2. Monetary policy Problem 2.1. Consider a consumer who receives an income of Y at the beginning of each month and spends it evenly throughout the month on consumption. This income is put in a deposit bearing an annual interest rate of R. with monthly capitalization of interest. In order to spend the earned money, the consumer must rst transfer the money to a free but interest-free checking account. However, each transfer - regardless of the amount transferred - costs the consumer time and transaction fees in the total amount of FC (xed cost). a) How much money does the consumer keep on average in the checking account? What does this amount depend on? b) What is the total cost of keeping money in the account? c) How many transfers are made by the consumer in a month? d) Present the money demand function. e) Which money demand determinants are not considered in this model? Problem 2.2. Consider an economy described by the following equations: IS: Y = 2125 15000R LM: Y = 1,25 *%+ 75003 I = 250 6000B where nominal money supply in equilibrium equals M5 = 100. In such an economy, the potential output is 1225. a) Derive the formula of the aggregate demand function. b) Determine the level of prices and output in the long-run equilibrium. Show your answer on a chart. 0) By how much GDP and the prices increase in the short run, if the central bank increases the money supply by 100? Assume that the economy functions in line with the assumptions of the lS-LM model. d) By how much GDP and the prices increase in the long run, if the central bank increases the money supply by 100? Assume that the economy functions in line with assumptions of the classic AS-AD model. e) What is the difference between points (0) and (d)? Describe what happens in the economy between the short- and long-run. Plot both cases on the chart. Problem 2.3. In one economy, the potential output is 1,000 units, inflation expectations equal are = 2% and the natural rate of unemployment is a = 4%. The basic relationships in the economy in the short term can be described by the following equations: Okun's Law: F Y % = 0,12(U, m Philips curve 1:, = ne - 0,2(Ut -5) Calculate by how much GDP must drop for the inflation rate to drop by 1 percentage point (the so-called sacrice ratio)