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E305 Steve Russell Spring 2024 Solutions for Assignment 1, Part C-2 When we last saw the Seven Kingdoms of Westeros, a private mint owned by Tywin Lannister had produced a large number of coins, called dragons, each of which had a denomination of seven stars. The most recent dragon coins had been minted at an actual mint equivalent of 10.2 stars per Troy ounce, so that each star in these coins represented 1/10.2 (or 5/51) ≈ 0.098 Troy ounce of silver, and each coin contained 7/10.2 (or 35/51) ≈ 0.686 Troy ounce of silver. The mint had been defrauding the public: its original dragon coins had been minted at a mint equivalent of 8½ stars per Troy ounce, and it wanted the public to believe that was still the case, for the more recent ones. Before it began the fraud, each star had represented 1/ 8.5 (or 2/17) ≈ 0.118 Troy ounce of silver, and each (undebased) dragon coin contained 7/ 8.5 (or 14/17) ≈ 0.824 Troy ounce of silver. Afterwards, a star in debased coins represented only 1/10. 2 ≈ 0.098 Troy ounces of silver, and a debased dragon coin contained only 7/10.2 ≈ 0.686 Troy ounces. The debased dragon coins also weighed a bit less than the originals: 49/50 = 0.98 Troy ounce, compared to 1 Troy ounce for the undebased coins. Before the debasement was discovered, a dragon coin of either type could buy 14 loaves of bread. They were believed to contain 7/8.5 = 14/17 (≈ 0.824) Troy ounce of silver, and the price of bread, in monetary silve r, was 1/17 ≈ 0.0588 Troy ounce per loaf. Although a Troy ounce of raw, uncoined silver would trade for 14 loaves of bread, a Troy ounce of silver contained in coins (monetary silver) would buy 17 loaves. The reason for this was the superior convenience of coins for trade. After the debasement was discovered, it continued to take 14/17 ≈ 0.824 Troy ounce of monetary silver to buy 14 loaves of bread. So an undebased dragon coin would still buy 14 loaves of bread. But a debased dragon coin wouldn’t, because it was now known to contain only 7/10.2 (or 35/51) ≈ 0.686 Troy ounces of silver. The price of bread rose from its initial level of 1/2 (0.5) star per loaf to 3/5 (0.6) star per loaf, if the bread was purchased with debased dragon coins. There were 75,000 original, undebased dragon coins in circulation at the beginning of the revolution, along with 110,000 newer, debased dragon coins. Since the new dragon coins were more common, the basic monetary unit of Westeros became the debased-coin star. 15. a. How many debased dragon coins did it now take to buy 14 loaves of bread? A debased coin contained 35/51 Troy ounces of monetary silver, and 14 loaves of bread cost 14/17 Troy ounces of monetary silver. 35 51 6 14 14 2 17 51 17 35 5 5 3 ÷ = × = × = = 1.2 .

2 b. [1] Consequently, how many debased dragon coins did it take to buy an undebased dragon coin? [2] Given that both coins had a denomination of 7 stars, what was the value of a undebased star, in debased stars? [3] And what was the value of a n un debased dragon coin, in debased stars? [1] 1.2, since 1 undebased dragon also will buy 14 loaves of bread. [2] Also 1.2, since an undebased dragon coin is worth 1.2 times as much as a debased dragon, and they’re both represent the same number of stars. [3] 7 × 1.2 = 8.4. 16 . What was the money supply of the Seven Kingdoms, in debased stars? Hint: Remember that the debased dragon coins were worth more than 7 stars. (75,000 × 8.4) + (110,000 × 7) = 630,000 + 770,000 = 1.4 million stars. As we’ve seen, bread was the only final good in the Seven Kingdoms. Total annual production of bread was 14 million loaves. The final- goods velocity of money, in the kingdoms, was 6: the average coin was used to purchase bread six times per year. Additional information for Question 17: The Quantity Theory’s equation of exchange is M V P y × = × . In this equation, M represents the money supply in monetary units (here, stars) and V is the final-goods velocity of money (here, in transactions per year), y is real GDP, and P is a price index for final goods that’s associated with real GDP. In this very simple economy, there is only one final good (bread), so we don’t need to use a price index, and we can think of real GDP as being measured in loaves of bread. Consequently, P represents the price of a loaf of bread, in stars, y represents the total quantity of bread produced, in loaves, and P y × is the total market value of the bread produced, in stars. 17. a. According to the simple quantity theory, what should the price of bread have been, in stars per loaf? Hint: Given the values for M , V and y that you’ve calculated or been given, you should be able to use the equation of exchange to solve for P . M V P y × = × ; 1.4 6 14 8.4 14 P P × = × ⇒ = = 0.6; 0.6 stars/loaf b. At this point in the monetary history of the Seven Kingdoms, were the simple quantity theory and the theory of coin valuation by weight consistent with each other? Yes. They both imply that the price of a debased star should be 0.6 stars/loaf. At this point, a rebellion broke out that led to a revolution in the Seven Kingdoms. King Aerys of House Targaryen was killed and replaced by King Robert of House Baratheon, the leader of the rebellion. The new government in King’s Landing purchased all the private mints, including the Lannister mint – paying generous prices – and took over the coinage and monetary system of

3 the Seven Kingdoms. Lord Petyr Baelish, commonly known as Littlefinger, was appointed Master of Coin. As the title suggests, one of the most important duties of the Master of Coin was managing the government mints. King Robert expected the mints to produce a good deal of revenue for him, in order to feed soldiers who had fought on his side and not yet been demobilized. Under the new monetary system Littlefinger constructed, the basic monetary unit remained the star. But he introduced a new coin, called a “stag,” which had an engraving of a stag (the symbol of House Baratheon) on one side. He ordered the government mints to begin minting silver-based stag coins, setting the mint equivalent at 12.5 stars per Troy ounce . A stag coin weighed a bit less than debased dragon coin: 14/15 ≈ 0.9 33 Troy ounce. He announced that these stag coins would be legal tender, at a rate of 7 stars per coin, for all payments in the Seven Kingdoms. In addition, as a concession to Tywin Lannister – who had intervened in the rebellion on Robert’s behalf, and whose son had killed King Aerys – he announced that the debased dragon coins the Lannister mint had produced also would be legal tender for seven stars (so that stags and debased drgaons had the same denomination), and that the undebased dragon coins that mint had produced would be legal tender for 8.4 stars. 18 . a. How much silver, in Troy ounces, did one star in stag coins represent? The silver mint equivalent was 12.5 stars per Troy ounce. So a star represented 1/12.5 = 2/25 = 0.08 Troy ounce of silver. b. How much silver, in Troy ounces, was there in a stag coin? Since a stag coin had a denomination of 7 stars, it contained 7 × 2/25 = 14/25 = 0.56 Troy ounce of silver. 19 . a. What was the fineness of the stag coins, in percent, rounded to the nearest tenth of a percent? 15 15 14 14 14 25 15 25 14 25 = × = = 3/5 = 0.6 (60 percent) b. What was the debasement rate of stag coins, in percent, relative to the debased dragon coins? We can use the formula ' ' ME ME ME − , where ME is the debased-dragon mint equivalent (10.2) and ' ME is the stag mint equivalent (12.5). We get 12.5 10.2 2.3 0.184 12.5 12.5 − =  (18.4 percent). Initially, Littlefinger announced a mint price of 10 ½ stars per Troy ounce . But he also announced that the mint would buy silver, at that price, only in the form of debased dragon coins. The mint would take care of the task of melting them down.

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4 20. Assuming the price of bread remains 0.6 stars per loaf , paid in any form of legal tender money, a. How much bread could a person buy with an undebased dragon coin? ( Hint: Remember how many stars the coin is legal tender for.) 8.4/0.6 = 14 loaves b. [1] If a person sold an undebased dragon coin to the mint, how many stars in stag coins would he be paid? ( Hint: Remember that even a debased dragon coin did not contain a full Troy ounce of silver.) [2] How much bread could he buy with those coins? [1] 14/17 × 10.5 = 147/17 ≈ 8.65. [2] (147/17)/0.6 ≈ 14.4 loaves. c. Would he be willing to sell the coin to the mint, or not? Yes, since 14.4 > 14. Littlefinger continued this policy until the mint had bought 42,500 undebased dragon coins. 21. a. How many Troy ounces of silver did the mint end up with? 42,500 × 14/17 = 35,000 b. How many stars in stag coins did it pay the sellers? 35,000 × 10.5 = 367,500 c. [1] How many stars in stag coins did it mint? [2] How many stag coins? [1] 35,000 × 12.5 = 437,500 [2] 437,500/7 = 62,500 At this point, Littlefinger reduced the mint price to 9 stars per Troy ounce . 22. Under the same bread-price assumption as in Question 20, a. [1] If a person sold an undebased dragon coin to the mint, how many stars in stag coins would he be paid? [2] How much bread could he buy with those coins? [1] 14/17 × 9 = 126/17 ≈ 7.41. [2] (126/17)/0.6 ≈ 12.35 loaves. b. Would people still be willing to sell undebased coins to the mint? No: 12.35 < 14.

5 c. How many undebased dragon coins were left? (That is, how many hadn’t been sold to the mint?) 75,000 – 42,500 = 32,500 The remaining undebased dragon coins were a bit awkward to use as money, because a seller had to be willing to accept them in payment at a 20 percent premium, even though they looked almost exactly like the more common debased dragon coins. They could be traded, as a commodity, for 14 loaves of bread (see Part C-1), which is the same amount of bread they could be used to buy. And there was always the chance Littlefinger might restore the mint price to 10½ , or higher. So these coins were withdrawn from circulation : either traded for bread, or saved for future trade, or for future sale to the mint. 23. Under the same bread-price assumption as in Question 20, and the current mint price (9 stars per loaf), a. How much bread could a person buy with a debased dragon coin? 7/0.6 = 11 2/3 (close to 11.67) loaves b. [1] If a person sold a debased dragon coin to the mint, how many stars in stag coins would she be paid? [2] How much bread could she buy with the coin? [1] 35/51 × 9 = 315/51 ≈ 6.18. [2] (315/51)/0.6 ≈ 10. 29 loaves. c. Would people be willing to sell debased dragon coins to the mint? No: 10.3 < 11.7 . 24. Under the same bread-price assumption as in Question 20 , and the current mint price (9 stars per loaf), a. How much bread could a person obtain, in trade, for a Troy ounce of raw silver? 14 loaves b. [1] If a person sold a Troy ounce of raw silver to the mint, how many stars in stag coins would he be paid? [2] How much bread could he buy with those coins? [1] 9 [2] 9/ 0.6 ≈ 15 loaves. c. Would people be willing to sell raw silver to the mint? Yes: 15 > 14 .

6 After the mint had produced 27,500 additional stag coins, Littlefinger directed it to reduce the mint price to 7 stars per Troy ounce , the same value the Lannisters had used. 25. Under the same bread-price assumption as in Question 20, and at this mint price, a. Would any additional silver be sold to the mint? No. b. How much silver had the mint purchased, before it reduced the mint price? (27,500 × 7)/12.5 ≈ 15,400 Troy ounces. c. How much had it paid to the sellers of this silver? 15,400 × 9 = 138,600 stars. 26 . a. What was the total number of stars’ worth of stags minted? (62,500 × 7) + (27,500 × 7) = 437,500 + 192,500 = 630,000 b. What was the total number of stars’ worth of stags paid to the people who sold silver to the mint? 367,500 + 138,600 = 506,100 stars c. What was the mint’s gross seigniorage revenue, in stars? 630,000 – 506,100 = 123,900 stars d. What were its minting costs? ( Hint: Use the same minting-costs percentage from Part 1 of this assignment, applied to the total number of stars minted.) 0.1 × 630,000 = 63,000 stars e. What were its net profits? 123,900 – 63,000 = 60,900 stars f. How much bread could it buy with this revenue? 60,900/0.6 = 101,500 loaves of bread 27. a. After all this had played out, what was the money supply of the Seven Kingdoms, in stars? Hint: Remember that the undebased dragons the mint didn’t purchase don’t count (see above), and that the other undebased dragons were sold to the mint and melted down: see above. But the debased dragons do count, along with the stags that were minted. 630,000 + 770,000 = 1.4 million stars

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7 b. According to the quantity theory, what was the price of bread, per loaf? 0.6 stars/loaf, as before, since the money supply did not change. King Robert congratulated Littlefinger on a job well done. He’d obtained more than 100,000 loaves of bread, for the army, by minting new coins. But there had been no increase in the price of bread. 28 . How was this possible? In particular, how could Littlefinger have minted hundreds of thousands of stars’ worth of new coins, without increasing the price level? 90,000 stag coins were minted, but 90.000 debased dragon coins went out of circulation, either by being melted down or by being saved and/or used for trading. Since both types of coins had a denomination of 7 stars, the money supply did not change. 29 . [1] After the revolution, were debased dragon coins and stag coins – both of which had a denomination of seven stars – trading with each other by weight, or by tale? [2] Why was this possible? [1] They were tradiing by tale. [2] This was possible because the purchasing power of both types of coins, if used as money, was at least as great as their value in trade. 30. In the final analysis, where did the revenue Littlefinger earned for the government come from? It came from taking silver out of the old coins. Littlefinger took silver out of old coins, replacing them with an equal number of new coins with less silver. And it was the silver he took out of the old coins that allowed him to min the new coins he kept as seigniorage revenue.

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