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Independent random samples of size n, and n, are taken from the normal populations N(1,of) and N(#2,02 ) respectively. (i) Write down the sampling distributions of X, and X2 and hence determine the sampling distribution of X1 - X2 , the difference between the sample means. (ii) Now assume that of = o} = 02 (a) Express the sampling distribution of X - X, in standard normal form. (b) State the sampling distribution of (m - D)S/ + (12 - 1)S] (c) Using the N(0,1) distribution from (a) and the x- distribution from (b), apply the definition of the / distribution to find the sampling distribution of X - X, when o is unknown.1. With reference to the Federal Reserve's M1 and M2 measures of the money supply, please indicate whether funds held in each of the forms listed below are included only in M1, only in M2, in both M1 and M2, or in neither M1 nor M2. . Money market mutual fund shares. b. Bank reserves. C. Demand deposits. d. Small (under $100,000) certificates of deposit. e. Currency in circulation. 2. Suppose that the Federal Reserve conducts an open market operation in which it purchases $100 in US Treasury bonds from a private saver. a. In an economy without banks, by how much, in dollar terms, will the total money supply increase as a result of this open market operation? b. In an economy with banks in which all members of the nonbank public immediately deposit all of the currency they receive, but in which all banks engage in 100 percent reserve banking, by how much will the total money supply increase as a result of this open market operation? C. In an economy with banks, in which all banks choose a 10% reserve ratio and in which all members of the nonbank public immediately deposit all of the currency they receive, by how much will the total money supply increase as a result of this open market operation? d. In an economy with banks, in which all banks choose a 10% reserve ratio, but in which all members of the nonbank public hold 50% of the funds they receive as currency and deposit the remaining 50%, will the change in the total money supply resulting from this open market operation be greater than or less than the amount you answered for part (c), above? 2 3. Please answer the following questions, regarding the Federal Reserve's federal funds rate targeting strategy. a. Suppose that the Federal Reserve wants to hold its federal funds rate target constant but banks' demand for reserves decreases at any given interest rate. When faced with this shift in demand, what does the Fed have to do to keep the federal funds rate near its target: does it have to conduct an open market operation in which it buys US Treasury bonds or an open market operation in which it sells US Treasury bonds? b. Suppose instead that banks' demand for reserves at any given interest rate remains unchanged, but that the Federal Reserve wants to increase its target for the federal funds rate. What does the Fed have to do to make the equilibrium federal funds rate rise to match the new, higher target: does it have to conduct an open market operation in which it buys US Treasury bonds or an open market operation in which it sells US Treasury bonds?4. Suppose that two banks - the First National Bank and the Second National Bank - have balance sheets as shown below. For both banks, as in our in-class discussions, "other assets" simply refers to the value of bank buildings, office equipment, ATM machines, and other physical assets that the bank owns and uses in the course of its day-to-day operations. First National Bank Assets Liabilities Reserves $10 Deposits $100 Loans $130 Shareholders' Equity $50 Other Assets $10 Second National Bank Assets Liabilities Reserves $50 Deposits $100 Loans $50 Shareholders' Equity $10 Other Assets $10 a. Suppose the First National Bank experiences a $40 deposit outflow. Is the First National Bank illiquid, insolvent, or neither? b. Suppose the Second National Bank experiences a $40 deposit outflow. Is the Second National Bank illiquid, insolvent, or neither? C. Now suppose instead that nothing happens to the First National Bank's deposits, but that some of the consumers and businesses who borrowed from the First National Bank default on their loans, so that the First National Bank's manager is forced to conclude that $40 in loans will never be repaid. Is the First National Bank illiquid, insolvent, or neither? d. Likewise, suppose that nothing happens to the Second National Bank's deposits, but that some of the consumers and businesses who borrowed from the Second National Bank default on their loans, so that the Second National Bank's manager is forced to conclude that $40 in loans will never be repaid. Is the Second National Bank illiquid, insolvent, or neither? W 5. Consider a supply and demand diagram for money like the one we studied in class, with the quantity of money on the horizontal (x) axis and the "goods price of money" on the vertical (y) axis. a. Suppose first that real GDP rises and that, as a result, the consumers who and firms that are buying more goods and services want to hold more money at any given level of prices. In the diagram, will this shift the demand curve for money to the left or to the right? b. As a result of this shift in the money demand curve, what will happen to the economywide level of prices - that is, to the "dollar price of goods" - will it rise, fall, or stay the same? C. Now, suppose instead that the demand curve for money remains unchanged, but that the Federal Reserve conducts an open market operation that works to increase the money supply. In the diagram, will this shift the supply curve for money to the left or to the right? d. As a result of this shift in the money supply curve, what will happen to the economywide level of prices - that is, to the "dollar price of goods" - will it rise, fall, or stay the same? 6. Please indicate whether each of the events listed below explains: why the aggregate demand curve slopes down, why the aggregate demand curve might shift, why the short-run aggregate supply curve slopes up, or why the short-run aggregate supply curve might shift. (Note: in each case, only one of these four possibilities will be true). a. Workers, expecting higher inflation in the future, succeed in negotiating for higher wages today. b. The economywide level of prices falls, so that the real value of monetary wealth rises; hence, consumers are willing to buy more goods and services. C. Business confidence improves, leading firms to invest more. d. Consumer confidence improves, leading consumers to spend more.7. Suppose that the Federal Reserve acts to increase the money supply. a. In the aggregate demand/aggregate supply diagram, will this monetary policy action work initially to shift the aggregate demand curve, the short-run aggregate supply curve, or the long-run aggregate supply curve? (Note: focusing for now on just the short-run effects of the change in policy, only one of these curves will shift.) b. In which direction will the curve you mentioned above shift: to the left or to the right? When the curve you mentioned above shifts, what will the short-run effect on the economywide level of prices be: with it rise, fall, or stay the same? d. When the curve you mentioned above shifts, what will the short-run effect on real GDP be: will it rise, fall, or stay the same? e. When the curve you mentioned above shifts, what will the short-run effect on unemployment be: will it rise, fall, or stay the same? 8. This last question builds directly on the previous one. Suppose that after observing the short-run effects of the increase in the money supply, the Federal Reserve decides not to reverse that policy action and, instead, leaves the money supply at its new, higher level permanently. a. Given that the Federal Reserve does not reverse its initial policy action, how will the economy move from the short-run equilibrium you described in question 7, above, to a new long-run equilibrium: through a shift in the aggregate demand curve, through a shift in the short-run aggregate supply curve, or through a shift in the long-run aggregate supply curve? (Note: focusing now just on the transition from the short run to the long run, only one of these curves will shift.) b. In which direction will the curve you mentioned above shift: to the left or to the right? C. Compared to its level in the initial long-run equilibrium, will the economywide level of prices in the new long-run equilibrium be higher, lower, or the same? d. Compared to its level in the initial long-run equilibrium, will real GDP in the new long-run equilibrium be higher, lower, or the same