# MEC-003 QUANTITATIVE METHODS Solved Assignment 2019-2020

Course Code: MEC-003/ MEC-103

Asst. Code: MEC-003/103/TMA/2019-20

Total Marks: 100

Title Name |
## MEC-003 Solved Assignment 2019-20 |

University |
IGNOU |

Service Type |
Solved Assignment (Soft copy/PDF) |

Course |
MA(ECONOMICS) MEC |

Language |
ENGLISH |

Semester |
2019-2020 Course: MA(ECONOMICS) MEC |

Session |
2019-20 |

Short Name |
MEC-003 And MEC-103 (English) |

Assignment Code |
MEC-003/103/TMA/2019-20 |

Product |
Assignment of MA(ECONOMICS) 2019-2020 (IGNOU) |

Submission Date |
For July 2019 session, you need to submit the assignments by March 31, 2020, and for January 2020 session by September 30, 2020 for being eligible to appear in the termend examination. Assignments should be submitted to the Coordinator of your Study Centre. Obtain a receipt from the Study Centre towards submission. |

Answer all the questions. Each question in Section A carried 20 marks while that in Section

B carries 12 marks.

Section A

1. What is differential equation? How do you apply differential equations in Economics?

Discuss the role of initial condition in solving a differential equation. If your objective is to

examine the stability of equilibrium, show with the help of an example, how a second-order

differential equation can address your concern.

2. (a) What is the normal probability distribution function? State its properties.

(b) The concentration of impurities in a semiconductor used in the production of

microprocessors for computer is a normally distributed random variable with mean 127

parts per million (ppm) and standard deviation 22 parts per million. A semiconductor is

acceptable only if its concentration of impurities is below 150 parts per million. What is

the proportion of the semiconductors that are acceptable for use? (The area under the

standard normal curve for the value of Z=1.05 is 0.3531)

Section B

3. Explain the relevant considerations of making a choice between one-tailed and two-tailed

tests. How would you determine the level of significance in the above tests?

4. How would you determine linear dependence of a matrix? Define the rank of a matrix in

terms of its linear independence.

5. A monopolist’s demand curve is given by P = 100 – 2q.

(a) Find the marginal revenue function.

(b) At what price is marginal revenue zero?

(c) What is the relationship between the slopes of the average revenue and marginal

revenue curves?

7

6. Solve the following linear programming problem in x1 and x2.

Min C = 0.6×1 + x2

Sub to 10 x1 + 4 x2 ≥ 20

5 x1 + 5 x2 ≥ 20

2 x1 + 6 x2 ≥ 12

x1 , and x2 ≥ 0.

7. Write short notes on the following:

(i) Eigen vectors and Eigen values

(ii) Taylor’s expansion

(iii) Mixed strategy equilibrium

(iv) Kuhn-Tucker condition

MEC-003, MEC-03, MEC 003, MEC 03, MEC003, MEC03, MEC-3, MEC3, MEC