Question 1:
The IS curve and the LM curve are both plots of interest rate verses aggregate output. Yet in one curve a high aggregate demand corresponds to a high interest rate, and in the other curve a high aggregate demand corresponds to a low interest rate.
a) How can it be that one slopes up, and the other slopes down?
b) Explain in your own words (100 to 400 words), why the IS curve slopes down.
c) Explain in your own words (80 to 200 words), why the LM curve slopes up.
d) Calculate both the interest rate and aggregate demand in a given year if :-
• The IS curve is given by Y = 500 - 100 r
• The LM curve is given by r = (Y - 100) / 100
• The aggregate demand in the given equations are expressed in billions of dollars.
• The interest rate is given in percent. (i.e. a 5% interest rate means that r = 5.)
Show your result both algebraically and graphically.
e) What will happen to the interest rate in part d) if the supply of money is increased. Justify your answer.
f) What will happen to the aggregate demand in part d) if the supply of money is increased. Justify your answer.
Question 2:
This question requires you to develop code in R. All of the code requires you to use the function simshare(), given in example 3.2 from the study book.
It is not enough to provide code that works. The code needs to be easy for the marker to understand. All of the code needs to be properly indented (example 3.2 is not indented), and marks will be removed for poor coding even if the code works. Please see the coding guidelines under Misc near the top of the home page for the course.
You need to include the code in your submitted PDF as well as at least one instance of a resulting plot. In addition, your assignment submission must have a runnable copy of your code, which the marker will examine and run in R.
As the simulations depend on random numbers, You should get very different or slightly different result each time you run the code.
Hints in the form of code snippets are available on the home page under a link called "Useful code snippets".
a) Produce a program in R that will plot 6 simulations of a share values in a single plot. Use different colors so that the viewer may discern 6 different curves:-
• Inital share value: $15
• (a) Growth parameter per day: 20% per year divided by 365 days giving the daily rate.
• (sigma) Daily volatility: 0.01.
• Period: 100 days
b) Produce a program in R that will produce a histogram of the value of a PUT option at the maturity date, using the values given in part
a). The strike price is 15. The histogram will show the frequency of each data range over 200 simulations.
Example 3.5 features a function that estimates the expected value of a CALL option, and you should pattern your code after that. Note that Example 3.5 already performs averaging, and you do not want this in your histogram.
c) Produce a program in R that will plot a graph of the expected value of a put option verses the strike price. Find the expected value for each given strike price by averaging over 50 simulations. The values from part a) should be used, and the strike price should vary between 0 and 30.