2023 1 50 points total 5 points for each of 8 parts plus 10 for diagram The | Assignments Online

 

 

 

1.  (50 points total – 5 points for each of 8 parts plus 10 for diagram)

The production technology of a firm is given in the table below.

 

Table 1:  Production Technology of a Firm

Number  of workers	Units of output	MPN
0	0
1	48
2	84
3	108
4	128
5	143
6	155
7	165

 

a. Define the marginal product of labor,, explain how it relates to the production function (with N on horizontal axis and Y on vertical axis) and find the marginal product of labor (MPN) for each level of employment (fill in the third column of table).

 

b. Assume that the price of a unit of output is $10. Calculate the number of workers that will be hired if the nominal wage rate = $190. Calculate the number of workers the firm will hire if the nominal wage is $140. Calculate the number of workers that the firm will hire if the nominal wage is $110.

 

 Draw a production function and real labor demand curve vertically with the PF on top, labeling point A as the wage / price combo of $190 / $10, point B as the $140 / $10 combo, and point C as the $110 / $10 wage / price combo. A correct and completely labeled diagram is worth 10 points

 

c. What could cause wages to fall like this (name and support 2 reasons)?

 

d. Why exactly does the firm’s behavior change when the nominal wage fall like it did,  all else constant? In particular, explain exactly why the firm changes their labor input when nominal wages fall from $190 to $140,all else constant (point A to B). Make sure you refer to the profit maximizing condition when answering this question.

 

e. Let’s return back to the initial conditions in the beginning of part b, with prices at $10 and nominal wages at $190 (point A).  Now we let prices change and fall from $10 to $9.  What could cause such a change (name at least 2 reasons)?

 

f. Locate this ‘new’ point (W= $190, P=$9) as point D on your two diagrams.  Similar to part d) why exactly does the firm’s behavior change when price fall from $10 to $9, all else constant? Make sure you refer to the profit maximizing condition when answering this question, just as you did in part d. above.

 

g. Let’s return to point A, the initial conditions where the nominal wage rate = $190 and the price of a unit of output = $10. Assume that a new technology increases the number of units of output that each worker can produce by 50%.  Calculate the number of workers that the firm will hire and the number of units of output that will be produced (fill in the table below).

 

Table 2: Effects of New Technology

Number  of workers	Units of output	MPN
0	0
1
2
3
4
5
6
7

 

 

Now locate this point as point E on both diagrams.

 

h. Comment on the macroeconomic implications of this technology shock (as in assume many firms in the economy experience similar technology shocks) on:  prices (inflation), employment, the unemployment rate, economic growth, real wages (assume workers can bargain for higher nominal wages), the stock market via the profit implications, and the budgetary implications for the Government (make sure you  refer to each economic variable).

 

2. (50 points total – 5 for each of 8 parts and 10 for diagram)

 

For the new Real World State College season MTV is looking for Penn State students. Students are asked to produce “drama” as a part of their contract. The marginal productivity of labor curve is given by MPN = 135-2N.

 

The supply of Penn State students is given by N_s = 30 + 2 w; where w is the real wage per hour.

 

a)  Compute equilibrium values for the real wage and employment.

 

Illustrate this equilibrium on a labor market diagram in real wage space. Please be sure you label the diagram completely and label this initial equilibrium point as point A.  A correct and completely labeled diagram is worth 10 points

 

b) Now the Penn State student union successfully forces MTV to pay each student a minimum “happy valley living real wage” equal to 25.00 per hour.  That is, 25.00 per hour is the effective real minimum wage.  What is the level of employment now?

 

c)  Compare the number of people willing to work vs. the number of people MTV is willing to hire under this living wage program.  What do we call the difference in these values when the quantity of labor supplied exceeds the quantity of labor demanded?  Add these two points to your diagram and label these points as point(s) B. Make sure you identify the unemployed in your diagram.

 

d) The intuition part 1: Why exactly did we move along the labor demand curve?  In particular, why does the profit maximizing level of labor input change with the living wage program (make sure you write out the profit maximizing condition and explain why it has changed i.e., why does MTV rationally change their quantity demanded of labor the way they did)?

 

e) The intuition part 2.  We also experience a movement along the labor supply curve.  Explain the intuition here as in why are more people are willing to work using and explaining the substitution and income effects associated with labor supply. Which effect dominates and what has happened to the price of leisure given the living wage program?

 

f)  Suppose now that a new course offered by the Drama Department increases the productivity of each student (via an increase in human capital!) so that the NEW marginal product of labor equals MPN = 185 – 2N.  Find the equilibrium ‘market’ clearing wage and level of employment. Please show all work below.  

 

Please depict this new development on your original diagram labeling this new equilibrium point as point C. Be sure to label diagram completely.

 

g)   Compare the welfare of the workers under the two scenarios: 1) the living wage program vs. 2) no living wage program but the productivity shock as in part f.  In other words, are workers better off in part b) or are they better off in part f)? Be sure to explain.

 

h)  .Compare the welfare of the firm, the producer.  Is the firm better off in terms of profits in part b) or in part f)? Be sure to explain (feel free to refer to the plastering example and/or the new economy).

 

3. (40 points total – 5 for each of five parts and 15 points for diagram)

An economy’s aggregate production function is given by Y = A·K·N – N². The marginal product of labor for this production function is MPN = A·K – 2N.

 

a) Assume that A = 2 and K = 16. Suppose that the labor supply function for this economy is given by N^S = 4 + w. Find the equilibrium real wage rate, the full employment level of employment, and the full-employment level of output for this economy.

 

Draw a production function and labor demand curve vertically as we did in class (many times) and label this initial equilibrium point as point A. A correct and completely labeled diagram is worth 15 points

 

b) Suppose that a new innovation leads to an increase in total factor productivity so that A increases to 2.75. Everything else remains as in part a). Find the equilibrium real wage rate, the full employment level of employment, and the full-employment level of output for this economy and label on your diagrams as point B.

 

c) Let’s go back to our initial conditions (point A). Instead of a new innovation impacting the economy, assume that severe weather destroys a portion of the capital stock, so that K = 13. Everything else is as it was in part a). (In particular, A = 2.) 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 C.

 

d) Instead of a new innovation or bad weather impacting the economy (we are back to point A), suppose that there is a change in the supply of labor so that N^S = 7 + w (All else remains as in part a)). (In particular, A = 2 and K = 16.) 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 your diagrams as point D.

 

e)  Give two well supported answers as to why N^s might have changed as it did in part d) above.

 

 

1.      (25 points – 5 points each part) 

a.       On the Colbert Report,  March 17, 2008, Stephen Colbert makes fun of the fact that the unemployment rate fell even though less people are working (feel free to Google it).  Using the formula for the unemployment rate, show how this, the idea that the unemployment rate can fall even though less people are employed, is not as unusual as one may think. Be specific as to what happens, exactly, to the numerator and the denominator of the unemployment rate expression.

We are now going to use real economic data to confirm that this phenomenon, the fact that the unemployment rate can fall along with the employed did occur just as Stephen Colbert said. Stephen was referring to the one month change in the unemployment rate between January  and February 2008.

b.      Go to FRED and using the series UNRATE, confirm that the unemployment rate did fall between these two months (simply report the statistics from FRED)

c.       Using FRED again, search for NPPTTL (these are payrolls – the number of people working) and confirm that payrolls did decline between these two months.

d.      Finally, using FRED once again, search for UNEMPLOY (the number of people unemployed) and confirm that your reasoning in part a) above was correct.

e.       Suppose you are talking with someone, call her Mary,  shortly after this particular report came out. Mary was trying to convince you that this report, showing that the unemployment fell between January and February 2008, clearly indicates that labor market conditions are getting better.  Given that you know the facts, give Mary two specific reasons that suggest that labor market conditions are getting worse rather than better. 

2.      (20 points total, 5 points each part) The table below shows the ‘hypothetical’ basket(s) of consumption goods for a ‘typical’ Penn State college student for 2012 and 2013.  Answer the following questions using the information in the table.

2012 Basket for ‘typical PSU college student’				2013 Basket for ‘typical PSU college student’
Item	Price	Quantity		Item	Price	Quantity
Textbooks	$80	6		Textbooks	$90	6
Rent	$700	1		Rent	$800	1
PSU sporting events	$15	6		PSU sporting events	$20	3
Dinners in State College	$25	6		Dinners in State College	$25	8

a.       Calculate the rate of inflation between 2012 and 2013 assuming 2012 is the base year.  Please show all work.  Note, calculate the rate of inflation using price indexes.

b.      Now update the base year to 2013 and recalculate the rate of inflation between 2012 and 2013.  Again, show all work! Calculate the rate of inflation using price indexes.

c.       Which rate of inflation accounts for the substitution bias?  In your answer, identify and explain why, using relative prices, the substitution that this PSU college student rationally made. 

d.      Calculate the ‘Chain Weighted’ rate of inflation (again, show all work).

 

3.      (10 points) Discuss the problems associated with using the unemployment rate as a gauge of labor market conditions. In your answer, make sure you mention how underemployment, discouraged workers, and working under the table play a role in terms distorting the signal that we would want the unemployment rate and changes in the unemployment rate to send in terms of labor market conditions.

4.      (5 points) Go to FRED and search for UNRATE (the unemployment rate) and NROUST (NAIRU) and using the most recent available  data, compare the two.  How much and in what direction would the actual unemployment rate have to change to get us to full employment = NAIRU?  Note that NROUST is quarterly data so simply use the quarter that includes the month of the most recent UNRATE statistic.

5.      (25 points total) In this problem we are going to calculate real interest rates, both ex-post and ex-ante.  The data you need for this problem are given in the links below:

Nominal one year rates (i)            
Price index  CPI (P)          
Expected Inflation            

 

A couple of notes are in order:

 

Expected inflation data is one year hence – so for example,  expected inflation for the period from July 2010 to July 2011 is given in July 2010 and if you view the data, the expected inflation during this time is 2.7% = π^e.

 

To calculate the actual rate of inflation, for example, during the July 2010 to July 2011 period you need to take the percent change in P = %Δ P.  Using the CPI data, we have the price index equaling 217.6 in 7/2010 (beginning of August given the end of month data) and 225.4 in 7/2011 (end of July, 2011).  Note, this is a 12 month period. The actual rate of inflation during this time is 3.58% = π

 

When using the one year nominal interest rate to calculate the all important real rate(s) of interest we need to be careful.  For example, using the same one year time period (July 2010 – July 2011) we simply use the one year rate given as of July 2010.  Think of buying the bond in July 2010, putting it in a safety deposit box (or under your mattress, a coffee can, etc.) and then cashing it in when it matures in July 2011 (you get your principal times whatever the nominal interest rate is).  In viewing the data, the one year rate in July 2010 is 0.29%.  So clearly (and by design of the Fed), both the ex-ante and ex-post real rate are negative during this period and differ because expected inflation was not equal to actual inflation.

 

a.       (10 points) Calculate the ex-ante and ex-post real rate of interest between June 2008 and June 2009 (note that June 2009 is the last month of the Great recession – the official recovery, began in July of 2009).  Why are these real rates so different? Again, please show all work.

b.      (10 points) We know that most decisions are in part, based on expectations of the future.  Suppose we have two people who are trying to decide whether to consume today (assume it is currently June 2008) or save for the future and consume one year later, in June 2009.  One person, let’s call him Joe,  is basing their decision on the ex-ante real rate of interest like most of us do.  The other person who has a crystal ball, we’ll call her Crystal, can see exactly what the actual rate of inflation is going to be and thus, has perfect foresight and bases their decision on the ex-post real rate.  Given the difference in the ex-ante and ex-post real rates above, who would be more likely to save and who would be more likely to spend? Explain in detail and feel free to use the shopping cart example we used in lecture.

We discussed the ‘evils’ of deflation.

c.       (5 points) Given your response in part b) above, is the behavior of either Joe or Crystal consistent with the ‘evils’ of deflation? Why or why not. Explain.

 

6.       (15 points total) Use the information in “Study shows costs of living for working families leveling off in Pa.” to answer the following questions:

a.       (5 points) Using Allegheny county as the base county, what is the price index in Centre county? In Chester county? Please show your work.

b.      (10 points) If you are currently making $75,000 per year in Centre county, how much would you need to make in Allegheny county to have the same real purchasing power as you have in Centre county?  Answer the same question for Chester county (i.e., how much do you need to make in Chester county to have same purchasing power as you do with $75,000 in Centre county).

7.      (10 points) A friend of mine came to Penn State in the 1970s and told me that sticky buns at the College Diner cost $.75 (75 cents) in December of 1976.  Using the CPI and assuming that the price of sticky buns rose in exact proportion to the CPI, what would the current price of sticky buns have now so that the ‘real price’ of sticky buns remains constant. Use the most recent available data for the CPI and please show work.