To: IQBAL LATIF who wrote (44735 ) 10/2/2003 3:47:13 AM From: IQBAL LATIF Respond to of 50167 One Hundred Interesting Mathematical Calculations, Puzzles, and Amusements: Number 20: The Federal Reserve Problem The Federal Reserve Problem A man named Alan Greenspan is Chair of the Federal Reserve Board, and Chair of the Federal Reserve System's Open Market Committee. The Federal Reserve is our country's central bank: it is responsible for setting interest rates. The interest rate is set in percent per year. Currently, the interest rate on short-term U.S. Treasury bonds is one percent per year: buy $1,000 of Treasury bonds now, and the U.S. government will pay you $1,000(1 + 1%) = $1,000(1.01) = $1,010 back in a year. Interest rates matter because the higher the interest rate the less likely companies are to spend money building new buildings and factories and buying new machines. When interest rates are high, they say, "Couldn't we make more money by lending out our cash than by using it to build new buildings and factories and buy more machines to make more stuff to sell?" When interest rates are low, they say, "Couldn't we make more money by taking some of the cash we loaned out--the people who borrowed it are hardly paying us any interest, after all--and use it instead to build new buildings and factories and buy more machines to make more stuff to sell?" When interest rates are high, spending on buildings, factories, and machines is low. People who work in construction or machine making lose their jobs. As they lose their jobs, they stop buying as much for their households, and this means that businesses that make the things they would have bought find themselves losing money and yet more people lose their jobs. The Federal Reserve staff calculate that the relationship between the country's unemployment rate and interest rates is: u = x + 0.6(r) Where u is the unemployment rate (a number like 6%, or .06), r is the interest rate (a number like 1%, .01), and x is a number that jumps around over time and represents the strength of other forms of demand--it is the result of the combination of consumers' optimism, government spending, foreign demand for U.S.-made products, and a lot of other factors that the Federal Reserve staff tracks. Just before September 11, 2001, the Federal Reserve staff believed that x was equal to 1.4% (.014), and the Federal Reserve's Open Market Committee had set the interest rate r to 6%. What does the equation above predict the value of the unemployment rate would be? In fact, the unemployment rate on the eve of September 11, 2001 was about 5%, and that made the Federal Reserve happy. The Federal Reserve is charged by law with avoiding inflation--unwarranted rises in prices--and it fears that an unemployment rate below 5% produces rising inflation. Thus the Federal Reserve wants to keep the unemployment rate from going below 5% (because it is supposed to keep inflation from rising), and the Federal Reserve wants to keep the unemployment rate from going above 5% (because unemployment is a bad thing: the more people are unemployed, the more people are poor and unhappy). Then came the terrible events of September 11, 2001. Their effects on the economy are perhaps least important, but I think about them because economics is what I do. The terror-attack made a lot of businesses worried about spending money on factories, other buildings, and machines. In the judgment of the Federal Reserve staff, the terror-attack on September 11, 2001, increased the number x in the equation above from 0.014 to 0.044. What should the Federal Reserve have done in response if it wanted to keep the unemployment rate from rising above 5%? In fact, the Federal Reserve did reduce interest rate r to 1%. But unfortunately it looks like the number x increased not to .044 but to .054, so we have a current unemployment rate of... what? Now the Federal Reserve has a problem. It doesn't want to reduce the interest rate r even more, because it fears that if the interest rate is lower than 1% that a lot of banks will find it impossible to make money, and will close down. So right now the Federal Reserve is sitting around hoping that the number x in the equation above is about to go down, so that the unemployment rate will soon fall from 6% down to 5%. Posted by DeLong at 04:38 PM | Permanent Link