E the fed decides to conduct massive amounts of open

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e. The Fed decides to conduct massive amounts of open market purchases and get the real rate of interest all the way down to -5% Recalculate the optimal bundle for Homer and add this point to your graph and label as point C* C . (Note, point C* C incorporates the shock to Homer’s future income in part c). 8 Homer is better off because both his future and current consumption has increased.

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c* = c f * = f. Is Homer better or worse off due to the fall in the real rate of interest? Explain be- ing sure to discuss exactly how the substitution and income effects play a role in Homer's consumption decisions. rates of interest) on consumption, all else constant? To answer this question, as- sume we have an equal amount of "Dagwoods" and "Homers" so we can simply add the change in Dagwood's consumption to the change in Homer's consump- tion. Please give the actual change in consumption, given this expansionary pol- icy. 9 Since Homer is a spender, he is better off with lowering interest rates. He will substitute spending for saving, allowing his consumption to increase. Since he is not earning a negative interest rate from saving, he does not lose money like Dagwood.
Change in Dagwood’s consumption: Change in Homer’s consumption: Net change in consumption: b. Now consider the case where Homer is credit constrained and thus, cannot qualify for cheap loans since his balance sheet is a wreck. As such, the real rate of inter- est that Homer faces is 10% (r = 0.10), and not the ultra-low negative real rate = -.05 that Dagwood (who has a solid balance sheet) faces. Please re-answer part a) above, assuming that Homer faces a real rate of 0.10 and Dagwood faces a real rate of (-.05). Use the actual numbers, that is, add the change in Dagwood's con- sumption (you already did this in 3a) to the change in Homer's consumption, given that he faces a real rate of 0.10, all else constant (i.e., after his y f rose). Change in Dagwood’s consumption: Change in Homer’s consumption: Net change in consumption: c. Are your results consistent with this graph of Personal Consumption Expenditures from FRED? Why or why not? No it is not consistent with the graph of personal consumption expenditures from FRED because their graph is s increasing in the most recent years while ours is decreasing.

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We are now going to derive and draw (depict) two desired savings functions for Homer and Dagwood respectively. Note importantly that savings in the present context is defined simply as y-c, that is, current income minus current consumption. Note also that savings can be positive or negative, it depends on whether you are a saver or borrower. In this assignment, Homer is the borrower so his savings is negative where Dagwood is the saver, and thus, his savings are positive. To derive a savings function we let real interest rates vary and map out the corresponding change in desired savings, all else constant. d. Using the results from 1c and 1e, where a = \$20K, derive the desired savings function (for Dagwood) labeling the point from 1c as point A and the results from 1e as point B. Connect the points and we have the savings function for Dagwood.

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