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If the required reserve ratio is 10 percent, currency in circulation is $400 billion, checkable deposits are $800 billion, and excess reserves total $0.8 billion, then the monetary base is

Keynes’s model of the demand for money suggests that velocity is ________ related to ________.

[25 points] a. Use the Lagrange method to interpolate the following data: b. If you add a data point as follows: use your answer in part a to nd the new polynomial which interpolate all data.  

[25 points] You are given the following system of linear equations: Where C and D are unknowns. What is the approximate solution for this system using the least-squares method?  

The long-run rate of unemployment to which an economy always gravitates is the

*************************Optional Problem [25 points] *************************   Find   where using eigenvalue decomposition of A.    

If aggregate demand equals output,

The quantity theory of inflation indicates that if the aggregate output is growing at 3% per year and the growth rate of money is 5%, then inflation is

[25 Points] Consider the following nonlinear system of equations: Use two iterations of Newton’s method to approximate a solution of this system with the initial guess (x0 , y0)T = (1, 1).  

BONUS:  Suppose you have a linear correlation coefficient of either 1 or -1 (which indicates perfect linear correlation, or that the response variable is wholly determined by a linear polynomial based on the predictor variable). What would be the corresponding value of the test statistic given a test to determine whether r shows positive or negative correlation? Explain your answer in writing below, using relevant formula and mathematical analysis.