Exam



Exam 1 – Econ 304 – Chuderewicz – Spring 2015

Name ____________KEY__________________ Last 4 (PSU ID) __________

Section: Please Check:

Sparks ______________

Keller ______________

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 = 240

Test time = 120 minutes

One minute for every two points

To help with time management if spreading time evenly

Question #1 = 55 points..... 28 minutes

Question #2 = 50 points ......25 minutes

Question #3.1 = 35 points.... 17 minutes

Question #3.2 = 45 points ....22 minutes

Question #4 = 55 points..... 27 minutes

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

1. (50 points total) Suppose we have Dagwood, who has a current income of $600K and expected future income of $300K. He has zero in current wealth and zero in expected wealth.

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 negative 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))(600 + 0) + 300 + 0] / (2 + (-.05))

C* = 446.15

[pic]

(10 points for a completely labeled graph – be sure to label the no lending / no borrowing point(s) = NL/NB and the slope of the budget constraint(s))

b) (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 5% (0.05). Recalculate the optimal bundle for Dagwood and add this point to your graph and label as point C*B.

C* = [(1 + (.05))(600 + 0) + 300 + 0] / (2 + (.05))

C* = 453.7

c) (10 points) Did the Fed policy of raising interest rates work in term of lowering current consumption consistent with preventing overheating? Explain being sure to discuss exactly how the substitution and income effects play a role here. Be sure to define what the income and substitution effects are and how they play a role in Dagwood’s decision to alter his previously optimal bundle (we are comparing part a) to part b)). 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.

NO - Dagwood is a saver and cares most about his" 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 + (-.05) (600) = 570 vs. (1 + .05) (600) = 630....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 .95 units 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

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. 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, and label as point C*C (this is of course after the Fed raised rates to 5%).

C* = [(1 + r)(y + a) + yf + af] / (3 + 2r)

C* = [(1 + (.05))(600 + 0) + 300 + 0] / (3 + 2(.05))

cf = 300, c = 600

e) ( 5 points) Janet Yellen and the Fed are again really happy with incoming economic data and are very much worried about overheating and raise real rates again to equal .10 (10%). Given his change in preferences as above in part d), recalculate the optimal bundle for Dagwood and add this point to your graph and label as point C*D.

C* = [(1 + r)(y + a) + yf + af] / (3 + 2r)

C* = [(1 + (.10))(600 + 0) + 300 + 0] / (3 + 2(.10))

cf = 300, c = 600

f) (5 points) Did the Fed policy of raising interest rates work in term of lowering current consumption consistent with preventing overheating? Explain being sure to discuss exactly how the substitution and income effects play a role here.

No, since Dagwood 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 (neither a saver nor a borrower) ...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.

g) (5 points) In the space below, derive and draw Dagwood's savings function (this is after Dagwood went to the doctor. i.e., use the information from parts d) and e) only.

[pic]

h) (5 points) Given your results from part d) and e) above, what are the implications as to

the power of monetary policy with regard to influencing consumption? Assume that there are many consumers in the economy just like Dagwood after he went to the doctor. Please explain.

Absolutely No power

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 new fishing pole cost 2000 fishing hours (this is your output) and the rate of depreciation is 5% (0.05).

The real interest rate is 5% (.05).

And the expected marginal product of capital is given by MPKf = 400 – 10K.

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 = [(.05 + .05) 2000] / (1 - .20) = 250 fishing hours

b) How many fishing poles should you buy to maximize profits? Show work (5 points)

250 = 400 - 10K.........K* = 15

Draw a uc/K graph depicting the state of affairs and label this initial profit maximizing condition as point A.

[pic]

A correctly drawn and completely labeled diagram is worth 10 points

Now conditions change. The following two shocks occur simultaneously:

i) the US $ depreciates and since you buy your poles from abroad, the poles become more expensive and now cost 2400 fishing hours.

ii) the expected marginal product of capital changes and is now MPKf = 420 – 5K.

c) Resolve for K* and show as point B on your uc/K diagram ( 5 points).

uc = [(.05 + .05) 2400] /(1 - 20) = 300

300 = 420 - 5K ..........K* = 24

d) Given the two shocks as above, explain the intuition underlying the change in 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 = 15, uc = 300, MPK = 420 - 5(15) = 345, since uc=300 is LESS than MPK=345, the firm needs to buy 9 fishing poles to get back to profit maximization where uc = MPK = 300 when K=24

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 = 15 .... MPK = 420 - 5(15) = 345 ...... so the Fed needs to get the uc = 345......

345 = [(r + .05) 2400] /(1 - 20)...... r = .065

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.

[pic]

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 = 8 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 = 8 x 10 - (20 + 9w)

w= 6, N = 74, Y = 3182

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]

(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 .

• A goes up from 8 to 9.

b) (5 points) Given the change in NS and A, 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 = 9 x 10 - (30 + 9w)

w= 6, N = 84, Y = 4032

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 question is worth 10 points so please be specific and complete!

@ N = 74, MPN = 9 x 10 - 74 = 16. The wage needed to attract 74 workers is

74 = 30 + 9w... w = 4.888 so @ N = 74, the MPN = 16, w = 4.88. The firm will hire more workers since MPN > w at N = 74. 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 = 84, w = MPN = 6.

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 _____3182__.

And the new Y (after the change in conditions) here ___4032___.

Initial conditions in the goods market

Cd = 1001 + .50(Y-T) – 500r

Id = 590 – 500r

G = 100

T= 100

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 = 3182 - [1001 + .5(3182 - 100) - 500 r ] - 100

S = 540 + 500r

540 + 500r = 590 – 500r

r = .05............S = 565 = I

Draw a Sd = Id diagram in the space below locating this initial equilibrium as point A.

[pic]

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 ALONG WITH A CHANGE IN DESIRED INVESTMENT.

• The desired investment function changes and is now Id = 715 – 500r

• The consumption function is now: Cd = 1301 + .50(Y-T) – 500r

e) (5 points) What could cause such a change in the desired investment function? Please give three specific reasons.

3 uc 'shifters'

1) lower τ

2) higher ITC

3) lower Pk

2 mpk 'shifters'

1) higher A

2) higher AS (animal spirits)

f) (10 points) Given these changes (i.e., changes in A, Y, Id and C) 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 = 4032 - [1301 + .5(4032 - 100) - 500 r ] - 100

S = 665 + 500r

665 + 500r = 715 – 500r

r = .05

S = 690 = 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.

[pic]

Consumption at point A: Cd = 1001 + .50(3182 - 100) – 500(.05) = 2517

Consumption at point B: Cd = 1301 + .50(4032 - 100) – 500(.05) = 3242

The budget constraint shifted out parallel to the right (interest rate did not change) for two reasons 1: income went up from 3182 to 4032 and 2: something shifted the Cd function as in a rise in a, yf , af or CC.

Consistent with the economy being in the midst of a recovery: Y went up - consumption function shifted up, investment went up (most pro-cyclical variable out there)!

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 = 420 – 200rw

Y = 2000

T = 200

G =500

China Initial Conditions

CdF = 480 + .4(YF – TF) – 300rw

IdF = 370 – 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

S = 1600 - [480 + .4(1600 - 400) - 300 r ] - 300

S = 340 + 300r

[380 + 200r] - [420 - 200r] + [340 + 300r] - [370 - 300r] = 0

-70 + 1000r = 0 .............r* = .07

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(.07) = 394

I = 420 - 200(.07) = 406

NX = -12

CHINA

S = 340 + 300(.07) = 361

I = 370 - 300(.07) = 349

NX = + 12

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 absorption (specific with each component of absorption) in each country to its income. Explain (5 points).

The US is spending beyond its means - its absorption (C + I + G) is 12 greater than its income

C = 1106

I = 406

G= 500

C + I + G = 2012.......Y = 2000

China is the saver - its absorption is 12 lower than its means (income)

C = 939

I = 349

G = 300

C + I + G = 1588.......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.

[pic]

15 points for correct and completely labeled diagrams

Now China experiences a shock to their desired investment function so that the new desired investment function in China is given by:

IdF = 400 – 300rw

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)

[380 + 200r] - [420 - 200r] + [340 + 300r] - [400 - 300r] = 0

-100 + 1000r = 0 .............r* = .10

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. as to what happened to absorption in the US and why?

USA

S = 380 + 200(.10) = 400

I = 420 - 200(.10) = 400

NX = 0 (A TRADE BALANCE!)

CHINA

S = 340 + 300(.10) = 370

I = 400 - 300(.10) = 370

NX = 0 (A TRADE BALANCE!)

YES, THE RESULTS ARE CONSISTENT WITH THE US GOING TO AA - THE US WAS SPENDING BEYOND ITS MEANS BEFORE THE SHOCK BY 12, NOW IT IS LIVING WITHIN ITS MEANS - INCOME EQUALS ABSORPTION. WHEN INVESTMENT IN CHINA WENT UP, REAL RATES HAD TO GO UP TO FINANCE IT AND WHEN THAT HAPPENED, ABSORPTION IN THE US FELL - CONSUMPTION - HOUSEHOLDS SUBSTITUTE AWAY FROM CURRENT CONSUMPTION TOWARDS FUTURE CONSUMPTION AND WHEN r RISES, THE UC OF CAPITAL RISES SO INVESTMENT FALLS AS WELL SINCE AT THE SAME K, UC IS GREATER THAN MPK (DUE TO THE HIGHER r NEEDED TO FINANCE THE INCREASE IN CHINA'S INVESTMENT)

HOW THE INVESTMENT WAS FINANCED - INTERCEPT CHANGED BY 30, RATES WENT UP BY .03.......C IN US WENT DOWN BY .03 X 200 = 6 AND I IN US WENT DOWN BY .03 X 200 = 6 ....SO ABSORPTION IN US FELL BY 12, EXACTLY WHAT WAS NEED TO BALANCE TRADE - FOR CHINA, THE CHANGES WERE 9 AND 9 RESPECTIVELY (.03 X 300) FOR A TOTAL OF 18 - 18 + 12 = 30! THIS IS HOW THE SHOCK WAS ABSORBED... AFTER THE SHOCK OF 30.....ABSORPTION IN THIS WORLD ECONOMY FELL BY 30 DUE TO HIGHER RATES.

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