lie could pass through the walls of Breidablik, home of the god of truth, so when Balder started having frightening nightmares about his own demise, the other Aesir gods took them seriously. Unlike gods in other pantheons, the Norse gods were not immortal. They cataloged everything that might possibly cause Balder harm, from weapons to diseases to creatures. With the list in hand, Balders mother, Frigg, set out to exact assurances from everything in the nine worlds not to harm Balder. This wasnt hard because he was so universally loved. When she had completed her mission, Frigg returned to Gladsheim, the gods meeting hall, for a celebration. After a few rounds of drinks and toasts, the gods decided to test Balders invulnerability. A pebble thrown at Balder bounced off without hurting Balder, in honor of its oath. Larger weapons were used, including Thors axes and all refused to hurt the god. Loki the Trickster Loki is known as a trickster god. Sometimes he was mischievous, but he hadnt really been malicious. The giants were evil, but Loki, who was the son of a giant, hadnt been known as such. It seems his self-appointed job was to stir things up when things were going well. Its a Loki-type action that one wishes to avert when telling an actor to break a leg before a performance. Loki was disturbed by all the gaiety and decided to do something about it, so in disguise as a disgusting old hag, he went to Frigg while she was at Fensalir taking a break from the festivities. What was going on at Gladsheim, he asked her. She said it was a celebration of the god Balder. Loki-in-disguise asked why, then, were people throwing weapons at him? Frigg explained about the promises shed exacted. Loki kept at her asking questions until she finally revealed that there was one thing she hadnt asked because she thought it too small and inconsequential. That one thing was mistletoe. With all the information he needed, Loki set off to the forest to get himself a branch of mistletoe. He then returned to the festivities at Gladsheim and sought out Balders blind brother, Hod, god of darkness, who was in a corner because he couldnt aim and therefore couldnt participate in the test of Balders invulnerability. Loki told Hod he would help him take aim and handed Hod a piece of apparently innocuous mistletoe to throw. Hodur was grateful and accepted the offer, so Loki steered Hods arm. Hod launched the branch, which caught Balder in the chest. Balder died instantly. The gods looked towards Hod and saw Loki beside him. Before they could do anything, Loki fled away. Celebration turned to lamentation since the most beloved of the gods had died. Odin alone was aware of how disastrous this event really was for them all, for he knew that with the loss of light and truth, the end of the world, Ragnarok, was due soon. A funeral pyre was made that was so enormous the gods had to ask the help of the giants. They then placed their most valuable worldly possessions as gifts upon the pyre. Odin placed his golden armband Draupnir. Balders wife fell down dead of grief at the pyre, so her body was placed beside her husbands. [  The most beautiful and beloved of the gods, Balder, son of Odin, had been slain by his blind brother wielding a misletoe shaft aimed by Loki. Balders wife had joined him on the funeral pyre. After their funeral, they were in the world called Niflheim.] An attempt was made to resurrect Balder, but due to more of Lokis mischief, it failed. The goddess of death, Hel, promised that Balder could return to earth if every living creature shed tears of grief for Balder. It looked as though it would work, for everyone loved Balder, but Loki arranged for a single exception. Loki disguised himself as the giantess Thok. As Thok, Loki was too indifferent to cry. And so, Balder could not return to the land of the living. Balder and his wife remained in Niflheim. Another son of Odin, Vali,  revenged  the death of Balder, but not by getting back at  Loki. Instead, Vali slew his brother, the blind god Hod. Loki, who had fled the initial scene of Balders death in Gladhseim, and then re-appeared in disguise as the giantess Thok, tried to get to safety by turning into a salmon. The salmon-Loki hid in a waterfall. But the Aesir, who knew where he was, tried to catch him in a net. Loki was too clever for that and jumped right over the net. Thor, however, was fast enough to catch the leaping fish in his bare hands. Then Loki was bound in a cave with venom dripping onto his body, which caused him to writhe in pain - until the worlds end in Ragnarok. (The story of  Prometheus  has a similar punishment.) Sources Ragnarok. Timelessmyths.com. Roberts, Morgan J. Norse Gods and Heroes. Myths of the World, Reprint edition, Metro Books, December 31, 1899.