Break Even Analysis
Overview
Break even analysis is an analysis used to help understand the trade off between price increases and lost demand. \
Specifically, when considering a price increase,
the break even point is the amount of lost units sold that exactly negates the positive benefit of
higher prices. That is, it asks the question, by how much would sales have to fall in order for the price increase to
have no effect on profit.
Calculation
Starting with the basic profitability equation:
{% \pi = q \times p - fc - q \times vc %}
where
- {% q %} - units sold
- {% p %} - price
- {% fc %} - fixed costs
- {% vc %} - average variable costs
Denoting the original prices with a subscript of 0, and the new prices of a subscript of 1, we get
{% \pi_0 = q_0 \times p_0 - fc - q_0 \times vc_0 %}
{% \pi_1 = q_1 \times p_1 - fc - q_1 \times vc_1 %}
then
{% \pi_1 - \pi_0 = q_1 \times (p_1 - vc_1) - q_0 \times (p_0 - vc_0) %}
setting equal to zero
{% q_1 \times (p_1 - vc_1) = q_0 \times (p_0 - vc_0) %}
then we get
{% q_1/q_0 = (p_0 - vc_0)/ (p_1 - vc_1) %}
