Assignment Code: ASST BECC 104/TMA/ July 2023 and January 2024

Course Code: BECC-104

Assignment Name: Mathematical Methods in Economics

Year: 2023-2024

Verification Status: Verified by Professor

Assignment A

Answer the following Long Category questions in about 500 words each. Each question carries 20 marks. Word limit will not apply in the case of numerical questions. 2 x 20 = 40

Assignment B

Answer the following Middle Category questions in about 250 words each. Each question carries 10 marks. Word limit will not apply in the case of numerical questions. 3 X 10 = 30

Q8) Explain the concept of maximum value function.

Ans) The concept of a maximum value function is a fundamental idea in mathematics and optimization theory. In essence, a maximum value function represents the highest attainable output or result within a given set of inputs or domain. It is a function that maps input values to output values and provides a clear understanding of the peak or optimal point within that domain.

In mathematical terms, for a function f(x), the maximum value function identifies the largest value that f(x) can achieve over its entire domain or within a specific range of interest. This maximum value is often denoted as , and the corresponding input value that yields this maximum is referred to as .

The concept of a maximum value function is prevalent in various fields, including economics, engineering, physics, and computer science. It plays a critical role in decision-making processes, resource allocation, and problem-solving. For example, in economics, firms aim to maximize their profit function by determining the level of production or pricing strategy that yields the highest profit. Similarly, in engineering, optimization algorithms seek to find the maximum value function to design efficient systems or structures.

To identify the maximum value of a function, mathematical techniques such as calculus, optimization algorithms, and critical point analysis are often employed. These methods help locate the input values at which the function reaches its peak, allowing for informed decision-making and the efficient utilization of resources. In summary, the concept of a maximum value function is fundamental in various disciplines, facilitating the identification of optimal solutions and outcomes.