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11th Standard English Medium Economics Subject Mathematical Methods for Economics Book Back 3 Mark Questions with Solution Part - I

Published on: 10/06/2021

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Std: 11th Standard - Economics

chapter: - Book back Questions

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Questions:

Generic 3

5 x 3 = 15

If a firm faces the total cost function TC = 5 + x² where x is output, what is TC when x is 10?

Solve the following linear equations by using Cramer's
x₁ - x₂ + x₃ = 2;
x₁ + x₂ - x₃ = 0;
-x₁ - x₂ - x₃ = -6

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.

Solve for x quantity demanded if 16x - 4 = 68 + 7x

Illustrate the uses of Mathematical Methods in Economics.

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Answers Key:

Generic 3

5 x 3 = 15

TC = 5 + 10² (∴ x = 10)
= 5 + 100 = 105
TC = 105

x₁ - x₂ + x₃ = 2;
x₁ + x₂ - x₃ = 0;
-x₁ - x₂ - x₃ = -6
\(\Delta =\left|\begin{array}{ccc} 1 & -1 & 1 \\ 1 & 1 & -1 \\ -1 & -1 & -1 \end{array}\right| \)
=1(- 1 - 1) + 1(- 1 - 1) + 1(- 1 + 1)
= - 2 - 2 + 0 = -4
\(\Delta x =\left|\begin{array}{ccc} 2 & -1 & 1 \\ 0 & 1 & -1 \\ -6 & -1 & -1 \end{array}\right| \\\)
=2 (- 1 - 1) + 1 (0 - 6) + 1(0 + 6)
= - 4 - 6 + 6 = -4
\(\Delta y =\left|\begin{array}{ccc} 1 & 2 & 1 \\ 1 & 0 & -1 \\ -1 & -6 & -1 \end{array}\right|\)
=1 (0 - 6) - 2(- 1 - 1) + 1( - 6 + 0)
= - 6 + 4 - 6 = -8
\(\Delta z =\left|\begin{array}{ccc} 1 & -1 & 2 \\ 1 & 1 & 0 \\ -1 & -1 & -6 \end{array}\right| \)
=1( - 6 - 0) + 1(- 6 - 0) + 2(- 1 + 1)
= - 6 - 6 + 0 = -12
\(x =\frac{\Delta x}{\Delta}=\frac{-4}{-4}=1 \)
\(y =\frac{\Delta y}{\Delta}=\frac{-8}{-4}=2 \)
\(z =\frac{\Delta z}{z}=\frac{-12}{-4}=3\)

\(\mathrm{AR}=\frac{\text { Revenue function }}{\text { no.of units }}=\frac{600 \mathrm{q}-0.03 \mathrm{q}^{2}}{\mathrm{q}}=600-0.03 \mathrm{q}=\mathrm{AR} \)
\(\mathrm{MR} =\frac{\mathrm{d}}{\mathrm{dq}}(\mathrm{TR}) \)
\(=\frac{\mathrm{d}}{\mathrm{dq}}(600 \mathrm{q})-\frac{\mathrm{d}}{\mathrm{dq}}\left(0.03 \mathrm{q}^{2}\right) \)
\(=600-2(0.03) \mathrm{q} \)
\(=600-0.06 \mathrm{q}=\mathrm{MR} \)
\(\mathrm{AC} =\frac{150 \mathrm{q}+60,000}{\mathrm{q}}=150+\frac{60,000}{\mathrm{q}}=\mathrm{AC} \)
\(\mathrm{MC} =\frac{\mathrm{d}}{\mathrm{dq}}(\mathrm{TC}) \)
\(=\frac{\mathrm{d}}{\mathrm{dq}}(150 \mathrm{q})+\frac{\mathrm{d}}{\mathrm{dq}}(60,000)=150+0=150=\mathrm{MC}\)

16x - 4 = 68 + 7x
16x - 7x = 68 + 4
9x = 72;
x = 8

(i) Mathematical methods help to present the economic problems in a more precise form.
(ii) It helps to explain economic concepts.
(iii) It helps to use a large number of variables in economic analysis.
(iv) To quantify the effect of any economic activity implemented by government.