Contents

## MEC-003/MEC-103 QUANTITATIVE METHODS

## Solved Assignment 2020-2021

Course Code: MEC-103

Asst. Code: MEC-103 / TMA/2020-21

Total Marks: 100

Title Name |
## MEC-003/MEC-103 Solved Assignment 2020-21 |

University |
IGNOU |

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

Course |
MA(ECONOMICS) MEC |

Language |
ENGLISH |

Semester |
2020-2021 Course: MA(ECONOMICS) MEC |

Session |
2020-2021 |

Short Name |
MEC-003/MEC-103 (ENGLISH) |

Assignment Code |
MEC-103 / TMA/2020-21 |

Product |
Assignment of MA(ECONOMICS) 2020-2021 (IGNOU) |

Submission Date |
For July 2020 session, you need to submit the assignments by March 31, 2021, and for January 2021 session by September 30, 2021 for being eligible to appear in the term end examination.Assignments should be submitted to the Coordinator of your Study Centre. Obtain a receipt from the Study Centre towards submission. |

Section A

1) Consider the utility function 𝑢 = 𝑓(𝑥1 … 𝑥𝑛 ) where 𝑥𝑖

, 𝑖 = 1,2, … , 𝑛 are the quantities of the n goods consumed. Let

the price of good 𝑥𝑖 be 𝑃

𝑖

, 𝑖 = 1,2, … , 𝑛. Let M be the consumer’s income. Show that the Lagrangian multiplier of the

utility maximization problem equals the marginal utility of income.

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 and standard deviation 22. A semiconductor is

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

semiconductors are acceptable for use? (The area under the standard normal curve for the value of z = 1.5 is

0.668).

Section B

3) Distinguish between the characteristics of first and second order difference equations. Give examples of economic

problems that are solved with the help of each category of such equations.

4) Solve the following linear programming problem:

Min 𝐶 = 0.6𝑥1 + 𝑥2

subject to 10𝑥1 + 4𝑥2 ≥ 20

5𝑥1 + 5𝑥2 ≥ 20

2𝑥1 + 6𝑥2 ≥ 12

𝑥1 𝑎𝑛𝑑 𝑥2 ≥ 0

5) Suppose a large jar contains eight red balls, six yellow balls, and six blue balls. Two balls are to be selected at random

from the jar, and the first ball selected will not be placed back into the jar.

(a) What is the probability that the first ball will be red and the second yellow?

(b) What is the probability that neither will be red?

6) Suppose the technology matrix is

A =

0.2 0.3 0.2

0.4 0.1 0.2

0.1 0.3 0.2

Let the final demand vector be D =

10

5

6

Find the level of production of the three goods.

7) (a) What is a test statistic?

(b) Distinguish between one-tailed and two-tailed tests.

(c) What is p- value?

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