Breakeven Analysis

Breakeven Analysis

The total cost equation is a straight line with a positive slope, indicating that total cost increases as production volume or demand increases, with the fixed cost representing the y-intercept of the equation (Equation 2-5 and Figure 2-4). .

The total revenue function is a concave-down parabola (for a linear price-demand relationship), indicating that the total cost function may intersect it at two points – representing breakeven points where no profit or loss occurs. Producing below or above the demand levels at these intersections results in a loss, while operating between them yields a positive profit.

The breakeven point occurs when total revenue equals total cost (same as setting the profit function in Equation 2-7 to zero.):

Therefore, 

The two breakeven demand values, where neither profit nor loss occurs, can be found by solving:

Equation 2-10

With the profit conditions met, the discriminant (the term inside the square root in the numerator of Equation 2-9 is positive, ensuring two distinct, real, and positive breakeven demand values.