Please answer allquestions. You must show all work or points will be taken off.
Please answer all questions. You must show all work or points will be taken off.
1. (60 points total) 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 = $300K and his future expected income = $150K. He has no wealth (neither current nor expected) since he lives like today is his last! Homer faces a real interest rate of - 0.05.(negative 5%). Please answer the following questions.
a) (5 points) State clearly what the slope of any budget line represents, in general, and then refer to this specific case (i.e., what is the slope of Homers budget constraint and what does this mean exactly? Be specific. (5 points)
The BC represents the opportunity set available to the consumer and the slope refers to the relative price of current consumption in term of future consumption. In this particular case, the slope of Homer's budget constraint is - (1 + (-.05)) meaning that the price of one unit of current consumption is .95 (1+ (-.05)) units of future consumption.
b) (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 initial point as C*A.
C* = [(1 + r)(y + a) + yf + af] / (3 + 2r)
C* = [(1 + (-.05))(300 + 0) + 150 + 0] / (3 + 2(-.05))
C* = cf = 150.....c = 300
(10 points for a completely labeled graph – be sure to label the no lending / no borrowing point =
NL/NB) Use space above.
c) (5 points) Janet Yellen and the Fed are finally happy with the way the economy is headed and to be honest, is now fearful of overheating. As such, the Fed tightens and the real rate of interest rises to 0% (0.00). Recalculate the optimal bundle for Homer and add this point to your graph and label as point C*B.
C* = [(1 + ( 0.00))(300 + 0) + 150 + 0] / (3 + 2(0.00))
C* = cf = 150.....c = 300
d) (5 points) Did the Fed policy work as in cooling the economy as measured by the change in Homer's consumption? That is, did Homer's consumption fall? Why or why not? Explain using the income and substitution effects.
No, since Homer is consuming at his NL/NB point, he doesn't care about his FV of current resources nor does he care about his PV of his future resources - he lives paycheck to paycheck ...thus, there is no income effect - there is also no substitution effect so the policy of a higher interest rate to 'cool' the economy did not work.
e) (5 points) Marge is worried about saving for the kids' college education and does some research investigating whether most consumers have spending patterns like Homer. She encounters the life cycle theory of consumption and finds that this popular economic theory suggests that the way to maximize life time utility is to perfectly smooth consumption through time. She also notices that given Homer's age, he should be in a 'savings' mode. Marge discusses this new development with Homer and convinces him to change his preferences to that of a perfect smoother, like our friend Dagwood. Resolve for Homers optimal basket and label as point C*C on a NEW diagram.
C* = [(1 + (0.00))(300 + 0) + 150 + 0] / (2 + (0.00))
C* = 225
DRAW A NEW DIAGRAM DEPICTING THIS NEW POINT AS C*C . (10 points for a completely labeled graph – be sure to label the no lending / no borrowing point = NL/NB) Use the space below.
f) (5 points) Janet Yellen and the Fed still believe the current and future state of the economy is strong and thus, to make sure the economy does not overheat, raise rates again so that the new real rate of interest is .05 (5%). Resolve for Homer’s new optimal consumption point and label as point C*D on the ‘new’ diagram above.
C* = [(1 + (0.05))(300 + 0) + 150 + 0] / (2 + (0.05))
C* = 226.83
h) (5 points) Did this contractionary monetary policy work in term of lowering current consumption (assume there are a bunch of Homers that have changed preferences like this Homer did)? Why or why not, explain using the income and substitution effects. If you were advising Janet Yellen and the Fed, what would you tell her to do to lower consumption and why?
No, HOMER IS NOW A SAVER, for a saver , they care most about the Future Value of present resources which is defined as:
FV = (1 + r) (y + a) so that when r rises, so does their future value of present resources and since they are effectively richer, and that they are a consumption smoother, they will spread the gain and consume more in both periods – with numbers: FV= (1 + 0) (300) = 300 vs. (1 + .05) (300) = 315....not what the Fed had in mind in terms of preventing overheating.
According to the substitution effect, when r rises, the price of present consumption in terms of future consumption goes up so they should substitute away from current consumption towards future consumption – consistent with preventing overheating – more formally, the price of (one unit) current consumption went from 1 unit of future consumption to 1.05 units of future consumption.
Pcc = 1+r/1…… when r rises, so does the price of current consumption in terms of future consumption
I WOULD TELL YELLEN TO LOWER RATES... MAKE THE SAVERS POORER SO THEY CONSUME LESS!
i) (5 points) Without drawing any graphs, compare what Homer’s savings function looked like before Marge talked him into being a smoother to what his savings function looked like after Marge talked him into becoming a perfect smoother. Did the tighter monetary policy work in terms of lowering current consumption in either case?
THE SAVINGS FUNCTION WAS VERTICAL AT ZERO BEFORE HOMER CHANGED HIS PREFERENCES - NO POWER IN POLICY AND NEGATIVELY SLOPED AFTER HE BECAME A PERFECT SMOOTHER AND SAVER. SO POLICY DID NOT WORK IN EITHER CASE.
2. (50 points total)You own a fleet of offshore fishing boats and you need to determine how many fishing poles you need to buy to maximize profits. Please answer the following questions given the information below. Please be sure to SHOW all work!
A brand newfishing pole cost1600fishing hours (this is your output) and the rate of depreciation is 2% (0.02).
The real interest rate is 8% (.08).
And the expected marginal product of capital is given by:
MPKf = 400 – 5K.
There is a tax on capital so tao (τ) = 20% (.20)
a) What is the (tax adjusted) user cost of capital and what is this user cost expressed in?(Show work) (5 points)
uc = [(.08 + .02) 1600] / (1 - .20) = 200 fishing hours
b) How many fishing poles should you buy to maximize profits? Show work(5 points)
200 = 400 - 5K...... K* = 40
Draw a uc/K graph depicting the state of affairs and label this initial profit maximizing condition as point A.
A correctly drawn and completely labeled diagram is worth 10 points
Now conditions change. The following two shocks occur simultaneously:
i) the US $ appreciates and since you buy your poles from abroad, the poles become cheaper and now cost 1400 fishing hours.
ii) the expected marginal product of capital changes and is now MPKf = 300 – 5K.
c) Resolve for K* and show as point B on your uc/K diagram ( 5 points).
uc = [(.08 + .02) 1400] /(1 - .20) = 175
175 = 300 - 5K ...... K* = 25
d) Given the two shocks as above, explain the intuition underlying the changein the profit maximizing level of fishing poles (i.e., why does the firm change its behavior?), making sure you refer to the firm’s profit maximizing condition (write it out!). Be specific and write this like you were a professional economist! Be sure to compare the actual user cost to the actual MPKf after the shocks, holding K constant at its level from part b).(10 points).
@ K = 40, MPK = 100, UC = 175.....UC > MPK ...... SELL 15 FISHING POLES SO THE MPK RISES TO (5 X 15) BY 75 TO 175....BACK TO PROFIT MAXIMIZATION
e) Suppose that the Federal Reserve had a goal to get the capital stock (the number of fishing poles purchased) back to its initial level as in part b. Given the two shocks as above, what would they have to do to the real rate of interest to achieve their objective? Please show all work and I am looking for a specific number (i.e., r = ?). Please add this development to your diagram as point C. (5 points).
WHAT IS MPK WHEN K = 40....MPK = 100, NEED TO GET UC TO = 100
100 = [(r + .02) 1400] /(1 - .20)...... r = .037
f) Finally, draw a desired investment diagram (completely labeled with the relevant shift variables (with the appropriate values as in τ = .20, etc.) noted next to the function in parentheses) depicting the initial equilibrium as point A (simply draw a negatively sloped ID curve going through point A). Label the initial level of desired investment as IdA. Note importantly that we do not have numbers for desired investment, but that’s ok, we are focusing on the change in desired investment. Then show, as point B, the level of desired investment after the change in the price of capital and the change in the expected MPK. Finally, show how the Fed policy maps to your investment diagram and label as point C with the corresponding level of investment labeled as IdC.
A completely labeled and correct diagram is worth 10 points (make sure you include the relevant shift variables in parentheses or points will be taken off).
3. PART 1 (35 points total for this part) This problem is broken into two parts that are totally connected to each other. In this first part of the question, you apply Chapter 3 (labor mkt., etc) material and in PART 2, you get to use Chapter 4 (goods market equilibrium) material. Please take all calculations to two decimal places where appropriate except with real interest rate calculations (PART 2), where you need to take the calculation to three decimal places, if appropriate. PLEASE SHOW ALL WORK AND COMPLETELY LABEL ALL DIAGRAMS.
The following equations characterize a country’s closed economy.
Production function: Y = A·K·N – N2/2
Marginal product of labor: MPN = A·K – N.
where the initial values of A = 10 and K = 10.
The initial labor supply curve is given as: NS = 20 + 9w.
a) (10 points) Find the equilibrium levels of the real wage, employment and output (show work).
w = 10 x 10 - (20 + 9w)
w= 8, N = 92, Y = 4968
In the space below, draw two diagrams vertically with the labor market on the bottom graph and the production function on the top graph. Be sure to label everything including these initial equilibrium points as point A.
(10 points for completely labeled and correct diagrams)
We now have numerous changes to our economic conditions (all is not constant). Think of all these changes happening together, that is, we go from one state of economic affairs to a different state of economic affairs. Below are the changes.
- The labor supply changes and is now: NS = 30 + 9w .
- K goes up to 11.
b) (5 points) Given the change in NS and K, repeat part a) (i.e., find the equilibrium levels of the real wage, employment and output). Add these results to your labor market and production function diagrams respectively and label as point(s) B. Be sure to label the diagram completely with the relevant shift variables in parentheses next to the function.
w = 10 x 11 - (30 + 9w)
w= 8, N = 102, Y = 6018
c) (10 points) Why exactly did the firm change their behavior? To answer, calculate the MPN and w at the same N and compare.Then explain what the firm does and why and what the worker does and why. This questions is worth 10 points so please be specific and complete!
@ N = 92, MPN = 10 x 11 - 92 = 18. The wage needed to attract 92 workers is
92 = 30 + 9w... w = 6.888 so @ N = 92, the MPN = 18, w = 6.88. The firm will hire more workers since MPN > w at N = 92. As they hire workers, the MPN falls and in order to hire more workers, they need to increase the price of leisure.. what we call the real wage. This process will continue until we return to the profit maximizing condition where at N = 102, w = MPN = 8.
3. PART 2 (NEW GRADER – 45 points total for PART 2)
Before we start this problem, put the initial Y as computed in part a) here ____4968______.
And the new Y (after the change in conditions) here ___6018______.
Initial conditions in the goods market
Cd = 1584 + .50(Y-T) – 500r
Id = 800 – 500r
G = 300
T= 200
d) (10 points) Given the initial conditions, solve for the equilibrium real rate of interest (that clears the goods market) and the associated levels of desired savings and desired investment.
S = 4968 - [1584 + .5(4968 - 200) - 500 r ] - 300
S = 700 + 500r
700 + 500r = 800 – 500r
r = .10...... S = 750 = I
Draw a Sd = Id diagram in the space below locating this initial equilibrium as point A.
10 points for correct and completely labeled diagram (be sure to put relevant shift variables in parentheses next to each function).
NOW WE TAKE INTO ACCOUNT THE CHANGES FROM PART 1 (I.E., THE CHANGE IN OUTPUT) ALONG WITH THE CHANGES BELOW:
- The desired investment function changes and is now Id = 1000 – 500r
- The consumption function is now: Cd = 1909 + .50(Y-T) – 500r
e) (5 points) What could cause such a change in the consumption function? Please give three specific reasons.
CF HAS SHIFTED UP!....4 possibilities..only need 3 : a up, Yf up, af up, CC up
f) (10 points) Given these changes (i.e., changes in Y, Id and Cd) calculate the new equilibrium levels of the real interest rate, desired savings and investment. Please add this new equilibrium point to your diagram and label as point B.
S = 6018 - [1909 + .5(6018 - 200) - 500 r ] - 300
S = 665 + 500r
900 + 500r = 1000 – 500r
r = .10
S = 950 = I
g) (10 points) - (5 points for discussion and 5 points for correct and completely labeled diagram) Now it is time to apply your knowledge of the 2 period consumption model to this problem. In the space below, draw and use the two period consumption model and depict the movement from point A to point B. Assume that the consumer is a borrower and a perfect smoother so the no-lending no-borrowing point is to the left (west) of the consumption points. Be sure to calculate the actual level of consumption before (point A) and after (point B) all the changes and add these actual numbers to your graph. Explain why your graph changed the way it did. Make sure you label your graph completely. Now the discussion: Are the results with regard to the change in income, change in consumption, and the change in investment consistent with the economy heading into a recession or consistent with the economy in the midst of a recovery. Please explain and be as specific as possible.
Cd = 1584 + .50(4968 - 200) – 500(.10)
Cd = 3918
Cd = 1909 + .50(6018 - 200) – 500(.10)
Cd = 4768
Consumption went up for two reasons: an increase in Y and an increase in the consumption function … either a rise in a, af, yf, or CC - SINCE Y, I, AND C ALL WENT UP IT IS CONSISTENT WITH A RECOVERY!!
4. (55 points total) We assume that the world consists of two large open economies, USA and China.
USA Initial Conditions
Cd = 400 + 0.4(Y-T) – 200rw
Id = 410 – 200rw
Y = 2000
T = 200
G =500
China Initial Conditions
CdF = 480 + .4(YF – TF) – 300rw
IdF = 360 – 300rw
YF = 1600
TF = 400
GF = 300
a) What is the equilibrium interest rate that clears the international goods market? Show all work (10 points).
USA
S = 2000 - [400 + .4(2000 - 200) - 200 r ] - 500
S = 380 + 200r
CHINA
S = 1600 - [480 + .4(1600 - 400) - 300 r ] - 300
S = 340 + 300r
[380 + 200r] - [410-200r] + [340 + 300r] - [360 -300r] = 0
-50 + 1000r = 0 ...... r* = .05
b) Now calculate the levels of desired savings and investment for each country at this equilibrium world real interest rate (5 points).
USA
S = 380 + 200(.05) = 390
I = 410-200(.05) = 400
NX = -10
CHINA
S = 340 + 300(.05) = 355
I =360 -300(.05) = 345
NX = + 10
c) Which country is ‘spending beyond its means’ and which country is the saver? What exactly do we mean by the phrase ‘spending beyond its means’ in this context. Be sure to define and use the word absorption in your answer and compare the level of in each country to its income. Explain (5 points).
USA is spending beyond its means - by this phrase we mean absorption (C + I + G) is greater that the income we generate Y. Absorption in the US is 2010, Y = 2000, Absorption in China is 1590, Y =1600.
Draw two diagrams side by side, with the US on the left and the China on right. Locate this initial equilibrium as points A on both diagrams Be sure to label diagram completely with only the relevant shift variables in parentheses.
15 points for correct and completely labeled diagrams
Now the Chinese Fiscal authorities decide to increase government purchases by 25 to equal 325. We assume that the government spending multiplier is zero.
d) (10 points) Resolve for the world real interest rate that clears the international goods markets along with the ‘new’ Sd and Id for each country and add these results to your diagram labeling this new equilibrium as point B on both of your diagrams. (10 points)
China's saving function falls by 25 = 315 + 300r
S = 1600 - [480 + .4(1600 - 400) - 300 r ] - 325
S = 315 + 300r
[380 + 200r] - [410-200r] + [315 + 300r] - [360 -300r] = 0
-75 + 1000r = 0 ...... r* = .075
USA
S = 380 + 200(.075) = 395
I = 410-200(.075) = 395
NX = 0
CHINA
S = 315 + 300(.075) = 337.5
I =360 -300(.075) = 337.5
NX = + 0
e) (10 points) Now comment on what has happened to the trade balance for each country and relate to the movie clip from Colbert about spending beyond our means. Recall that Fareed Zakaria (the guest) suggested that we (the US) needed to go to alcoholics anonymous (AA). Are your results consistent with the US going to AA? Why or why not? Explain and please be specific. What has happened to absorption in the US and why? How exactly was the 25 increase in G in china financed?
YES , the US has gone to AA since we are not spending beyond our means anymore ---- Absorption (C + I + G) = Y !!! Absorption in the US fell since real world interest rates had to go up to finance the increase in G in China. In particular, rates went up by 2.5% (.025) and since the parameter on r in both the Consumption function and Investment function in the US is 200, C and I both fall by 5 (.025 x 200) which means that absorption in the US fell by 10, which is exactly consistent with going to AA. In China, those same parameters are 300 so C and I in China both fall by 7.5 (.025 x 300) which totals 15. A fall in C and I in US = 10, the fall in C and I in China = 15 - that is how the G in China is financed. C falls since the price of current consumption rises and consumers substitute away from current consumption to future consumption and when r rises, at the same K, uc > MPK, firms sell machines (I falls) until MPK rises to the higher uc caused by the higher r!
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