The following four (4) problems are based on the following information:

AMZN closed at $1,162.35 on 2017.12.01. A 2018.03.16 call option with a strike price of $1,000 sells for $182.30.

1. What is the intrinsic value of this option?

2. What is the time value of this option?

3. Your fancy computer estimates the volatility of AMZN as σ = 20.00 % and the risk free rate is r = 3.00 %. Given this information, what is the Black-Scholes value of this option? Feel free to use Excel or R to answer this problem.

4. Given the Black-Scholes value obtained in the previous problem, would you enter a long (buy) or short (sell/write) position in this option?

Find the closed formula solution to each of the following recurrence relations with the given initial conditions. Use an iterative approach and show your work! What is a_100? a) a_n=a_(n-1)+2,a_0=3 b) a_n=a_(n-1)+2n+3,a_0=4 c) a_n=2a_(n-1)-1,a_0=1 d) a_n=-a_(n-1),a_0=5

Suppose there are two closed economies: Economy A and Economy B. Economy A has a high average rate of time preference relative to economy B’s low average rate of time preference. (1) Describe the differences you would expect to see with respect to interest rates and levels of investment in the two economies. (2) Describe what would occur if these countries were open to international capital flows. (This is the key to answering Bernanke’s question)

3. Saving and net flows of capital and goods

In a closed economy, saving and gross investment must be equal, but this is not the case in an open economy. In the following problem, you will explore how saving and gross investment are connected to the international flow of capital and goods in an economy. Before delving into the relationship between these various components of an economy, you will be asked to recall some relationships between aggregate variables that will be useful in your analysis.

Recall the components that make up GDP. National income (Y) equals total expenditure on the economy’s output of goods and services. Thus, where C = consumption, I = gross investment, G = government spending, and NX = net exports, Y is defined as follows:

Y = (C - I + G + NX) / (C + I + G - NX) / (C + I + G + NX) / C + I - G - NX) PICK ONE

National saving (S) is the income of the nation that is left after paying for government spending and consumption. Therefore, S is defined as follows:

S = (Y - C) / (Y - I - C) / (Y - C - G) / (Y - I) PICK ONE

Rearranging the previous equation and solving for Y yields Y = (S + I) / (S + I + C) / (S + C + G) / (S + C) PICK ONE

Plugging this into the original equation showing the various components of income results in the following relationship:

S = (I + G + NX) / (I + NX) / (C + G + NX) / (G + NX) PICK ONE

This is equivalent to S = (G + NCO) / (C + G + NCO) / (I + NCO) / (I + G + NCO) PICK ONE

since net exports must equal net capital outflow (NCO, also known as net foreign investment).

Now suppose that a country is experiencing a trade deficit. Determine the relationships between the entries in the following table and enter these relationships using the following symbols: > (greater than), < (less than), or = (equal to).

Outcomes of a trade deficit [pick one for each bracket]

Net Exports [ < , = , >] 0

Imports [ <, =, >] Exports

C + I + G [<, =, >] Y

Gross Investment [<, =, >] Saving

0 [<, =, >] Net Capital Outflow

Consider a closed economy. The goods market is represented by the following equations:

C = 160 + 0.6YD
I = 100 + 0.2Y – 500i

T = 100
G = 100
YD = Y - T

1. Derive the IS equation from the equilibrium position Y = Z ≡ C + I + G and draw the IS curve on the graph.

In the money market, the real money demand is (M d/P) = Y – 1,500i; and the real money supply is (Ms/P) = 600.

2. Derive the LM relation and draw the LM curve on the graph where you draw the IS curve.

3. Solve for the equilibrium output Y and equilibrium interest rate i when both goods market and money market are at the equilibrium. Identify this equilibrium point on the graph in part (1).

4. Suppose now the government spending (G) increases from 100 to 200.
On the IS-LM graph in part (1) illustrate the effect of this increase in government spending on the IS or LM curve and mark the new equilibrium output Y and interest rate i.

5. Following this increase in government spending, how much will be the new equilibrium output Y and interest rate i?

6. How much is the multiplier of government spending?

7. Following the government spending increase, does the equilibrium investment I decrease or increase?

8. Suppose at the same time that the government spending increases, FED would use the monetary policy tool to accommodate such an expansionary fiscal policy to keep the equilibrium interest rate unchanged. Under this circumstance, how much would be the new equilibrium output (Y)? How much is the ‘multiplier’ of the government spending in this case?

9. In practice, how does FED achieve such an accommodation policy as mentioned in part (9). Illustrate the effect of this policy on an IS-LM graph. As a result, how much does the real money supply (Ms/P) need to increase to remain the equilibrium interest rate unchanged when the government spending increases?

1. Find the closed formula solution to each of the following recurrence relations with the given initial conditions. Use an iterative approach and show your work! What is a100 ?

1. an=an-1+2, a0=3
2. an=an-1+2n+3, a0=4
3. an=2an-1-1, a0=1
4. an=-an-1, a0=5

3.Consider a series RLC circuit.
a) When the capacitor is charged and the circuit is closed, find the condition for the current to be oscillatory.
b) When the circuit is connected to an AC source V = ?0 cos??, find the voltage across the inductor and the
angular frequency at which the voltage across the inductor is maximized.

Consider a closed economy as represented by the following equations:

C = 100 + .5YD
I = 200 + .1Y – 800i T = 200
G = 200
YD = Y - T

(1) Derive the IS equation from the equilibrium position of goods market. Draw the IS curve on the graph. (10 points)In the money market, assume the real money demand is (M d/P) = Y – 1,000i; and the real money supply is (Ms/P) = 700.
(2) Derive the LM relation and draw the LM curve on the graph in part (1).

(3) Solve for the equilibrium output Y and equilibrium interest rate i when both goods market and money market are at the equilibrium. Identify this equilibrium point on the graph you draw in part (1).

(4) Suppose now the tax decreases from 200 to 100. As a result of this tax cut, how much is the new equilibrium output Y? Calculate the multiplier of tax cut.

(5) Suppose now the tax remains at 200, but the government spending G increases from 200 to 300. Calculate the government spending multiplier.

The Kingdom of Elfwood (A closed Economy in the LR) has been battling to increase production of Candy but have not been able to succeed. Their economy can be expressed as: C = 400+0.60(Y-T) T = Y*0.8 G =4000 I = 750-100r Y=5000 It turns out that the King of Elfwood has a sweet tooth for Candy and has been levying back breaking taxation on its population. The King has hired you to come up with some possible ideas as to how Elfwood could increase its production in the future? However, the king does not want to reduce his consumption of Candy, not does he want to run a budget deficit. For question 1, Make sure you also talk of how it impacts the economies agents and aggregate values (C,I,S and Y)

Question 1 Could policies to change Investor pattern work? Provide 1 numerical possibility and explain how this change could be achieved. Make sure you are able to properly articulate what you want to

and how those changes will make there way in the economy. Here I am looking for you to provide me with a possible numerical change, and to explain how you would achieve it.

Question 2

The King then asked you if you believe that he should reduce his consumption of Candy? Which would reduce Government expenditures and Tax revenue by the same proportion. Would this help in achieving its goal? Provide and example where Government expenditures drop by 25%

2. (Monty Hall) Suppose you are on a game show and are presented with three closed doors
marked door 1, 2, and 3. Behind one door is a prize and behind the other two are goats.
Suppose the host allows you to select one door, but the following two rules apply:
• Before it is opened the host opens one of the two unselected doors that has a goat behind
it.
• The host then allows you to switch your choice to the remaining door or stay with your
original choice.
Say you select door 1. If the host then opens door 3 to reveal a goat, compute the probability
the prize is behind door 2. To do this, use the following events:
• D1 = The prize is behind door 1
• D2 = The prize is behind door 2
• D3 = The prize is behind door 3
• H1 = the host opens door 1
• H2 = the host opens door 2
• H3 = the host opens door 3
In other words, compute P(D2 | H3). What would you do in this situation, stay or switch?
Hint: Use Bayes’ Theorem and the Law of Total Probability