Samacheer Kalvi 11th Economics Guide Chapter 12 Mathematical Methods for Economics

Students can download 11th Economics Chapter 12 Mathematical Methods for Economics Questions and Answers, Notes, Samcheer Kalvi 11th Economics Guide Pdf helps you to revise the complete Tamilnadu State Board New Syllabus, helps students complete homework assignments and to score high marks in board exams.

Tamilnadu Samacheer Kalvi 11th Economics Solutions Chapter 12 Mathematical Methods for Economics

Samacheer Kalvi 11th Economics Mathematical Methods for Economics Text Book Back Questions and Answers

PART – A

Multiple Choice Questions:

Question 1.
Mathematical Economics is the integration of ………………………
(a) Mathematics and Economics
(b) Economics and Statistics
(c) Economics and Equations
(d) Graphs and Economics
Answer:
(a) Mathematics and Economics

Samacheer Kalvi 11th Economics Guide Chapter 12 Mathematical Methods for Economics

Question 2.
The construction of demand line or supply line is the result of using ……………………..
(a) Matrices
(b) Calculus
(c) Algebra
(d) Analytical Geometry
Answer:
(d) Analytical Geometry

Question 3.
The first person used the mathematics in Economics is ……………………..
(a) Sir William Petty
(b) Giovanni Ceva
(c) Adam Smith
(d) Irving Fisher
Answer:
(b) Giovanni Ceva

Samacheer Kalvi 11th Economics Guide Chapter 12 Mathematical Methods for Economics

Question 4.
Function with single independent variable is known as ……………………..
(a) Multivariate Function
(b) Bivariate Function
(c) Univariate Function
(d) Polynomial Function
Answer:
(c) Univariate Function

Question 5.
A statement of equality between two quantities is called ………………………
(a) Inequality
(b) Equality
(c) Equations
(d) Functions
Answer:
(c) Equations

Question 6.
An incremental change in dependent variable with respect to change in independent variable is known as ………………………
(a) Slope
(b) Intercept
(c) Variant
(d) Constant
Answer:
(a) Slope

Samacheer Kalvi 11th Economics Guide Chapter 12 Mathematical Methods for Economics

Question 7.
(y – y1) = m(x-x1) gives the ……………………….
(a) Slope
(b) Straight line
(c) Constant
(d) Curve
Answer:
(b) Straight line

Question 8.
Suppose D = 50 – 5P. When D is zero then ………………………….
(a) P is 10
(b) P is 20
(c) P is 5
(d) P is -10
Answer:
(a) P is 10

Samacheer Kalvi 11th Economics Guide Chapter 12 Mathematical Methods for Economics

Question 9.
Suppose D = 150 – 5P. Then, the slope is ………………………
(a) -5
(b) 50
(c) 5
(d) -50
Answer:
(d) -50

Question 10.
Suppose determinant of a matrix ∆ = 0, then the solution ……………………..
(a) Exists
(b) Does not exist
(c) Is infinity
(d) Is zero
Answer:
(b) Does not exist

Samacheer Kalvi 11th Economics Guide Chapter 12 Mathematical Methods for Economics

Question 11.
State of rest is a point termed as ………………………
(a) Equilibrium
(b) Non – Equilibrium
(c) Minimum Point
(d) Maximum Point
Answer:
(a) Equilibrium

Question 12.
Differentiation of constant term gives ……………………..
(a) One
(b) Zero
(c) Infinity
(d) Non-infinity
Answer:
(b) Zero

Samacheer Kalvi 11th Economics Guide Chapter 12 Mathematical Methods for Economics

Question 13.
Differentiation of xn is ………………………
(a) nx(n-1)
(b) nx(n+1)
(c) Zero
(d) One
Answer:
(a) nx(n-1)

Question 14.
Fixed Cost is the ……………………. term in cost function represented in mathematical form.
(a) Middle
(b) Price
(c) Quantity
(d) Constant
Answer:
(d) Constant

Samacheer Kalvi 11th Economics Guide Chapter 12 Mathematical Methods for Economics

Question 15.
The first differentiation of Total Revenue function gives ………………………..
(a) Average Revenue
(b) Profit
(c) Marginal Revenue
(d) Zero
Answer:
(c) Marginal Revenue

Question 16.
The elasticity of demand is the ratio of ……………………….
(a) Marginal demand function and Revenue function
(b) Marginal demand function to Average demand function
(c) Fixed and variable revenues
(d) Marginal Demand function and Total demand function
Answer:
(b) Marginal demand function to Average demand function

Samacheer Kalvi 11th Economics Guide Chapter 12 Mathematical Methods for Economics

Question 17.
If x + y = 5 and x – y = 3 then, Value of x ………………………
(a) 4
(b) 3
(c) 16
(d) 8
Answer:
(a) 4

Question 18.
Integration is the reverse process of ……………………….
(a) Difference
(b) Mixing
(c) Amalgamation
(d) Differentiation
Answer:
(d) Differentiation

Samacheer Kalvi 11th Economics Guide Chapter 12 Mathematical Methods for Economics

Question 19.
Data processing is done by ……………………….
(a) PC alone
(b) Calculator alone
(c) Both PC and Calculator
(d) Pen drive
Answer:
(c) Both PC and Calculator

Question 20.
The command Ctrl + M is applied for ………………………
(a) Saving
(b) Copying
(c) Getting new slide
(d) Deleting a slide
Answer:
(c) Getting new slide

PART – B

Answer the following Questions in one or two sentences.

Question 1.
1f 62 = 34 + 4x what is x?
Answer:
62 – 34 = 4x ⇒ 28 = 4x
28 ÷ 4 = 1x ∴ x = 7

Samacheer Kalvi 11th Economics Guide Chapter 12 Mathematical Methods for Economics

Question 2.
GIven the demand function q = 150 – 3p, derive a function for MR?
Answer:
Demand function q = 150 – 3p
\(\frac{dq}{dp}\) = -3
Samacheer Kalvi 11th Economics Guide Chapter 12 Mathematical Methods for Economics img 1

Question 3.
Find the average cost function where TC = 60+ 10x + 15x2
Answer:
Formula = \(\frac{TC}{x}\)
Average cost function = \(\frac{60}{x}\) + \(\frac{10x}{x}\) + \(\frac { 15x^{ 2 } }{ x } \)
Average cost = \(\frac{60}{x}\) + 10 + 15x

Samacheer Kalvi 11th Economics Guide Chapter 12 Mathematical Methods for Economics

Question 4.
The demand function is given by x = 20 – 2p – p2 where p and x are the price and the quantity respectively. Find the the elasticity of demand for p = 2.5?
Answer:
ed = \(\frac{p}{x}\) \(\frac{dx}{dp}\)
\(\frac{dx}{dp}\) = -2-2p
Samacheer Kalvi 11th Economics Guide Chapter 12 Mathematical Methods for Economics img 2

Samacheer Kalvi 11th Economics Guide Chapter 12 Mathematical Methods for Economics

Question 5.
Suppose the price p and quantity q of a commodity are related by the equation q = 30 – 4p – p2 find
(I) ed at p = 2
(II) MR
Answer:
(I)
Samacheer Kalvi 11th Economics Guide Chapter 12 Mathematical Methods for Economics img 3

(II) MR – [Marginal Revenue]
MR = \(\frac{dq}{dp}\)
Given q = 30 – 4p – p2
\(\frac{dq}{dp}\) = 0 – 4(1) – 2p2-1
\(\frac{dq}{dp}\) = -4 – 2p

Samacheer Kalvi 11th Economics Guide Chapter 12 Mathematical Methods for Economics

Question 6.
What is the formula for elasticity of supply if you know the supply function?
Answer:
Elasticity of supply = \(\frac{dq}{dp}\)
Samacheer Kalvi 11th Economics Guide Chapter 12 Mathematical Methods for Economics img 4

Question 7.
What are the main menus of MS word?
Answer:
Samacheer Kalvi 11th Economics Guide Chapter 12 Mathematical Methods for Economics img 5a

Ms word is a word processor, which helps to create, edit, print and save documents for future retrieval and reference.

PART – C

Answer the following questions in one paragraph:

Question 1.
Illustrate the uses of Mathematical Methods in Economics?
Answer:
Uses of Mathemetical Methods in Economics:

  1. Mathematical Methods help to present the economic problems in a more precise form.
  2. Mathematical Methods help to explain economic concepts.
  3. Mathematical Methods help to use a large number of variables in economic analyses.
  4. Mathematical Methods help to quantity the impact or effect of any economic activity implemented by Government or anybody. There are of course many other uses.

Samacheer Kalvi 11th Economics Guide Chapter 12 Mathematical Methods for Economics

Question 2.
Solve for x quantity demanded if 16x – 4 = 68 + 7x?
Answer:
16x – 4 = 68 + 7x
16x – 7x = 68 + 4
9x = 72
x = \(\frac{72}{9}\) = 8
∴ x = 8

Question 3.
A firm has the revenue function R = 600q – 0.03q2 and the cost function is C = 150q + 60,000, where q is the number of units produced. Find AR, AC, MR and MC?
Answer:
(I) Average Revenue = \(\frac{R}{q}\)
\(\frac { 600q-0.03q^{ 2 } }{ q } \) = \(\frac{600q}{q}\) – \(\frac { 0.03q^{ 2 } }{ q } \)
AR = 600 – 0.03q

(II) Average Cost = \(\frac{C}{q}\)
= \(\frac{150q}{q}\) + \(\frac{60000}{q}\)
AC = 150 + \(\frac{60000}{q}\)

(III) Marginal Revenue = \(\frac{dR}{dq}\)
R = 600q – 0.03q2
\(\frac{dR}{dq}\) = 600 – (0.03) (2q)
MR = 600 – 0.06q

(IV) Marginal Cost = \(\frac{dC}{dq}\)
C = 150q + 60000
MC = 150

Samacheer Kalvi 11th Economics Guide Chapter 12 Mathematical Methods for Economics

Question 4.
Solve the following linear equations by using Cramer’s rule?
x1 – x2 + x3 = 2;
x1 + x2 – x3 = 0;
– x1 – x2 – x3 = -6
Answer:
x1 – x2 + x3 = 2
x1 + x2 – x3 = 0
– x1 – x2 – x3 = -6
AX = B
Samacheer Kalvi 11th Economics Guide Chapter 12 Mathematical Methods for Economics img 6

Samacheer Kalvi 11th Economics Guide Chapter 12 Mathematical Methods for Economics

Question 5.
If a firm faces the total cost function TC = 5 + x2 where x is output, what is TC when x is 10?
Answer:
TC = 5 + x2
TC = 5 + 102
TC = 5 + 100
∴TC = 105

Question 6.
If TC = 2.5q3 – 13q2 + 50q + 12 derive the MC function and AC function?
Answer:
\(\frac{dc}{dq}\) = MC
AC = \(\frac{TC}{q}\)
\(\frac{dc}{dq}\) = 2.5(3)q2 – [13 × 2]q + 50
MC = 7.5q2 – 26q + 50
AC = \(\frac { 2.5q^{ 3 }-13q^{ 2 }+50q+12 }{ q } \)
∴ AC = 2.5q2 – 13q + 50 + \(\frac{12}{q}\)

Samacheer Kalvi 11th Economics Guide Chapter 12 Mathematical Methods for Economics

Question 7.
What are the steps involved in executing a MS Excel sheet?
Answer:

  1. MS – excel is used in data analysis by using formula.
  2. A spread sheet is a large sheet of paper which contains rows and columns.
  3. The intersection of rows and columns is termed as cell.
  4. MS – Excel 2007 version supports up to 1 million rows and 16 thousand columns per work sheet.

MS Excel Start From Various Options:

(I) Click Start → Program → Micro Soft Excel
(II) Double click the MS Excel Icon from the Desktop

Worksheet:
MS – Excel work sheet is a table like document containing rows and columns with data and formula

There are four kinds of calculation operators. They are:

  1. Arithmetic
  2. Comparison
  3. Text Concatenation [link together]
  4. Reference

MS – Excel helps to do data analysis and data presentation in the form of graphs, diagrams, area chart, line chart etc.

PART – D

Answer the following questions in about a page:

Question 1.
A Research scholar researching the market for fresh cow milk assumes that Qt = f (Pt, Y, A, N, Pc) where Qt is the quantity of milk demanded, Pt is the price of fresh cow milk, Y is average household income, A is advertising expenditure on processed pocket milk, N is population and Pc is the price of processed pocket milk.
Answer:

  1. What does Qt = f (Pt, Y, A,N, Pc) mean in words?
  2. Identify the independent variables.
  3. Make up a specific form for this function.

(Use your knowledge of Economics to deduce whether the coefficients of the different independent variables should be positive or negative.)

1. Qt is the function of Pt, Y, A, N, Pc
Pt – Price of fresh cow milk
Y = Average household income
A = Advertising expenditure on processed pocket milk
N = Population
Pc = Price of processed pocket milk

2. Identify the Independent variables.
“Y” = Average household income
“N” = Population [“N” are Independent Variables]
Pc = Price of processed pocket milk
“Pc” = depending “Pt”
= Pc depending “A”
“A” = depending “N”
∴ Pc depending “Pt”, “A”, and “N”.

3. Make up specific form for this function [use your knowledge of Economics to deduce whether the co-effecients of the different independent variables should be positive or negative]

  • “Pc ” = Price of processed pocket milk
    When the price of processed milk increases and quantity demanded of fresh milk decreases.
  • “N” = Population
    When the population increases and quantity of milk demanded Increases.
  • “A” = Advertising expenditure on processed pocket milk
    When advertising expenditure on processed pocket milk increases the quantity of milk demanded. Increases.

“Y” – Average household Income
When average household income Increases and quantity of milk demanded Increases.
“Pt” – Price of fresh cow milk
When price of fresh cow milk Increases quantity of milk demanded decreases.
∴ Qt = (-Pt) (+Y) (+A) (+N) (- Pc)
(-) means decreases; (+) means Increases
∴ Qt = [- Pt + Y + A +N – Pc]

Samacheer Kalvi 11th Economics Guide Chapter 12 Mathematical Methods for Economics

Question 2.
Calculate the elasticity of demand for the demand schedule by using differential calculus method P = 60 – 0.2Q where price is –

  1. Zero
  2. ₹20
  3. ₹40

Answer:

Samacheer Kalvi 11th Economics Guide Chapter 12 Mathematical Methods for Economics img 7Samacheer Kalvi 11th Economics Guide Chapter 12 Mathematical Methods for Economics img 8

Samacheer Kalvi 11th Economics Guide Chapter 12 Mathematical Methods for Economics

Question 3.
The demand and supply functions are Pd = 1600 – x4 and Ps = 2x2 + 400 respectively. Find the consumer’s surplus and producer’s surplus at equilibrium point?
Answer:
Pd = 1600 – x2
Ps = 2x2 + 400
Pd = Ps
1600 – xc = 2x2 + 400
⇒ 1600 – x2 – 2x2 – 400 = 0
⇒ -3x2 + 1200 = 0
x2 = \(\frac{1200}{3}\) = \(\frac{400}{1}\)
x = ±\(\sqrt{400}\)
x = 20

When x = 20
Pd = 1600 – x2
= 1600 – (20)2
= 1600 – 400 = 1200
Pd = 1200
Ps = 2x2 + 400
= 2(20)2 + 400 = 2(400) + 400
Ps = 1200
Consumer’s Surplus (CS):
Samacheer Kalvi 11th Economics Guide Chapter 12 Mathematical Methods for Economics img 13

Producers Surplus(PS):
Samacheer Kalvi 11th Economics Guide Chapter 12 Mathematical Methods for Economics img 9

Samacheer Kalvi 11th Economics Guide Chapter 12 Mathematical Methods for Economics

Question 4.
What are the ideas of Information and communication technology used in economics?
Answer:
Introduction: Information and communication Technology [ICT] is the infrastructure that enables computing faster and accurate. The following table gives an idea of range of technologies that fall under the category of ICT.
Samacheer Kalvi 11th Economics Guide Chapter 12 Mathematical Methods for Economics img 10

The evaluation of ICT has five phases:
They are evaluation in:

  1. Computer
  2. PC – Personal Computer
  3. Microprocessor
  4. Internet
  5. Wireless links

In Economics, the uses of mathematical and statistical tools need the support of ICT for:

  1. Data Compiling
  2. Editing
  3. Manipulating
  4. Presenting the results

Samacheer Kalvi 11th Economics Mathematical Methods for Economics Additional Important Questions and Answers

PART – A

Multiple Choice Questions:

Question 1.
The point of intersection of demand line and supply line is known as ……………………
(a) Equilibrium
(b) Intersect
(c) Mid point
(d) Equal
Answer:
(a) Equilibrium

Samacheer Kalvi 11th Economics Guide Chapter 12 Mathematical Methods for Economics

Question 2.
…………………… is a rectangular array of numbers systematically arranged in rows and columns within brackets.
(a) Maths
(b) Geometry
(c) Graph
(d) Matrix
Answer:
(d) Matrix

Question 3.
……………………. means a change in the dependent variable with respect to small change in independent variable.
(a) Differential
(b) Differentiation
(c) Differentiating
(d) Derivative
Answer:
(a) Differential

Samacheer Kalvi 11th Economics Guide Chapter 12 Mathematical Methods for Economics

Question 4.
……………………….. is an addition to the total cost caused by producing one more unit of output.
(a) Marginal Cost
(b) Marginal Product
(c) Marginal Concepts
(d) Marginal Revenue
Answer:
(a) Marginal Cost

Question 5.
Consumer’s surplus theory was developed by the ………………………….
(a) Alfred Marshall
(b) Adam Smith
(c) Lionel Robbinson
(d) Malthus
Answer:
(a) Alfred Marshall

Question 6.
……………………… is a word processor.
(a) MS Word
(b) Micro processor
(c) Scanner
(d) Personal computer
Answer:
(a) MS Word

Samacheer Kalvi 11th Economics Guide Chapter 12 Mathematical Methods for Economics

Question 7.
……………………. is the infrastructure that enable computing faster and accurate.
(a) Information and Communication Technology
(b) Information and Computer Technology
(c) Information and Connection Technology
(d) Information and Communication Technology
Answer:
(d) Information and Communication Technology

Question 8.
…………………… is used in data analysis by using formula.
(a) MS Word
(b) Microsoft
(c) Word processer
(d) Microprocessor
Answer:
(b) Microsoft

Samacheer Kalvi 11th Economics Guide Chapter 12 Mathematical Methods for Economics

Question 9.
……………………. is a table like document containing rows and columns with data and formula.
(a) Work Excel
(b) Work Microsoft
(c) Work Processor
(d) Work Sheet
Answer:
(d) Work Sheet

Question 10.
……………………… helps to do data analysis and data presentation in the form of graphs.
(a) MS Excel
(b) Microsoft
(c) Start Excel
(d) Microprocessor
Answer:
(a) MS Excel

ACTIVITY

Question 1.
The petrol consumption of your car is 16 Kilometers per litre. Let x be the distance you travel in Kilometers and p the price per litre of petrol in Rupees. Write expressions for demand for Petrol?
Answer:
x – Total distance in Km.
p – Price per litre in rupees.
Equation of demand function joining two data points (16, 1) and (8, 2) respectively.
"Samacheer
Samacheer Kalvi 11th Economics Guide Chapter 12 Mathematical Methods for Economics img 11

– 8y + 8 = x – 16
x – 16 – 8 + 8y = 0
x + 8y – 24 = 0
x = 24 – 8y
y = p
∴ The demand function x = 24 – 8p
Demand ∝ \(\frac{1}{Price}\)

Samacheer Kalvi 11th Economics Guide Chapter 12 Mathematical Methods for Economics

Question 2.
Make up your own demand function and then derive the corresponding MR function and find the output level which corresponds to zero marginal revenue?

Question 3.
Use an Excel spreadsheet to calculate values for Quantity of demand at various prices for the function Q = 100 – 10P then plot these values on a graph?

Question 4.
Open MS – Word and put the title as PRESENT AND ABSENT OF STUDENTS and insert the table and collect the data for all classes of your school and find the class of highest absentees in a month. Justify with reason for the absentees in a paragraph by using MS Word?

Activity 2, 3 and 4 can be done by the students individually.

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