Question

# 130 total points

Economics 304

Homework #3 - Dagwood and Homer and the Savings

Function

Due Wednesday, 9/25 at the beginning of class - you must hand in homework in the section you are registered in - no late papers accepted!

Instructions: Please show all work or points will be taken off. Good luck!

1)(40 points) From a couple year ago. (a WSJ article)

With Stocks Surging, Americans Are Saving at 12-Year Low

I

Here are a couple excerpts:

U.S. household net worth has risen from $56 trillion in 2008 to $97 trillion in the third quarter of 2017.

The saving rate may have been depressed in December by households deferring income for 2018 in anticipation of lower tax rates, and by spending in anticipation of a tax windfall this year.

And the graphic:

Suppose we have Dagwood, who has a current income of $180K and expected future income of $100K. He has $ 20K in current wealth (i.e., 'a' = $20K), He has zero expected future wealth (i.e., af = 0).

Dagwood's behavior is consistent with the life-cycle theory of consumption. For one, he perfectly smoothes consumption and two, since he is in his peak earning years, he is saving now so that he can maintain his current level of consumption in the future. Given that Dagwood faces a real interest rate of - 0.04, answer the following questions.

a) (5 points) Calculate Dagwood's optimal consumption bundle showing all work. Then draw a completely labeled graph (the two period consumption model) depicting this initial optimal consumption bundle as point C*A (please use the space below). Note, for all C* calculations, round down to one decimal point.

(15 points for a completely labeled graph - be sure to label the no lending / no borrowing points = NL/NB and the slope of each budget constraint)

b) (5 points) Now Dagwood experiences gains in current wealth, current income, future income and future expected wealth, just like in the article! The new numbers: current income = 250K, current wealth = 50K, expected income = 200K and expected wealth = 100K. Resolve for Dagwood's optimal bundle and label as point C*B on your graph.

c) (5 points) In steps Jerome Powell and the Fed. Given that the economy appears to be on sound footing, the Fed raises interest rates so that the real rate of interest rises to 0.07. Recalculate the optimal bundle for Dagwood and add this point to your graph and label as point C*C. (Note, point C*C incorporates the shock to wealth in part b))

d) (10 points) Is Dagwood better or worse off due to the rise in the real rate of interest? Explain, being sure to discuss exactly how the substitution and income effects play a role here.

2. (40 points total) Dagwood's neighbor, Homer Simpson, does not abide by the life cycle theory of consumption. Homer has a "let's live life like it's our last day" mentality and thus, he prefers to consume more today, relative to the future. In particular, Homer prefers to consume exactly twice as much today (c), relative to consumption next period (cf). Homer's current income equals $150K and his future expected income = $150K. He has no wealth (neither current nor expected) since he lives like today is his last! Homer faces an initial real interest rate of -0.04, just like our friend Dagwood. Please answer the following questions.

a) (5 points) Solve for Homer's optimal consumption basket today (C*) and his optimal consumption basket next period (Cf*). Please provide a completely labeled graph depicting these results and label this point as C*A.

(15 points for a completely labeled graph - be sure to label the no lending / no borrowing points = NL/NB and the slope of each budget constraint)

b) (5 points) Homer goes to work and the rumor being spread around the work place is not good. Homer works in the 'green energy' field and given the new head of the EPA, green energy grants are being cut. Homer is forced to take a pay cut so that his current income (Y) falls to $100K and his future expected income also falls to 100K (a permanent shock to his income). Recalculate the optimal bundle for Homer and add this point to your graph and label as point C*B.

c) (5 points) In steps Jerome Powell and the Fed. Given that the economy appears to be on sound footing, the Fed raises interest rates so that the real rate of interest rises to 0.07. 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 current income in part b))

d) (10 points) Is Homer better or worse off due to the RISE in the real rate of interest? Explain being sure to discuss exactly how the substitution and income effects play a role in Homer's consumption decisions. Also, comment on whether these income and substitution effects work in the same or opposite direction (i.e., is it a tug of war or do they work in the same direction?) in this particular case. Please include actual numbers when discussing the income and substitution effects or points will be taken off.

3)(50 points total) We are now going to graph savings functions for Dagwood and Homer and compare and contrast the slope and shifts of each. Savings in this problem is defined as: S = Y - C.......Y is current income and C is current consumption.

a)(25 points total) We are going to graph two savings functions for Dagwood. The first savings function to draw refers to the savings initially, before Dagwood income, wealth, etc. changes. Calculate the level of savings at the point CA* and label as point A on your diagram. Now you need to do some work. Calculate the level of savings if Dagwood did not receive any changes in income, wealth, expected income, and expected wealth. Hint: you simply need to calculate what Dagwood's consumption would have been under these conditions and then calculate his savings.... label this as point B, connect points A and B and we have Dagwood's first savings function. Be sure to label graph completely, you have real numbers

The second savings function is after the change in Dagwood's income, wealth, expected income and expected wealth. Label as point C, Dagwood's saving at point CB* and then label as point D, Dagwood's saving at point CC*. Connect points C and D and we have the second savings function for Dagwood. Be sure to label your diagram completely including all the shift variables that we are holding constant along any savings function with the signs ( + or - ) above the shift variables.

i) What has happened to Dagwood's savings rate and is it consistent with the WSJ article?

point distribution: 20 points for completely labeled graph along with showing all work to calculate savings for all points: A, B, C, and D and 5 points for answering i) above.

b)(25 points total) We are going to graph two savings functions for Homer. The first savings function to draw refers to the savings initially, before Homer gets the bad news at work. Calculate the level of savings at the point CA* and label as point A on your diagram. Now you need to do some work. Calculate the level of savings if Homer did not receive a change in his current income and expected income and Janet Yellen and the Fed raised interest rates to 0.07. Hint: you simply need to calculate what Homer's consumption would have been under these conditions and then calculate his savings.... label this as point B, connect points A and B and we have Homer's first savings function.

The second savings function is after the change in Homer's current and expected income. Label as point C, Homer's saving at point CB* and then label as point D, Homer's saving at point CC*. Connect points C and D and we have the second savings function for Homer. Be sure to label your diagram completely including all the shift variables that we are holding constant along any savings function with the signs ( + or - ) above the shift variables.

i)( Did Homer's savings increase or decrease because of his change in current and expected income - explain using the definition of savings: S = Y - C.

point distribution: 20 points for completely labeled graph along with showing all work to calculate savings for all points: A, B, C, and D and 5 points for answering i) above.

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