Exam 1 – Econ 304 – Chuderewicz – Fall 2014
Name ______KEY______Last 4 (PSU ID) ______
PLEASE PUT THE FIRST TWO LETTERS OF YOUR LAST NAME ON TOP RIGHT HAND CORNER OF THIS COVER SHEET – THANKS AND GOOD LUCK!!!
Total Points for exam = 240
Test time = 120 minutes
Approximately one minute for every two points
To help with time management if spreading time evenly
Question #1 = 60 points..... 30 minutes
Question #2 = 50 points ...... 25 minutes
Question #3.1 = 35 points.... 17 minutes
Question #3.2 = 45 points ....22 minutes
Question #4 = 50 points..... 25 minutes
Please answer all questions. You must show all work or points will be taken off.
1. (60 points total) This question was motivated by the comic below from October 4, 2014.
We have two consumers, Dagwood and Dagwood's barber who we will refer to from this point on as 'The Barber.' Dagwood and The Barber both prefer to perfectly smooth consumption, consistent with the lifetime theory of consumption. The initial conditions are the same for both consumers and are as follows.
Y (current income) = 300K
a (current wealth) = 0
Yf (expected future income) = 150K
af ( expected future wealth) = 100K
r (the current real rate of interest) = -.05 (negative 5%)
a) (5 points) Calculate Dagwood and The Barber's optimal consumption bundle showing all work. Since conditions are exactly the same for both consumers, you only need to do this calculation once.
C*A = [(1+ (-.05))(300) + 150 + 100] / (2+ (-.05)) = 274.36
THE BARBER af up by 100K.....= 200K
C*B = [(1+ (-.05))(300) + 150 + 200] /( 2+ (-.05)) = 325.64
r up to 10%
DAGWOOD
C*B = [(1+ .10)(300) + 150 + 100] / (2+ .10) = 276.19
THE BARBER
C*C = [(1+.10)(300) + 150 + 200] / (2+ .10) = 323.8
(20 points total) Now draw two completely labeled diagrams (the two period consumption model) depicting these initial optimal consumption bundles as points C*A. Please put the diagrams next to each other with the left diagram representing Dagwood and the right diagram representing The Barber. Note that C*A is exactly the same for both consumers.
10 points for each correct and completely labeled diagram
As you can tell from the comic above, The Barber is very optimistic about his 401K plan which is his retirement money - representing expected wealth = af. As such, The Barber's expected wealth has gone up to 200K (from 100K). Dagwood, on the other hand, is not so excited about the future since his retirement money is in bonds, not stocks, so his expectation of future wealth does not change.
b) (5 points) Calculate The Barber's new optimal consumption bundle showing all work and label as point C*B on the diagram representing The Barber.
Given the most recent payroll report (below) and the long and variable effectiveness lag in monetary policy, Janet Yellen and the Fed decide to raise real rates of interest to .10 (10%). This is the new real rate of interest faced by both consumers.
c) (5 points) Calculate Dagwood’s new optimal consumption bundle depicting his new optimal consumption bundle as point C*B.
d) (5 points) Calculate The Barber's new optimal consumption bundle depicting his new optimal consumption bundle as point C*C.
e) (10 points) Compare the reaction of Dagwood and The Barber, in terms of the change in their current period consumption, given the rise in the real interest rate, all else constant (this is after The Barber changes his af). Be sure to refer to the substitution and income effects and how they are similar/different for each consumer.
DAGWOOD - CONSUME MORE 276.19 VS 274.36 - SAVER CARES ABOUT FINANCING FUTURE CONSUMPTION THE MOST AND THEREFORE CARES MOST ABOUT THE FUTURE VALUE OF PRESENT RESOURCES:
FV = (1 + r) (Y + a), when r rises (-.05) to .10, DAGWOOD IS RICHER - INCOME EFFECT 'SAYS' CONSUME MORE
THE BARBER, THE BORROWER, CONSUME LESS - 323.8 VS 325.64, CARES MOST ABOUT THE PV OF FUTURE RESOURCES (TO FINANCE CURRENT CONSUMPTION): PV = (yF + aF)/ (1 + r), WHEN r RISES, THE PV OF FUTURE RESOURCES FALL - THE BARBER IS POORER, SHOULD CONSUME LESS
THE SUBSTITUTION EFFECT IS THE SAME FOR BOTH, HIGHER r, THE HIGHER THE COST OF PRESENT CONSUMPTION IN TERMS OF FUTURE CONSUMPTION, SUBSTITUTE AWAY FROM CURRENT TO FUTURE CONSUMPTION - IN SUM, SUBSTITUTION EFFECT IMPLIES CONSUME LESS TODAY
FOR DAGWOOD - INCOME AND SUB EFFECTS WORK IN OPPOSITE DIRECTION - INCOME EFFECT WINS
FOR THE BARBER - INCOME AND SUB EFFECTS WORK IN SAME DIRECTION
In the space below, draw the savings functions for both consumers, side by side as you did for the two period consumption model (Dagwood on left, The Barber on right). NOTE IMPORTANTLY THAT I DREW BOTH SAVING FUNCTIONS ON SAME GRAPH SO BARBER IS NECESSARILY ON LEFT (THE BORROWER) AND DAGWOOD (THE SAVER) ON RIGHT .
FOR THE BARBER
POINT A: S = Y - C ...... 300 - 325.64 = - 25.64
POINT B: S = Y - C ...... 300 - 323.8 = - 23.8
FOR DAGWOOD
POINT A: S = Y - C ...... 300 - 274.36 = 25.64
POINT B: S = Y - C ...... 300 - 276.19 = 23.81
10 points total (5 points each) for correct and completely labeled diagrams
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 costs 800 fishing hours (this is your output) and the rate of depreciation is 8% (0.08).
The real interest rate is 2% (.02).
The expected marginal product of capital is given by
MPKf = 200 – 2K.
Initially, there is no tax on capital so tao (τ) = 0% , but this will change.
a) What is the (tax adjusted) user cost of capital and what is this user cost expressed in? (Show work) (5 points)
UC = (.02 + .08) 800 = 80 FISHING HOURS
b) How many fishing poles should you buy to maximize profits? Show work (5 points)
80 = 200 - 2K ...... K* = 60
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
c) Now conditions change. The following two shocks occur simultaneously:
i) the government imposes a 20% tax on capital... so tao (τ) goes from zero to .20 (20%)
ii) the expected marginal product of capital changes and is now MPKf = 230 – 2K.
Resolve for K* and show as point B on your uc/K diagram ( 5 points).
.
UC = (.02 + .08) 800/ (1 - .20) = 100
100 = 230 - 2K ...... K* = 65
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).
AT K = 60 THE FIRM IS NO LONGER MAXIMIZING PROFIT SINCE AT
K = 60, UC UP TO 100, MPK UP TO 230 - 2 (60) = 110. SO AT K = 60, UC < MPK, 100 < 110, BUY 5 MORE FISHING POLES TO LOWER MPK TO = 100 = UC = 100 AND GET BACK TO PROFIT MAXIMIZING!
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).
NEED TO GET USER COST UP TO 110 (MPK = 230 - 2(60) = 110 WHEN K = 60 (THE GOAL)
((r + .18) 800)/ (1 - .20) = 110...... solve for r, r = .03
f) Finally, draw a desired investment diagram (completely labeled with the relevant shift variables 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 tao (τ) and MPKf. 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 = 6 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 = 6 x 10 - [20 + 9w]...... 10w = 40, w* = 4, N* = 56, Y = 1792
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 = 28 + 9w .
· K* goes down from 10 to 8.
b) (5 points) What could cause such a change in labor supply? Please give two specific and well supported reasons.
5 CHOICES
1) LOWER EXPECTED INCOME
2) LOWER WEALTH
3) LOOSER IMMIGRATION LAWS
4) MORE PARTICIPATION
5) DEMOGRAPHICS - MORE PEOPLE ENTERING THE WORKING AGE POPULATION
c) (10 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 = 6 x 8 - [28 + 9w]...... 10w = 20, w* = 2, N* = 46, Y = 1150
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 ___1792_____.
And the new Y (after the change in conditions) here ___1150______.
Initial conditions in the goods market
Cd = 100 + .50(Y-T) – 500r
Id = 796 – 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 = 1792 - [100 + .50(1792 - 100) – 500r] - 100
S = 746 + 500r
746 + 500r = 796 – 500r
r = .05, S = I = 771
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 ALONG WITH A CHANGE IN DESIRED INVESTMENT.
· The desired investment function changes and is now Id = 455 – 500r
e) (5 points) What could cause such a change in the desired investment function? Please give two specific and well supported reasons.
5 CHOICES:
1) HIGHER τ
2) HIGHER PK
3) LOWER ITC,
4) LOWER A,
5) LOWER AS
f) (10 points) Given these changes (i.e., changes in K*, Y, and Id, note, the new Id = 455 – 500r), 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 = 1150 - [100 + .50(1150 - 100) – 500r] - 100
S = 425 + 500r
425 + 500r = 455 – 500r
r = .03, S = I = 440
g) (10 points) Considering this entire problem, are your results consistent with the Great Recession - why or why not? Please be as specific as possible with regard to the changes in your savings function, investment function, and the change in labor supply. Be sure to connect what happened to these 3 functions in this problem to the real world.
SAVINGS FUNCTION - YES, OUTPUT FELL DURING GREAT RECESSION, CONSISTENT WITH THIS EXAMPLE