## Q

Sales

Cost

20,000

\$ 40,000

\$ 80,000

40,000

80,000

100,000

60,000

120,000

120,000

80,000

160,000

140,000

100,000

200,000

160,000

120,000

240,000

Profit

20,000 40,000 60,000

degree of operating leverage

Percentage change in profit from a 1% change in output

does firm B. For example, at a production level of 40,000 units, B is losing \$8,000, but A breaks even. Firm C is highly automated and has the highest fixed costs, but its variable costs rise slowly. Firm C has a higher breakeven point than either A or B, but once C passes the breakeven point, profits rise faster than those of the other two firms.

The degree of operating leverage is the percentage change in profit that results from a 1 percent change in units sold:

Degree of Operating Leverage =

Percentage Change in Profit Percentage Change in Sales An/n

The degree of operating leverage is an elasticity concept. It is the elasticity of profits with respect to output. When based on linear cost and revenue curves, this elasticity will vary. The degree of operating leverage is always greatest close to the breakeven point.

For firm B in Figure 8.13, the degree of operating leverage at 100,000 units of output is 2.0, calculated as follows:4

An/n

AQ/Q

(\$41,600 - \$40,000)/\$40,000 (102,000 - 100,000)/100,000

Here, n is profit and Q is the quantity of output in units.

For linear revenue and cost relations, the degree of operating leverage can be calculated at any level of output. The change in output is AQ. Fixed costs are constant, so the change in profit An = AQ(P - AVC), where P is price per unit and AVC is average variable cost. Any initial profit level n = Q(P - AVC) - TFC, so the percentage change in profit is

The percentage change in output is AQ/ Q, so the ratio of the percentage change in profits to the percentage change in output, or profit elasticity, is