ACFI7027 - Quantitative Methods For Finance Assessment

Assignment Task

Introduction to differential calculus

• Differentiation is a basic concept in mathematics
• It provides the basis for optimisation (i.e., finding maximums and minimums)
• It can be graphically represented (simplifying the intuition for it)
• Slope (gradient) of a straight line: the change in y divided by the corresponding change in x

What is the slope (gradient) of these lines?

The gradient changes with x

• Variable slope: the point is that the slope changes for different values of x, so slope is a function of x.
• If y = f(x) Slope = derivative = f’(x) [read: f dashed of x ] Consider a graph of y = f(x) at the point (x, f(x))

Then move along the curve a small distance to the point (x+∆x, f(x+∆x))

The slope of the line joining the two points is (f(x+∆x)-f(x))/∆x As ∆x → 0, the slope of this line → the slope of the tangent

Applications of marginal analysis

There are countless examples in Economics and Finance:

• Monopolists and perfect competitors deciding what to do based on marginal costs and revenues
• Firms deciding about their employment looking at the marginal product of labour 
• Marginal propensity to consume/save 

Activity

Identify the x and y coordinates and categorise the stationary points of the function:

•  y = x3 + 4x2 – 3x – 10

The form of the final assessment

• Practical skills
• 70% of the module mark
• Similar to the mid-term – explanation, not just calculations
• Four tasks instead of two, each with 25% weighting; two on econometrics; two on mathematics skills

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