Numeric Assignment, 2 Part.

Question Description

Part1

The labor share of income in the US.

For this problem, you will learn to use data from FRED. FRED is a repository of economic
data. For more information about FRED, consult the Introduction to FRED document
on the course website and/or ask your TA or course instructor.

Download the following data from FRED:

Series A
National income (A032RC1A027NBEA):
http://research.stlouisfed.org/fred2/series/A032RC1A027NBEA (Links to an external site.)

Series B
National income: Compensation of employees (A033RC1A027NBEA):
http://research.stlouisfed.org/fred2/series/A033RC1A027NBEA (Links to an external site.)

(Links to an external site.)Be sure that the data frequency is annual (Click the Edit Graph and choose ” Annual” in data frequency ). The date range is from January 1, 1947 to the most recent observations available, Jan 01, 2019.

(a) Use the data that you’ve obtained to create a measure of the labor share of total income by dividing employee compensation by national income for each year.

Hint1: Labor share of total income = LaTeX: Income:paid:to:labor:text{series B}div total:income:text{series A} $I$ n c o m e p a i d t o l a b o r series B ÷ t o t a l i n c o m e series A. You will get a series includes 73 numbers for 73 years.

Hint2: Use Excel.

Answer the following:
i. What is the average labor share of total income?
ii. In which year did labor receive the highest share of income? What was the share?
iii. In which year did labor receive the lowest share of income? What was the share?

(b) Plotting the labor share of income for the US with the y-axis ranging from 0 to 1 and with the x-axis represents time. Make sure that your plot is clearly labeled.

Part2

Instructions:
Follow the prompt below. You will need to create a spreadsheet. To do so, you may use any spreadsheet software, for example, Excel (available to UCI students here (https://www.oit.uci.edu/help/microsoft/software-for-students/office-365-pro-plus/Links to an external site.) ), OpenOffice Calc (available for free here (https://www.openoffice.org/product/calc.html (Links to an external site.)) ), LibreOffice Calc (available for free here (https://www.libreoffice.org/discover/calc/ (Links to an external site.)) ) or Google sheets (available for free here (https://www.google.com/sheets/about/ (Links to an external site.)) ).

To receive full credit, you will need to:
1. Upload your spreadsheet (click “file upload”), and use a text box in the spreadsheet for the written portion of the assignment.

2. Upload your spreadsheet (click “file upload”) with data and graphs. Submit a separate file (docx, or PDF) for the written portion of the assignment

If you have difficulties completing this assignment, make sure to attend the discussion section
dedicated to helping you out with numerical assignments, and don’t hesitate to ask questions in the
forum board or during office hours, we will be happy to help.

Questions:

Suppose that you have a standard Solow model with a Cobb-Douglas production function, $LaTeX: fleft(k_tright):=:Ak_t^{alpha}$ $f$ ( k t ) = A k t α. The central equation of the model can be written as $LaTeX: Delta:k_{t+1}=s:fleft(k_tright)-dk_t$ $Δ$ k t + 1 = s f ( k t ) − d k t.

(a) Derive the closed-form solution for steady-state capital stock, $LaTeX: k^{ast}$ $k$ ∗ , by hand. (5 points points)

(b) Suppose that A = 1, s = 0.2, d=0.1, and $α$ = 1/3. Create a new spreadsheet. In the top-left cell,
using your answer from (a), numerically solve for $LaTeX: k^{ast}$ $k$ ∗ (you should get a number). (5 points)

(c) Create a column in your spreadsheet corresponding to periods. Let these periods run from
period 0 to period 100. Create additional columns for capital stock, output, consumption,
investment, depreciation, and change in capital stock . (2 points)

(d) Suppose that in period 0, the capital stock per worker equals its steady-state, computed in (b).
Compute and fill in for output, consumption, investment, depreciation, and change in capital stock in period 0. (3 points)

(e) Using the central equation of the Solow model, compute capital stock per worker in period 1.
Then repeat the process and fill in for output, consumption, investment, depreciation, and change in capital stock in period 1. (2 points)

(f) Iterate this process until you have filled all of the columns up to period 9. What is true about the
capital stock in periods 0 through 9 when the capital stock starts in the steady-state in period 0? (3
points)

(g) Suppose that in period 10, the saving rate increases to 0.25 and is expected to forever remain
there. What will happen to the capital stock in period 10? (2 points)

(h) Compute the capital stock in period 11, given the capital stock in period 10 and the new, higher
saving rate. Compute and fill in for output, consumption, investment, depreciation, and change in
capital stock in period 11. (1 point)

(i) Iterate and fill in all of the columns all the way to period 100. (2 points)

(j) Approximately how many periods does it take the capital stock to get halfway to its new, higher
steady-state value when s increases from 0.2 to 0.25? (5 points)

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