MEC-203 Archives - IGNOU CORNER

MEC-203: Quantitative Methods – Solved Assignment 2024-25 (All Questions Answered)

Write short notes on following: a) Homogeneous and Homothetic functions b) L’Hopital’s rule c) Order of a difference equation d) Cramer – Rao inequality

a) Homogeneous and Homothetic Functions Homogeneous Function: A function f(x, y) is said to be homogeneous of degree n if scaling all inputs by a constant λ results in the output being scaled by λⁿ. Mathematically, f(λx, λy) = λⁿf(x, y) Example: f(x, y) = x² + y² is homogeneous of degree 2. In economics,

Write short notes on following: a) Homogeneous and Homothetic functions b) L’Hopital’s rule c) Order of a difference equation d) Cramer – Rao inequality Read More »

For the function f(x) = cos(x), find (i) linear and quadratic approximations, and (ii) Maclaurin’s series expansion… [Full question continued]

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Part a) Approximations and Maclaurin Series of f(x) = cos(x) i) Linear and Quadratic Approximations We are given: f(x) = cos(x) To find linear and quadratic approximations, we use the Taylor series around x = 0 (Maclaurin series). Step 1: Derivatives of cos(x) f(x) = cos(x) f'(x) = -sin(x) f”(x) = -cos(x) f”'(x) = sin(x)

For the function f(x) = cos(x), find (i) linear and quadratic approximations, and (ii) Maclaurin’s series expansion… [Full question continued] Read More »

Consider the following Lagrange problem: Maximise f(u,v) = u + 3v subject to g(u,v) = u² + av² = 10. Use the envelope theorem… [Full question continued]

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Part a) Lagrange Problem and Envelope Theorem Given: Maximize: f(u, v) = u + 3v Subject to: g(u, v) = u² + av² = 10 We are told to apply the Envelope Theorem and estimate f* when a = 1.01 Step 1: Lagrangian Function L(u, v, λ) = u + 3v + λ(10 − u²

Consider the following Lagrange problem: Maximise f(u,v) = u + 3v subject to g(u,v) = u² + av² = 10. Use the envelope theorem… [Full question continued] Read More »

What is a standard error and why is it important? [Includes sub-question with failure data]

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Part a) What is Standard Error and Why is it Important? Definition: The Standard Error (SE) is a statistical term that measures the accuracy with which a sample distribution represents a population. In simpler terms, it tells us how much the sample mean (or proportion) is likely to vary from the actual population mean (or

What is a standard error and why is it important? [Includes sub-question with failure data] Read More »

Let J be the functional defined by J(y) = ∫ (y′² − y² + 2ty) dt from 0 to 1… [Full question continued]

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Introduction This question involves two problems related to the calculus of variations, which is a branch of mathematics concerned with finding functions that optimize functionals (integrals depending on functions and their derivatives). We are asked to find the extremals — functions y(t) or x(t) — that make the given functionals take on a maximum or

Let J be the functional defined by J(y) = ∫ (y′² − y² + 2ty) dt from 0 to 1… [Full question continued] Read More »

Consider a fishing optimal control problem which is defined by Pt = a + bpt − xt… [Full question continued]

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Introduction This question involves an optimal control problem in the context of renewable resource management—specifically, the fishing industry. The goal is to determine the optimal harvesting strategy (xt) that maximizes utility over time while accounting for population dynamics of the fish stock. We are also asked to derive the transversality condition and solve for the

Consider a fishing optimal control problem which is defined by Pt = a + bpt − xt… [Full question continued] Read More »

Consider an investor who at time t = 0 is endowed with initial capital of x(0)=x0 > 0… [Full question continued]

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Introduction This problem describes an optimal control problem in economics, specifically dealing with intertemporal consumption decisions made by an investor. The goal is to choose a consumption function c(t) over time interval [0, T] that maximizes utility from consumption while ensuring the investor remains solvent over time, meaning that capital remains positive. Let’s break it

Consider an investor who at time t = 0 is endowed with initial capital of x(0)=x0 > 0… [Full question continued] Read More »