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## 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

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

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

Question 7.

(y – y_{1}) = m(x-x_{1}) 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

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

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

Question 13.

Differentiation of x^{n} 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

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

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

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 = x

∴ x = 7

Question 2.

Given the demand function q = 150 – 3p, derive a function for MR?

Answer:

Demand function q = 150 – 3p

\(\frac{dq}{dp}\) = -3

Question 3.

Find the average cost function where TC = 60+ 10x + 15x^{2}

Answer:

TC = 60 + 10x +15x^{2}

Average Cost = \(\frac { TC }{ x }\)

= \(\frac{60+10 x+15 x^{2}}{x}\)

= \(\frac { 60 }{ x }\) + \(\frac { 10x }{ x }\) + \(\frac{15 x^{2}}{x}\)

AC = \(\frac { 60 }{ x }\) + 10 + 15x

Question 4.

The demand function is given by x = 20 – 2p – p^{2} where p and x are the prices and the quantity respectively. Find the elasticity of demand for p = 2.5?

Answer:

e_{d} = \(\frac{p}{x}\) \(\frac{dx}{dp}\)

\(\frac{dx}{dp}\) = -2-2p

Question 5.

Suppose the price p and quantity q of a commodity are related by the equation q = 30 – 4p – p^{2} find

(I) e_{d} at p = 2

(II) MR

Answer:

(I)

(II) MR – [Marginal Revenue]

MR = \(\frac{dq}{dp}\)

Given q = 30 – 4p – p^{2}

\(\frac{dq}{dp}\) = 0 – 4(1) – 2p^{2-1}

\(\frac{dq}{dp}\) = -4 – 2p

Question 6.

What is the formula for the elasticity of supply if you know the supply function?

Answer:

Elasticity of supply = \(\frac{dq}{dp}\)

Question 7.

What are the main menus of MS word?

Answer:

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 Mathematical Methods in Economics:

- Mathematical methods help to present the economic problems in a more precise form.
- Mathematical methods help to explain economic concepts.
- Mathematical methods help to use a large number of variables in economic analyses.
- Mathematical methods help to quantify the impact or effect of any economic activity implemented by the government or anybody.

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 – 0.03q^{2} and the cost function is C = 150q + 60,000, where q is the number of units produced. Find AR, AC, MR and MC?

Answer:

R = 600q – 0.03q^{2}

C = 150q + 60000

(i) AR = \(\frac { R }{ q }\)

= \(\frac{600 q-0.03 q^{2}}{q}\)

= \(\frac { 600q }{ q }\) – \(\frac{0.03 \mathrm{q}^{2}}{\mathrm{q}}\)

= AR = 600 – 0.0.q

(ii) AC = \(\frac { c }{ q }\)

= \(\frac { 150q + 60000 }{ q }\)

= \(\frac { 150q }{ q }\) + \(\frac { 60000 }{ q }\)

AC = 150 + (\(\frac { 60000 }{ q }\))

(iii) MR = \(\frac { dr }{ dq }\)

R = 600q – 0.03q

\(\frac { dR }{ dq }\) = 600 (1) – 0.03 (2q)

MR = 600 – 0.06q

(iv) MC = \(\frac { dc }{ dq }\)

C = 150q + 60000

\(\frac { dc }{ dq }\) = 150 (1) + 0

MC = 150

Question 4.

Solve the following linear equations by using Cramer’s rule?

x_{1} – x_{2} + x_{3} = 2;

x_{1} + x_{2} – x_{3} = 0;

– x_{1} – x_{2} – x_{3} = -6

Answer:

x_{1} – x_{2} + x_{3} = 2

x_{1} + x_{2} – x_{3} = 0

– x_{1} – x_{2} – x_{3} = -6

AX = B

Question 5.

If a firm faces the total cost function TC = 5 + x^{2} where x is output, what is TC when x is 10?

Answer:

TC = 5 + x^{2}

TC = 5 + 10^{2}

TC = 5 + 100

∴TC = 105

Question 6.

If TC = 2.5q^{3} – 13q^{2} + 50q + 12 derive the MC function and AC function?

Answer:

\(\frac{dc}{dq}\) = MC

AC = \(\frac{TC}{q}\)

\(\frac{dc}{dq}\) = 2.5(3)q^{2} – [13 × 2]q + 50

MC = 7.5q^{2} – 26q + 50

AC = \(\frac { 2.5q^{ 3 }-13q^{ 2 }+50q+12 }{ q } \)

∴ AC = 2.5q^{2} – 13q + 50 + \(\frac{12}{q}\)

Question 7.

What are the steps involved in executing a MS Excel sheet?

Answer:

- MS – Excel is used in data analysis by using formulas.
- A spreadsheet is a large sheet of paper that contains rows and columns.
- The intersection of rows and columns is termed a cell.
- MS – Excel 2007 version supports up to 1 million rows and 16 thousand columns per worksheet.

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 worksheet is a table like a document containing rows and columns with data and formula

There are four kinds of calculation operators. They are:

- Arithmetic
- Comparison
- Text Concatenation [link together]
- Reference

MS – Excel helps to do data analysis and data presentation in the form of graphs, diagrams, area charts, 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:

- What does Qt = f (Pt, Y, A,N, Pc) mean in words?
- Identify the independent variables.
- 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-efficient of the different independent variables should be positive or negative]

- “Pc ” = Price of processed pocket milk

When the price of processed milk increases and the quantity demanded of fresh milk decreases. - “N” = Population

When the population increases and the 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 the quantity of milk demanded Increases.

“Pt” – Price of fresh cow milk

When the price of fresh cow milk Increases the quantity of milk demanded decreases.

∴ Qt = (-Pt) (+Y) (+A) (+N) (- Pc)

(-) means decreases; (+) means Increases

∴ Qt = [- Pt + Y + A +N – Pc]

Question 2.

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

- Zero
- ₹20
- ₹40

Answer:

Question 3.

The demand and supply functions are P_{d} = 1600 – x^{4} and P_{s} = 2x^{2} + 400 respectively. Find the consumer’s surplus and producer’s surplus at the equilibrium point?

Answer:

P_{d} = 1600 – x^{2}

P_{s} = 2x^{2} + 400

P_{d} = P_{s}

1600 – xc = 2x^{2} + 400

⇒ 1600 – x^{2} – 2x^{2} – 400 = 0

⇒ -3x^{2} + 1200 = 0

x^{2} = \(\frac{1200}{3}\) = \(\frac{400}{1}\)

x = ±\(\sqrt{400}\)

x = 20

When x = 20

P_{d} = 1600 – x^{2}

= 1600 – (20)^{2}

= 1600 – 400 = 1200

P^{d} = 1200

P^{s} = 2x^{2} + 400

= 2(20)^{2} + 400 = 2(400) + 400

P^{s} = 1200

Consumer’s Surplus (CS):

Producers Surplus(PS):

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 the range of technologies that fall under the category of ICT.

The evaluation of ICT has five phases:

They are evaluation in:

- Computer
- PC – Personal Computer
- Microprocessor
- Internet
- Wireless links

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

- Data Compiling
- Editing
- Manipulating
- 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) Midpoint

(d) Equal

Answer:

(a) Equilibrium

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 a small change in the independent variable.

(a) Differential

(b) Differentiation

(c) Differentiating

(d) Derivative

Answer:

(a) Differential

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) Microprocessor

(c) Scanner

(d) Personal computer

Answer:

(a) MS Word

Question 7.

……………………. is the infrastructure that enables 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

Question 9.

……………………. is a table like a 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 the 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.

– 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 ∝ \(\frac{1}{Price}\)

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 the reason for the absentees in a paragraph by using MS Word?

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