Exam



Name ___________ KEY _________________ Last 4 (PSU ID) __________

Section: Please Check:

Section 001 - MWF: 9:05 - 9:55 AM : 114 Steidle Building __________

Section 002 - MWF: 11:15 AM - 12:05 PM : 104 Keller Building ____________

EXAM #1 - Spring 2019

PLEASE PUT THE FIRST TWO LETTERS OF YOUR LAST NAME ON TOP RIGHT HAND CORNER OF THIS COVER SHEET – ONLY NON-PROGRAMMABLE CALCULATORS ALLOWED. THANKS AND GOOD LUCK!!!

Total Points for exam = 310

Test time = 120 minutes

Approximately one minute for every two points

To help with time management if spreading time evenly

Question #1 = 70 points.....27 minutes

Question #2 = 70 points ......27 minutes

Question #3 = 45 points.... 17 minutes

Question #4 = 60 points ....23 minutes

Question #5 = 65 points..... 25 minutes

Please answer all questions. You must show all work or points will be taken off.

1. (60 points total) Suppose we have Dagwood, who has a current income of $300K and expected future income of $200K. He has zero in current wealth and zero in expected wealth.

Dagwood’s behavior is consistent with the life-cycle theory of consumption as his preferences are to perfectly smooth consumption. Given that Dagwood faces a real interest rate of 5% ( 0. 05). Please 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.

C* = [(1 + r)(y + a) + yf + af] / (2 + r)

C* = [(1 + (.05))(300 + 0) + 200 + 0] / (2 + (.05))

C* = 251.22

C* = [(1 + (.00))(300 + 0) + 200 + 0] / (2 + (.0))

C* = 250.00

C* = [(1 + (.00))(300 + 0) + 200 + 0] / (3 + 2(.00))

C* = cf = 166.66 c = 333.33

C* = [(1 + (-.05))(300 + 0) + 200 + 0] / (3 + 2(-.05))

C* = cf = 167.24 c = 334.48

[pic]

(10 points for a completely labeled graph – be sure to label the no lending / no borrowing points =

NL/NB) Use space above.

b) (5 points) Jerome Powell and the Fed are not happy with the state of the economy and worry about an impending recession. As a result, the Fed lowers rates so that the new real rate is 0% (zero percent). Recalculate the optimal bundle for Dagwood and add this point to your graph and label as point C*B

c) (10 points) Did the Fed policy work as in stimulating the economy as measured by the change in Dagwood's current consumption? That is, did Dagwood's consumption rise? Why or why not? Explain using the income and substitution effects. Please use actual numbers to support your answer.

NO..... Since Dagwood is a saver he cares most about his FV of present resources since he is financing future consumption with current (present) resources. When r goes down, FV = (1+r)(y + a) falls and therefore Dagwood is poorer and should spread the pain and consume less in both periods - this is the income effect. With numbers: FV = (1 + (.05)) 300 = 315 vs FV = (1 + (.00)) 300 = 300.

The substitution effect works in the opposite direction - when r goes down so does the price of current consumption = 1+r / 1. The price of current consumption goes from 1.05 units of future consumption to 1.00 units of future consumption - since the price of current consumption has gone down, Dagwood should substitute away from future consumption towards current consumption.

d) (5 points) Now Dagwood goes to the doctor and finds out that he is not as healthy as he thought (too many eating binges!). The doctor tells him that he is fine now but next period he is likely to be ill and that if you had anything in life that you really wanted to do (as in leisure), you should do it now (consume now!). As a result, Dagwood's preferences change so that he prefers to consume like our friend Homer, that is, Dagwood prefers to consume twice as much today relative to next period. Resolve for Dagwood's optimal consumption bundle, given these new preferences. Then draw a NEW graph (the two period consumption model) depicting this new consumption bundle as point C*C. (real rates are still zero %)

[pic]

(10 points for a completely labeled graph – be sure to label the no lending / no borrowing points =

NL/NB) Use space above.

e) (5 points) Jerome Powell and the Fed are still not happy with the state of the economy and as a result, the Fed lowers rates so that the new real rate is -5% (-.05). Recalculate the optimal bundle for Dagwood and add this point to your NEW graph and label as point C*D

f) (10 points) Did the Fed policy work as in stimulating the economy as measured by the change in Dagwood's current consumption? That is, did Dagwood's consumption rise? Why or why not? Explain using the income and substitution effects. Please use actual numbers to support your answer.

YES!..... Since Dagwood is a borrower he cares most about his PV of his future resources since he is financing current consumption with his future resources. When r goes down, PV = (yf + af) / (1 + r) rises and therefore Dagwood is richer and should spread the gain and consume more in both periods - this is the income effect. With numbers: PV = (200 + 0) / (1 + (.00)) = 200 vs PV = (200 + 0) / (1 + (-.05)) = 210.53

The substitution effect works in the same direction - when r goes down so does the price of current consumption = 1+r / 1. The price of current consumption goes from 1.00 units of future consumption to 0.95 units of future consumption - since the price of current consumption has gone down, Dagwood should substitute away from future consumption towards current consumption.

f) (15 points total, 10 points for graph, 5 points for showing work) In the space below, draw two savings functions (on the same diagram) for Dagwood. The first savings function is for the initial conditions, before Dagwood learns from the doctor that he is not as healthy as he thought he was. Label as point A where r = .05 and point B when r = 0% (zero present).

Now draw another savings function representing the conditions after Dagwood went to the doctor and changed his preferences to Homer type preferences. Label as point C where r = 0% (zero percent) and then point D, where r = -.05. You don’t need to put any shift variables for the savings functions since only preferences are changing. Please show work for each of the four points (A, B, C, D)

A: 48.78 = 300 - 251.22

B: 50 = 300 - 250

C: -33.33 = 300 - 333.33

D: -34.48 = 300 - 334.48

[pic]

10 points for correct and completely labeled graph

2) (70 points total) a)(10 points) The 2 graphics below are from previous FOMC meetings, one is from years ago and the other is quite recent. Calculate the neutral federal funds rate (just like on HW #4) for both panels being sure to show all work. Recall, its a weighted average.

LEFT [(1x 2.25)+(1 x 2.5)+(1 x 2.625)+ (4 x 2.75)+ (5 x 3.0)+ (1 x 3.25)+ (1 x 3.5) ] / 14 = 2.87%

RIGHT [(1 x 3.25)+(3 x 3.5)+(8 x 3.75)+ (3 x 4.00) + (2 x 4.25)] / 17 = 3.78%

[pic]

b)(15 points) Now calculate the two neutral (aka, natural, equilibrium) real rates (from both graphics), assuming as always, the inflation target is 2%. Which of the neutral real rates is from years ago and which one is more recent? Why such a big difference between the neutral real rates? Why such a change? Explain and be very specific! This worth 15 points! You may want to draw your graph below and then you can refer to it and use it to support your answer.

r* = 2.87% - 2% = .87% MORE RECENT

r* = 3.78% - 2% = 1.78% YEARS AGO

It has fallen since the aging population (baby boomers) are saving (expected income is falling) which increases saving along with the slow productivity growth lowering the investment in the economy (not worth investing in a low productivity growth environment - opposite of the New Economy). The increase in Savings combined with a decrease in Investment leads to a lower 'equilibrium' or 'natural' or 'neutral' real interest rate.

c)(15 points) Using the information above, draw a goods market equilibrium graph (in a closed economy) depicting exactly what is going on - Label as point A the conditions 'years ago' and label as point B the conditions 'more recent' Please label your graph completely consistent with your explanation above in part b).

[pic]

15 point for ccrrect and completely labeled graph

d)(20 points, 10 points for graph and 10 for explanation). We discussed how Jerome Powell, back in early October of last year (2018), stated that "we are far away from neutral" meaning that the Fed is going to continue raising rates (he spooked the markets with that comment). We also discussed the Dallas Fed article about the neutral funds rates and evaluated the following:

Separately, our economists find that their shorter-run r* estimates now exceed their longer-run estimates (see Chart A-2 for estimates of shorter-run r*). They attribute this divergence to recent fiscal stimulus and other factors that have boosted the confidence of households and firms, leading them to borrow and invest.

In the space below, redraw a goods market equilibrium graph (in a closed economy) as above but start at point B, the most recent conditions. Now add point C, consistent with the idea that the shorter-run r* exceeds the longer-run estimates. Add one percentage point to the real rate calculated from the more recent dot plot (again, point B above) above and label as point C on your diagram. Explain why, in words referring to your graph, the economists shorter-run r* estimates now exceed their longer-run estimates. Make sure you refer to the excerpt from the Dallas Fed (the italics above).

Shorter run r* is higher due to expansionary FISCAL POLICY - lower income taxes (T) will cause savings to fall - (higher short run r*) and the lower corporate tax rate will increase investment (higher short run r*). Also, higher consumer confidence will cause savings to fall (higher short run r*) and the higher business confidence (AS) will also cause investment to rise (higher short run r*)

[pic]

10 points for correct and completely labeled diagram

write your explanation here. ( more room on next page).

e)(10 points) What is meant by the phrase 'two percent is not enough'. In your answer, please make sure you mention what the Fed did to fight the most previous 3 recessions and how this fact relates directly to 'two percent is not enough.' Be sure to use the Fisher equation to help support your answer!

TWO PERCENT IS NOT ENOUGH REFERS TO THE INFLATION TARGET OF TWO PERCENT NOT BEING ENOUGH

The Fed lowered the federal funds rate by an average of 5.97 % to fight the most previous 3 recessions

IF r* is low, around 1%, then the Fed only has 3% of bullets (given inflation target) - if the neutral funds rate stays at 3%, the fed will not have enough ammunition (bullets = 3%) to fight the next recession, this is a BIG DEAL!

iff* = r* + π* ....... 3% = 1% + 2%

IF YOU RAISE INFLATION TARGET THE FED CAN 'BUY' BULLETS TO FIGHT NEXT RECESSION - SAY TO 4% - THAT WOULD GIVE THEM 5% OF RECESSION FIGHTING BULLETS!

iff* = r* + π* ....... 5% = 1% + 4%

3) (45 points) The following equations characterize a country’s economy.

Production function: Y = A·K·N – N2

Marginal product of labor: MPN = A·K – 2N.

where the initial values of A = 10 and K = 10.

The initial labor supply curve is given as: NS = 10 + 2w.

a)(5 points) Find the equilibrium levels of the real wage, employment and output (show work).

w = 10 x 10 - 2 (10 + 2w)

w= 16, N = 42, Y= 2436

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.

[pic]

(20 points for completely labeled and correct diagrams)

We now have a change to our economic conditions

• K goes down from 10 to 8.

b) (5 points) Find the new levels of the equilibrium real wage rate, the full employment level of employment, and the full-employment level of output for this economy and label (on both diagrams) as point B.

w = 10 x 8 - 2[10 + 2w] : w* = 12, N* = 34, Y = 1564

c) (15 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 15 points so please be specific and complete!

When N = 42, MPN = 8 x 10 - 2(42) = -4, the wage the firm needs to pay to attract 42 laborers = 16 as above.... MPN I ......Y - C - G > I ......Y > C + I + G..2500 > 2470...SINCE ABSORPTION (C + I + G) IS LESS THAN Y, r must fall to increase C and I to get back to equilibrium... when r falls by .03, C rises -600 x -.03 = 18, I rises by -400 x -.03 = 12, back to equilibrium where Y = C + I + G (2500 = 2500) or S = I (612 = 612)

f)(10 points) Are your results consistent with the conditions in the US economy since President Trump's election in November of 2016? Why or why not?

NO - NOT REALLY - THE SHOCK TO CONSUMPTION IS NEGATIVE INSTEAD OF POSITIVE - SHOULD BE POSITIVE - HIGHER WEALTH AND CC

INVESTMENT - NO, THE SHOCK IS NEGATIVE, SHOULD BE POSITIVE SINCE tao (corporate taxes) HAS FALLEN AND ANIMAL SPIRITS HAVE RISEN, BOTH POSITIVE ON INVESTMENT

5. (65 points total) We assume that the world consists of two large open economies, USA and China.

USA Initial Conditions

Cd = 420 + 0.5(Y-T) – 300rw

Id = 460 – 200rw

Y = 2400

T = 200

G =500

China Initial Conditions

Cd = 500 + .5(YF – TF) – 300rw

Id = 400 – 200rw

Y = 2000

T = 400

G = 300

a) (10 points) What is the equilibrium interest rate that clears the international goods market? Show all work

USA

S = 2400 - [420 + .5(2400 - 200) - 300 r ] - 500

S = 380 + 300r

CHINA

S = 2000 - [500 + .5(2000 - 400) - 300 r ] - 300

S = 400 + 300r

[380 + 300r] - [460 - 200r] + [400 + 300r] - [400 - 200r] = 0

-80 + 1000r = 0 .............r* = .08

b) (5 points) Now calculate the levels of desired savings and investment for each country at this equilibrium world real interest rate .

USA

S = 380 + 300(.08) = 404

I = 460 - 200(.08) = 444

NX = -40

CHINA

S = 400 + 300(.08) = 424

I = 400 - 200(.08) = 384

NX = + 40

c) (5 points) 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 absorption in each country to its income. Explain.

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 2440, Y = 2400, Absorption in China is 1960, Y =2000.

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.

[pic]

20 points for correct and completely labeled diagrams

We now have a change in conditions: US experiences some economic growth and output rises to 2500. All else remains the same.

d) (10 points) Resolve for the world real interest rate that clears the international goods market 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)

NEW SAVINGS FOR US

S = 2500 - [420 + .5(2500 - 200) - 300 r ] - 500

S = 430 + 300r

[430 + 300r] - [460 - 200r] + [400 + 300r] - [400 - 200r] = 0

-30 + 1000r = 0 .............r* = .03

USA

S = 430 + 300(.03) = 439

I = 460 - 200(.03) = 454

NX = -15

CHINA

S = 400 + 300(.03) = 409

I = 400 - 200(.03) = 394

NX = +15

e) (5 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.

THE US IS HEADED IN THE RIGHT DIRECTION - TRADE DEFICIT FELL FROM 40 TO 15 - STILL A LITTLE WAYS TO GO!

f)(10 points) We know that world output has gone up by 100 and we also know, via the equation below that the world's absorption has to rise by 100 (right hand side of the equation below). Explain where this 100 in additional output was absorbed in each country. Use specific numbers.

Yus + YChina = [C + I + G] US + [C + I + G] China

Real interest rates have fallen by .05... from .08 to .03. As a result, Consumption and Investment in both the US and China will rise.... for the US, C rises by 50 due to the increase in Y (mpc = .5) and rises -300 x -.05 = 15 due to lower r, I in US rises by 10 (-200 x (-.05), Same for China C up by 15, I up by 10- so the fall in r causes absorption to go up by a total of 50 plus the 50 rise in consumption in US due to (induced by) higher income

[pic]

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