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drawals into an economy affect its income and output? 6. Assume a simple Keynesian depression economy with a multiplier of 4 and an initial equilibrium $4,000. income of $3,000. Saving and investment equal $400, and assume full employment income is a. What is the MPC equal to? The MPS? b. How much would government spending have to rise to move the economy to full employment? C. Assume that the government plans to finance any spending by raising taxes to cover the increase in spending (it intends to run a balanced budget). How much will government spending and taxes have to rise to move the economy to full employment? d. From the initial equilibrium, if investment grows by $100, what will be the new equilibrium level of income and savings? 7. In modern politics, the word Keynesian often is synonymous with "big government" spending. Does this characterization accurately reflect the role of government in spurring economic activity? How would a tax cut be characterized today versus in Keynes's time? 8. Using the aggregate expenditures table below, answer the questions that follow. Income (Y), in US Dollars ($) Consumption (C) in US Dollars ($) Savings (S) in US Dolla 2,200 2,320 -120 2,300 2,380 -80 2,400 2,440 -40 2,500 2,500 0 2,600 2,560 40 2,700 2,620 80 2,800 2,680 120 2,900 2,740 160 3,000 2,800 200 a. Compute the APC when income equals $2,300 and the APS when income equals $2,800. b. Compute the MPC and MPS. C. What does the simple Keynesian multiplier equal? If investment spending is equal to $120, what will be equilibrium income? Generate a graph to show saving, investment, and equilibrium income.Simple linear regression is a statistical method that allows us to summarize and study relationships between two continuous (quantitative) variables: One variable, denoted X, is regarded as the predictor, explanatory, or independent variable. The other variable, denoted Y, is regarded as the response, outcome, or dependent variable. Suppose that we are given n-i.i.d observations { (x;, y;)}"_, from the assumed simple linear regression model Y = BIX + Bo + . Answer the following questions on simple linear regression. 5-a. Denote 1 and Bo as the point estimators of B, and Bo, respectively, that are obtained through the least squares method. Show, step by step, that the two point estimators are unbiased. Derive the least squares estimator of of and determine whether it is unbiased or not. Show your work step by step. 5-b. Calculate _'_1(yi - Bix; - Bo) (Bix, + Bo). Determine whether the point (X, Y) is on the line Y = 1X + Bo. Explain your reasoning mathematically. 5-c. Using the maximum likelihood estimation (MLE) technique, derive a point estimator for the coefficient B1 and the intercept Bo, respectively. Determine whether the point estimators that you obtained via MLE are unbiased or not. Justify your conclusion mathematically. 5-d. Calculate the variance of the four estimators from Questions 5-a and 5-c, respectively. Show your work step by step. 5-e. Suppose that we are using the simple linear regression model Y = B1 X + Bo + 1 while the true model is Y = 1X1 + B2X2 + Bo + 82 where Bo, B1, and B2 are constants. We assume that the distributions of &, and e2 are both N(0,02), i.e., normal distribution with variance o?. We further assume that the two noise variables are uncorrelated. Find the least squares estimator of B, in this case and determine whether the point estimator that you obtain is biased or not. If it is biased, calculate the bias.Chapter 10 question 10 10. Practice similar
