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Question Description

**Instructions**

For this assignment, you will have to use spreadsheet software (such as Excel). To get full credit, please submit your all of your answers in **one single spreadsheet file**. In order to write text in a spreadsheet, you can use “Insert Text.”

**Make sure to read carefully all of the instructions.**

**Goals**

- Being able to plot the IS curve in Excel
- Being able to use the spreadsheet to study the impact of different changes to parameters (“comparative statics”) or changes to the model assumptions

**Description of the economy**

Consider an economy identical to that described in the lecture. Potential output

$\stackrel{}{Y}$

is actual output. Consumption is given by

$C$

is the real short-term interest rate and

$\stackrel{}{r}$

For now, assume that the parameters are as follows:

$\stackrel{}{A}$¯ = 1

$\stackrel{}{L}$¯ = 1

$\stackrel{}{K}$¯ = 1

$\alpha $= 0.3

${\stackrel{}{a}}_{}$¯ c = 0.2

${\stackrel{}{a}}_{}$¯ g = 0.5

${\stackrel{}{a}}_{}$¯ i = 0.3

$\stackrel{}{x}$¯ = 0.3

$\stackrel{}{b}$¯ = 10

**Questions**

**(a) 2 points.** Input the parameter values in Excel (we will call this set of parameters “Baseline”). Add a row for the aggregate demand shock,

**(b) 2 points. **Compute the equilibrium long-run real interest rate,

**(c)** ** 4 points. **In the lecture notes, we derived the formula for the IS curve, which gives the relation between the short-run real interest rate

and the short-run output

$Y$

$Y$

We are now going to plot it. To do so we will need two columns: one column with values for the interest rate (in increments of 0.01 from 0 to 0.5), and another column with the corresponding values for the short-run output. Then we will be able to create a scatter plot with the column for short-run output on the x-axis and the column for short-run interest rate on the y-axis.

If you need help, you can follow these steps:

- Create a column for R. Input the first two values, R=0 and R=0.01, by hand. Select the two cells you just filled in and use the dropdown technique to fill in the cells below up to 0.5. You should get a column that looks like {0, 0.01, 0.02, 0.03,.., 0.5}.
- In the next column, compute

$Y$~ , using formula (1).*Note that when you enter a formula, if you would like one of the cells that the formula refers to to remain the same when you use the dropdown method (for example, you always want the formula to contain the value from B6, you don’t want the formula to be updated to B7, B8, etc.), you can use $ signs around the letter (using the previous example, you would write $B$6 instead of B6).* - To create the scatter plot, use the same method as you used in the Week 3 numerical assignment when you had to plot the Beveridge curve. Recall that we want R on the y-axis and

$Y$~ on the x-axis. Name this plot “Baseline IS curve.” Add axes titles and a legend to your graph.

By now your graph should look like this:

**(d)** ** 2 points. **Let’s do a few checks to make sure that the graph is correct. First, you expect the curve to be downwards-sloping (a higher interest rate should correspond to a lower short-run output, because it discourages investment and investment increases output). Is that the case? Second, because the aggregate shock so far is equal to

, is exactly equal to the long-run interest rate,

$r$

when

$Y$

**(e) 4 points.** In the column next to the one you used to input your original parameter values, let’s input a new set of parameter values. Increase “>

**(f)** ** 2 points. **How does the new IS curve compare to the original one? According to the baseline IS curve, a short-run interest rate of 0.4 would correspond to a short-run output of _____? According to the new IS curve, a short-run interest rate of 0.4 would correspond to a short-run output of ____? What does it mean for short-run output to be negative?

**(g)** ** 2 points. **We learned in the lecture that when the government spends 1 extra unit (that is, when

, but then also indirectly increases consumption. Indeed, the increase in

$G$leads to an increase in income by 1. This increase in income is going to be partially spent by households(a fraction

$x$

Note: You can check your answer using the numbers calculated fro questions (c) and (e). If you pick any column (any R), and compute the difference between the

$Y$

**(h)** ** 4 points. **Now assume that there is a natural disaster and half of the original capital stock,

**(i)** ** 3 points. **How does the new IS curve compare to the baseline IS curve? If you look at the equation for the IS curve, (1), you can see that it does not include

*Hint: Check which of the parameters present in the IS curve formula changed between the baseline and the new parameter values.*

**(j) 5 points. **Now we will change the equation for consumption, so that

$Y$

Using the same steps as described before, plot this new IS curve, assuming

$b$