NUMERICAL PROBLEMS
1. The monetary base is $1,000,000. The public always holds half its money supply as currency and half as deposits. Banks hold 20% of deposits in the form of reserves. Starting with the initial creation of the monetary base that accompanies the purchase by the central bank of $1,000,000 worth of securities from the public, show the consolidated balance sheet of the banks after they first receive deposits, after a first round of loans and redeposits, and after a second round of loans and redeposits.
(Hint: Don't forget that the public keeps only half its money in the form of bank deposits.)Show the balance sheets of the central bank, the banking system, and the public at the end of the process of multiple expansion of loans and deposits. What is the final value of the money supply?
2. Suppose the current price level in the United Kingdom is 128.40, and one year ago the price level was 126. Output is currently £2900, and potential output is £3000 (both in billions of 2015 pounds).
a. What value of the key interest rate would the Bank of England (BoE) choose if it followed the Taylor rule given by Eq. (14.6)?
b. Suppose that one year later, the price level has declined by 0.4%, output has declined by 1.3%, and potential output has increased 3%. In this new situation, what value of the key interest rate would the BoE choose if it followed the Taylor rule? What is the problem with setting the key interest rate to follow the Taylor rule in this case?
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