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Assignment: Solow Growth Model and Excel Practice

## Goals of the Assignment

There are two main goals for this assignment. First, it is meant to help improve your understanding of the mechanics of the Solow growth model that we covered in the first half of the class and to make sure you don’t forget about it before the final. Second, since many jobs for economics majors require at least a basic knowledge of Microsoft Excel, it is also meant to give you some practice with some of Excel’s basic features. If you do not have access to Excel, Google sheets will also work as a free alternative.

1. Set up the parameters of the model: Somewhere on your sheet, input the following numbers as values for each parameter. We will use numbers on your student ID to give each of you a unique setup (if any number is a 0, skip it and move to the next number and continue from there). We will assume a Cobb-Douglas production function
a) Set capital’s share of income  where X is the first number on your student ID divided by 2 (round to the nearest whole number).
b) Set the saving rate  where X is the second number of your student ID
c) Set the depreciation rate  where X is the third number of your student ID
d) Set the population growth rate  where X is the fourth number of your student ID
e) Set the technology growth rate  where X is the fifth number of your student ID. Calculate  using your values for  and .

2. Calculate steady state capital per effective worker, output per effective worker, and consumption per effective worker by hand.
3. Set the initial level of technology  and . Set  equal to half its steady state value that you calculated in

2. Put these three values in the first row of three separate columns in your spreadsheet.
4. Using Excel formulas (i.e. not calculating by hand), calculate , , , , ,  , and  putting each in the first row of their own column in your spreadsheet (you should now have 11 columns filled in total). You should be able to calculate all of these variables using , , , and parameters.
Yt= AtKαtL1−αt
α= 0.X
s= 0.X
δ= 0.0X
η= 0.0X
γ= 0.0X
?γγα
?A0 = 1 L0 = 1,000  ?k0
?y0  ?c0 k0 y0 c0 K0
Y0 C0
?k ?AL

5. Using the growth rates you set in part 1, use an Excel formula to calculate  and for 100 periods (so you should have 100 rows filled in with these values)
6. Using the law of motion for capital per effective worker, calculate  for 100 periods
7. Calculate values for the other 8 variables for 100 periods (carrying formulas down).
8. From the 100 values you have generated, create graphs of
a) Capital per effective worker (include a dashed line at the steady state level of capital that you calculated in 2)
b) The natural log of capital per worker
c) The natural log of aggregate capital
d) The growth rate of capital per worker and aggregate capital (use the difference in the logs as an approximation for the growth rate). You may put these on the same plot or separate plots.

## Setting up the Parameters of the Model

9. Copy the spreadsheet you have created into a new sheet. After period 100, change the saving rate to the value that optimizes steady state consumption (if you are already at this value, choose an arbitrary new value between 0 and 1). Using the new saving rate, starting in period 100, calculate values for all of your variables for 100 more periods (so you will now have 200 total values for each variable). Create a graph for the following variables (start from period 50, plot t=50 to t=200). For each graph, include a dashed line at both the original and new steady state values.
a) Capital per effective worker
b) Output per effective worker
c) Consumption per effective worker

10. Copy the original spreadsheet again onto a third sheet. Now double . Using the new growth rate, starting in period 100 calculate values for all of your variables forward to period 200. Create graphs (again starting in period 50) for
a) Output per effective worker (include dashed lines at both the original and new steady states))
b) The natural log of output per worker
c) The natural log of aggregate output
d) The growth rate of output per worker and aggregate output (again using the difference in logs). You may put these on the same plot or separate plots. 11. You should now have 13 graphs (or 11 if you combined the growth rate graphs). Put these together into a single document (final form must be pdf but any program works to create it), including a brief description (a few sentences) explaining what is happening in each of the three parts.