Financial Mathematics

Let be the coded variable such that 2013 = 0:
So years become:
Let = production values.

Create a table:

Step 1: Compute sums:

Number of terms:

Step 2: Apply least squares formula:
The equation of the trend line is:
Calculate slope and intercept:

So, the trend equation is:

Step 1: Calculate 4-year moving totals:
Add each set of 4 consecutive years:
2001–2004:
2002–2005:
2003–2006:
2004–2007:
2005–2008:
2006–2009:
2007–2010:
Step 2: Convert to 4-year centered moving averages:
Centered average is the average of two consecutive 4-year totals divided by 4.
E.g., (7870 + 7630)/8 = 1937.5
Continue for all valid periods and get centered values.
Step 3: Calculate seasonal index = (Actual / Moving Average) × 100 for mid-year
E.g., for 2003: Index = 2150, Avg ≈ 1937.5 SI =
Continue this for each year.
Step 4: Group years by quarter or season, average seasonal indices per group.
Then scale the average seasonal indices so that their total is 400 (for 4 seasons).

Marginal revenue (MR) is the derivative of total revenue (TR) with respect to quantity .
First, find total revenue: .
Now, differentiate with respect to to get MR:

Now substitute :

So, the marginal revenue when 2 units are sold is ₹14.