Consider a firm with production function given by q = f(E, K) = E^(1/4)K^(1/4), where E is number of workers and K is capital. The price of labor is w = 4 and price of capital is r = 8. The price of the output that firm produces is 20. The firm can adjust both its inputs.

1) Derive an expression for MRT S for this firm.

2) The firm wants to produce q0 units of output. What would be cost-minimizing combination of inputs (E, K) to produce q0 units of output. Note that this combination would be a function of q0.

3) Firm wants to maximize its profits. What is the profit maximizing level of inputs? How many units of output are produced? What is the firm’s profit if it produces at this optimal?

4) Consider a change in price of labor, such that w = 2. What would be the new optimal levels of both inputs? How does quantity of output produced change?

5) Decompose this change in inputs from part (3) to part (4), into scale and substitution effects

1. Liz has utility given by ?(?1,?2)=?1^7?2^3. If ?1=$10,?2=$15,and I = $100, find Liz’s optimal consumption of good 1. (Hint: you can use the 5 step method or one of the demand functions derived in class to find the answer).  

a) Using the information from question 1, find Liz’s optimal consumption of good 2.

3. Lyndsay has utility given by ??(?1,?2)=min {?1,?2}. If ?1=$2,?2=$4, ? ?=$12, find Lyndsay’s optimal consumption of good 1. (Hint: this is Leontief utility).

a) Using the information from question 3, find Lyndsay’s optimal consumption of good 2.

5. Anya has utility given by ??(?1,?2)=12?1+9?2. If ?1=$4,?2=$2, ?=$20, find Anya’s optimal consumption of good (Hint: this is linear utility).

a) Using the information from question 5, find Anya’s optimal consumption of good 2.

how to count the word of occurance in the text file

example input text file : "test1.txt
hello : 1
good : 1
morning: 1
how : 1
are : 2
you : 2
good : 1

example output text file : "test2.txt"
1 : 4
2 : 2
3 : 0
4 : 0
5 : 0

Which investment returns a greater future value at time 10; A or B

INVESTMENT A

INVESTMENT B

c++ programming

1. What will the following C++ code display?

int numbers[4]={99,87};

cout<<numbers[3]<<endl;

1. 87                            b. 0                                  c. garbage                        d. an error

2. What is the output of the following program segment?

double mylist[5];

for(int i=0; i<5; i++)

mylist[i]= (pow(i,2)+ 1 /2.0;

cout<<fixed<<showpoint<<setprecision(2);

for(int i=0; i<5; i++)

{ cout<<setw(5)<<mylist[i];

}

              a. .5           1.5        4.5        9.5        16.5

              b. 0.50      1.50      4.50      9.50     16.50

             c. 0.50      1.50      8.50     27.50     64.50

            d. 0.50      1.50      2.50      3.50      4.50

     15. what is stored in list after the following C++ statement is executed?

     int list [8];

list[0]=1;

list[1]=2;

for(int i=2; i<7; i++)

{

     list[i]= list[i-1] * list[i-2];

     cout<<setw(5)<<list[i];

}

1. 2    4    8   16   32          b. 2    4    8   16 256         c. 2    4    8   64 256        d. 2    4    8   32 256

16. What is the output of the following C++ segment?

      int i;

int list [8];

list[0]=1;

list[1]=2;

for(int i=2; i<7; i++)

{

     list[i]= list[i-1] * list[i-2];

     cout<<setw(5)<<list[i];

}

for(int i=2; i<7; i++)

{

if( i>3)

    list[i]= list[i]- list[i-1];

cout<<setw(5)<<list[i];

}   

    a.    2    4    16   32 256    2    4    8   28   228      b. 2    4    4   16 256    2    4    4   28      228

   c. 2    4    8   32       256     2     2    4   28 228      d. 2    4    8   32 256    2    4    4   28     228

Given int numbers[]= { 12,145,567,100,1001};

17. Write a function to indicate the position of the highest data?
18. Write a function to determine the maximum value of the numbers [];

Given:

struct nameType { string first_name;   string last_Name;      string middle_Name;   };

struct addressType { string address; string city; string state; string zip; };

struct courseType { string course_Name; int course_number; string major; };

struct dateType { int month; int day; int year;   };

struct studentType { nameType name; int student_ID; addressType address; dateType enrolled;};

19. How many of the following are invalid ?

studentType student;

studentType array[89];

courseType course;

nameType name;

student.gpa=4.0;

student.name.first_name="Robert";

student.course.course_Name="Chem";

array[0].enrolled=student.enrolled;

array[1].name.first_name="Jane";

1. 1                                        b. 3                             c. 2.                                  d. none

20. How of the following statements are invalid ?

studentType student;

studentType array[89];

courseType course;

nameType name;

student.gpa=4.0;

student.name="Robert";

student.course.="Chem";

array[0].enrolled=student.enrolled;

array[1].name.first_name="Jane";

1. 1                                     b. 3                                  c. 2                                   d. none

in C++

In the main function, declare a two-dimensional matrix array 5 by 5, read data from a file named “data.txt”. Suppose the data in the file are integers between 0 and 9. Write your main function to print out the left bottom below the diagonal of the matrix and keep the triangle shape. Note the numbers on the diagonal are not included in the output. An example is given as follows. (25 points)

Suppose the original matrix is

1 2 3 4 5

1 2 3 4 5

1 2 3 4 5

1 2 3 4 5

1 2 3 4 5

The output should be like as follows.

1

1 2

1 2 3

1 2 3 4

#include <iostream>

#include <iomanip>

#include <fstream>

using namespace std;

const int NUM = 5;

int main()

{

      // I - Declaring a five by five array

      /* II - Read data from data.txt and use them to create

             the matrix in the previous step*/

/* III – print out the left bottom below the diagonal of the matrix and keep the triangle shape. Note the numbers on the diagonal are not included in the output.

       read.close();

       return 0;

}

1. In the main function, declare a two-dimensional matrix array 5 by 5, read data from a file named “data.txt”. Suppose the data in the file are integers between 0 and 9. Write your main function to print out the left bottom below the diagonal of the matrix and keep the triangle shape. Note the numbers on the diagonal are not included in the output. An example is given as follows. (25 points)

Suppose the original matrix is

1 2 3 4 5

1 2 3 4 5

1 2 3 4 5

1 2 3 4 5

1 2 3 4 5

The output should be like as follows.

1

1 2

1 2 3

1 2 3 4

#include <iostream>

#include <iomanip>

#include <fstream>

using namespace std;

const int NUM = 5;

int main()

{

      // I - Declaring a five by five array

      /* II - Read data from data.txt and use them to create

             the matrix in the previous step*/

/* III – print out the left bottom below the diagonal of the matrix and keep the triangle shape. Note the numbers on the diagonal are not included in the output.

       read.close();

       return 0;

QUESTION 55

1. Which of the following is/are correct regarding the reasons an investor might consider investing in corporate bonds? (1) They have lower default risk than Treasuries. (2) They generally pay higher interest than Treasuries. (3) They generally offer some inflation protection via the semi-annual payment of coupons. (4) They offer higher security of principal than equities. (5) Convertible bonds may participate if the company’s shares rise in value.

   		a. 1, 2 and 3.
   		b. 2, 3 and 4.
   		c. 2 and 4.
   		d. 2, 4 and 5.

QUESTION 56

1. Which of the following would likely cause a bond to have a lower market value? (1) The issuer’s credit rating changed from A to AA. (2) The issuer’s credit rating changed from AA to A. (3) The YTM of comparable securities rose. (4) The YTM of comparable securities declined. (5) The bond included a call feature.

   		a. 1, 3 and 4.
   		b. 2 and 4.
   		c. 2, 3 and 5.
   		d. 2, 4 and 5.

1. ) Suppose a stock had an initial price of $37 per share, paid a dividend of $0.3 per share during the year, and had an ending share price of $50. Compute the percentage total return. Enter the answer in 4 decimals.

2. ) Calculate the arithmetic average of the following returns.

Year Return

1 0.18

2 0.08

3   0.11

4   -0.05

5 0.3

Enter the answer with 4 decimals.

3.) Calculate the standard deviation of the following returns.

Year Return

1 -0.18

2 -0.06

3   -0.09

4   0.21

5 0.08

Enter the answer with 4 decimals.

4. ) Calculate the variance of the following returns.

Year Return

1 -0.16

2 0.08

3   -0.08

4   0.14

5 -0.02

Enter the answer with 4 decimals.

Design a multiplexed communication system that can be used for 1 of 4 senders (sources) to send 3 bits to 1 of 2 receivers (destinations) using a 3-bit 4×1 multiplexer and a 2-bit 1×2 demultiplexer. Assume that the most significant of the 3 bits denotes the header containing the destination ID and that the 2 less significant bits denote the message. Represent both the 3-bit 4×1 multiplexer and a 2-bit 1×2 demultiplexer using block diagrams with all inputs and outputs labeled. Show which outputs of the multiplexer connect to which inputs of the demultiplexer!