Assume that the spot rate is €0.8144/$, the 180-day forward rate is €0.7933/$, and the 180-day dollar interest rate is 6 percent per year. What is the 180-day euro interest rate per year that would prevent arbitrage?

The consumer price index for the United States (U.S.) rose from approximately 121.4 in 1990 to approximately 199.3 in 2010.

a. How much inflation was there in the U.S. during the twenty-year period?

b. What is the significance of the consumer price index to a multinational corporation?

If the price level in Canada is C$18,500, the price level in France is €13,095, and the spot exchange rate is C$1.25/€, please answer the following questions:

a. What is the internal purchasing power of the Canadian dollar? (Hint: it may be best to calculate the purchasing power of C$10,000 first and divide by the price level of C$18,500 to obtain the number of consumption bundles for C$18,500).

b. What is the internal purchasing power of the euro in France? (Hint: it may be best to calculate the purchasing power of €10,000 first and divide by the price level of €13,095 to obtain the number of consumption bundles for €13,095).

c. What is the implied exchange rate of C$/€ that satisfies absolute PPP?

d. Is the euro overvalued or undervalued relative to the Canadian dollar? Explain the reasoning for your answer.

Consider two firms that sell differentiated products and compete by choosing prices. Their demand functions are Q1 = 72 – 3P1 + 2P2 and Q2 = 72 – 3P2 + 2P1 where P1 and P2 are the prices charged by firm 1 and 2, respectively, and Q1 and Q2 are the corresponding demands. All production costs are assumed to be zero.

(a) Suppose the two firms set their prices simultaneously and non-cooperatively. Find the resulting Bertrand-Nash equilibrium. What price does each firm charge, how much does it sell, and what profit does it make? [6%]

(b) Suppose now that the two firms collude and maximise joint profits. What will be the prices, quantities and profits for each firm in this case? Can the collusive prices be supported in a static one-shot game (i.e. if the firms only act once)? Explain. [7%]

(c) Suppose Firm 1 sets its price first and then Firm 2 sets its price after observing Firm 1’s choice. What price does each firm charge, how much does it sell, and what profit does it make. [6%]

(d) If Firm 1 could choose, would it prefer (a) to set its price first; (b) to set its price second; or (c) that they set prices simultaneously? [6%]

Test the hypotheses Ho:μ≤100,Ha:μ>100Ho:μ≤100,  Ha:μ>100 at  the 0.05 level of significance given that σ=12.2σ=12.2 and that a sample of size 17, taken from a normal distribution, produced a sample mean of 102.8. Which of the following is the correct conclusion?

1. Show the final relations in 3NF. Every relation name must be in all CAPS and your primary key(s) & foreign key(s) should be underlined. Be sure to identify relationships by stating "RELATION1.FK references RELATION2.PK".

B. Let's change the original assumption and allow a student to have multiple majors. Based on your answers to Part A, show an example of adding a second major to your second student, who has two siblings.

C. Did allowing multiple majors per student introduce redundancies? If so, let's normalize again and show your final relations in 3NF. Every relation name must be in all CAPS and your primary key(s) & foreign key(s) should be underlined. Be sure to identify relationships by stating "RELATION1.FK references RELATION2.PK".

C++

Text file contains numbers 92 87 65 49 92 100 100 100 82 75 64 55 100 98 -99

Modify your program from Exercise 1 so that it reads the information from the gradfile.txt file, reading until the end of file is encountered. You will need to first retrieve this file from the Lab 7 folder and place it in the same folder as your C++ source code. Run the program

#include <iostream>
using namespace std;

typedef int GradeType[100]; // declares a new data type:
float findAverage (const GradeType, int); // finds average of all grades
int findHighest (const GradeType, int); // finds highest of all grades
int findLowest (const GradeType, int); // finds lowest of all grades

int main()
{
GradeType grades; // the array holding the grades.
int numberOfGrades; // the number of grades read.
int pos; // index to the array.
float avgOfGrades; // contains the average of the grades.
int highestGrade; // contains the highest grade.
int lowestGrade; // contains the lowest grade.
// Read in the values into the array
pos = 0;
cout << "Please input a grade from 1 to 100, (or -99 to stop)" << endl;
cin >> grades[pos];

while (grades[pos] != -99)
{
pos++;
cin >> grades[pos];
}
numberOfGrades = pos--;
// call to the function to find average
avgOfGrades = findAverage(grades, numberOfGrades);
cout << endl << "The average of all the grades is " << avgOfGrades << endl;
  
highestGrade = findHighest(grades, numberOfGrades);
cout << endl << "The highest grade is " << highestGrade << endl;
  
lowestGrade = findLowest(grades, numberOfGrades);
cout << "The lowest grade is " << lowestGrade << endl;

return 0;
}
float findAverage (const GradeType array, int size)
{
float sum = 0; // holds the sum of all the numbers
for (int pos = 0; pos < size; pos++)
sum = sum + array[pos];
return (sum / size); //returns the average
}
int findHighest (const GradeType array, int size)
{
int highest = array[0];
for (int pos = 0; pos < size; pos++)
{
if ( highest < array[pos])
{
highest = array[pos];
}
}
return highest;
}
int findLowest (const GradeType array, int size)
{
int lowest = array[0];
for (int pos = 0; pos < size; pos++)
{
if ( lowest > array[pos])
{
lowest = array[pos];
}
}
return lowest;
}

1 Linear Algebra in Numpy
(1) Create a random 100-by-100 matrix M, using numpy method "np.random.randn(100, 100)", where
each element is drawn from a random normal distribution.
(2) Calculate the mean and variance of all the elements in M;
(3) Use "for loop" to calculate the mean and variance of each row of M.
(4) Use matrix operation instead of "for loop" to calculate the mean of each row of M, hint: create a vector
of ones using np.ones(100, 1)?
(5) Calculate the inverse matrix M−1
(6) Verify that M−1M = MM−1 = I. Are the off-diagnoal elements exactly 0, why?

The market demand curve is P = 90 − 2Q, and each firm’s total cost function is C = 100 + 2q2.

1. Suppose there is only one firm in the market. Find the market price, quantity, and the firm’s profit.

2.Show the equilibrium on a diagram, depicting the demand function D (with the vertical and horizontal intercepts), the marginal revenue function MR, and the marginal cost function MC. On the same diagram, mark the optimal price P, the quantity Q, and the average total cost ATC. Illustrate the firm’s profit. Hint: You don’t need to draw the AT C curve.

3.Using the demand function, find the elasticity of demand at the monopoly price and quantity.

4.Verify that the monopoly price and quantity satisfy the monopo- list’s rule of thumb for pricing.

5.What is the monopolist’s factor markup of price over marginal cost?

6.How does the monopolist’s factor markup of price over marginal cost compare to that of a perfectly competitive firm?

5. The equation of a demand function for a tourist attraction in Alaska is given by Q=3000-20P where Q is the number of helicopter flights demanded daily.

a. What is the change in quantity demanded when the price increases by $1.00?

b. What is the quantity demanded when P=0? What does this tell you in words?

c. What is the price when quantity demanded =0? What does this tell you in words?

d. Determine the quantity demanded of helicopter flights when the P= $125.

e. Plot your demand function with a price on the vertical axis indicating the intercepts and your answer to part d.

f. Now assume that supply is given as P=$125 +0.10Qs. Plot this on your graph above indicating the minimum selling price.

g. Determine the market equilibrium price and equilibrium quantity and show this on your graph.

h. If the seller charges a price of $100 will there be a surplus or shortage? Of how much? Show this on your graph.

Given a call warrant, with a strike price $112, the conversion ratio is 20, the price of the call warrant is $0.28 per warrant today, the delta of the call warrant is 65%. Given a put warrant, with a strike price $112, the conversion ratio is 20, the price of the put warrant is $0.21 per warrant today delta of the put warrant is 55%. Suppose the spot price of the underlying stock is $110. A. Suppose you buy 4000 units of the call warrant today, and also buy 4000 units of the put warrant today, draw a diagram to indicate the profit/loss of your portfolio at expiry. Under what circumstances, investors should adopt this investment strategy? B. Suppose you buy 100 shares of the stock at the spot price, and also buy 2000 units of the put warrant today, draw a diagram to indicate the profit/loss of your portfolio at expiry. Discuss the main advantages of this investment strategy.