Consider the following Keynesian consumption function: = 30 + 0.4, keeping in mind that indicates disposable income, which can be allocated only between consumption needs and savings. a. Derive the equation for savings. b. What is the defining formula for MPC in general? Explain in English what it means and what it measures. What is the value of MPC for the given consumption function. Interpret the value in English. c. What is the defining formula for MPS (Marginal Propensity to Save) in general. Explain in English what it means and what it measures. What is the value of MPS for the given consumption function. Interpret the value in English. d. Given that disposable income can get split only between consumption and savings, what is the logical relationship between MPC and MPS? e. What are the formulas for APC and APS in general? How should they be interpreted? Derive the expressions for APC and APS given the equations for consumption and savings in this question. f. Given that disposable income can get split only between consumption and savings, what is the logical relationship between APC and APS? g. Looking at the equations above, does, in general, MPC change with changes in disposable income? Under what condition(s) will it remain constant as disposable income changes? What about APC: does it, in general, change with disposable income? Under what condition(s) will it remain constant as disposable income changes?

Plot both consumption and savings relationships on one grid with consumption and saving shown on the vertical axis and disposable income on the horizontal axis. Using the property of the 45o line, explain and indicate where savings would be zero. j. Assuming that the desired aggregate expenditure is defined as the sum of desired consumption and investment expenditures in the absence of a government and foreign trade (AE = C + I). Let's assume that desired investment expenditures (I) is autonomous and fixed at $30 billion. First, given the absence of a government sector to tax economic activity and also pay households via transfer payments, what can be said about aggregate actual disposable income and actual national income? k. Taking into account your answer here, carefully write down the system of equations that define this macro economy? How many unknowns and equations is this system composed of? What is the equilibrium condition that defines the equilibrium actual national income? l. Taking into account your answer to part j, replace the equations you have for the components of AE into its defining expression given to you above. Interpret this equation. m. Given your answer to the previous part, what is the size of the marginal propensity to spend? Interpret it. n. Solve for equilibrium national income and indicate here every step you take. What are the equilibrium levels of desired consumption and investment expenditures> o. Putting actual income on the horizontal axis, precisely plot consumption and investment curves in a graph, and graphically derive the AE curve on the same plot. How can the equilibrium condition be shown on this plot? Clearly show the equilibrium point and the equilibrium national income. p. What is the size of the simple multiplier in this example? Interpret it. q. If due to extreme pessimism of both firms and households about future current desired investment declines to $15 billion and current desired consumption expenditures changes to = 15 + 0.4, explain in English how this affects the position of the curves and the equilibrium national income. Calculate the new equilibrium national income using the concept of the simple multiplier. r. If due to the pessimism about future, on top of the same changes in desired investment and consumption expenditures as in part (Q), the propensity to consume from disposable income household also declined by 62.5%, explain in English how this would all affect the position of the curves and the equilibrium income. This time show these changes in a graph and predict whether equilibrium national income should decline more or less than in previous part (Q). Calculate the new equilibrium using the new simple multiplier given the initial equilibrium. s. Now, calculate the new equilibrium national income after all the changes introduced in previous part (r) by solving the resulting new system of equations. Do you see any differences between the level of equilibrium national income you derive here and your answer to the previous part based on using the multiplier