Question

Two firms in the same industry sell their product at $10. The first firm has a total fixed cost of $100 and an average variable cost of $6; whereas the corresponding values for the second firm are $300 and $3.33 respectively. (a) Compute the sales elasticity of profit (ie. the percent change in total profit when sales increase by 1%) for the two firms at the point where each sells 60 units and also at the point where each sells 70 units. (b) What happens to this elasticity at the breakeven levels of output? (c) Comment on and interpret the elasticity values you computed above. The firm with the higher elasticity is said to be more highly leaveraged. What does this mean? How do you explain the difference between the elasticities of the two firms?

Answer 1

Solution

(a) Sales elasticity of profit :

When their sales are 60 and 70 units respectively:

1 st firm:

Sales revenue @ 60 units = $600 ; Fixed Cost = $100 ; Average Variable Cost = $6 / unit

So,Total Profit = 600 - (100 + (60 * 6)) => $140

When sales increase by 1 % from here means Sales = 60.6 units

=> Sales revenue = $606 ; Fixed Cost = $100 ; Average Variable Cost = $6 / unit

So Total profit = 606 - (100 + (60.6* 6)) => $142.4

So,when sales are increasing by 1%,the total profit is increasing from $140 to $142.40 i.e., by 1.71%

@70 units:

Sales revenue @ 70 units = $700 ; Fixed Cost = $100 ; Average Variable Cost = $6 / unit

So,Total Profit = 700 - (100 + (70 * 6)) => $180

When sales increase by 1 % from here means Sales = 70.7 units

=> Sales revenue = $707 ; Fixed Cost = $100 ; Average Variable Cost = $6 / unit

So Total profit = 707 - (100 + (70.7* 6)) => $182.8

So,when sales are increasing by 1%,the total profit is increasing from $140 to $142.40 i.e., by 1.55%

2 nd Firm:

Sales revenue @ 60 units = $600 ; Fixed Cost = $300 ; Average Variable Cost = $3.33 / unit

So,Total Profit = 600 - (300 + (60 * 3.33)) => $100.20

When sales increase by 1 % from here means Sales = 60.6 units

=> Sales revenue = $606 ; Fixed Cost = $100 ; Average Variable Cost = $6 / unit

So,Total profit = 606 - (300 + (60.6* 3.33)) => $104.20

So,when sales are increasing by 1%,the total profit is increasing from $140 to $142.40 i.e., by 3.99%

Sales @ 70 units:

Sales revenue @ 70 units = $700 ; Fixed Cost = $300 ; Average Variable Cost = $3.33 / unit

So,Total Profit = 700 - (300 + (70 * 3.33)) => $166.90

When sales increase by 1 % from here means Sales = 70.7 units

=> Sales revenue = $707 ; Fixed Cost = $300 ; Average Variable Cost = $3.33 / unit

So,Total profit = 707 - (300 + (70.7* 3.33)) => $177.569

So,when sales are increasing by 1%,the total profit is increasing from $140 to $142.40 i.e., by 6.39%

(b)

Break even levels of output

1 st firm : Fixed Cost / (Contribution per unit) i.e.,Total Fixed Cost / (Sales price per unit - total variable cost)

= 100 / (10-6) i.e., 25 units

Since it is the break-even point the total profit is $0

When sales increase by 1 % from here means Sales = 25.25 units

=> Sales revenue = $252.50 ; Fixed Cost = $100 ; Average Variable Cost = $6 / unit

So Total profit = 252.50 - (100 + (25.25* 6)) => $1

2 nd firm

= 300 / (10-3.33) i.e., 44.97 units

Since it is the break-even point the total profit is $0

When sales increase by 1 % from here means Sales = 45.42 units

=> Sales revenue = $454.2 ; Fixed Cost = $300 ; Average Variable Cost = $3.33/ unit

So,Total profit = 454.2- (300 + (45.42* 3.33)) => $ 2.95

So,elasticity increases at these break-even points

The fims with high amounts of elasticity levels are more leveraged.These companies have higher costs in the form of fixed costs.So, their break-even levels of outputs are more.So,the variability of total profit with variability of sales (sales elasticity of profit) is more in these companies.So, in these companies the risk (in terms of variability of total profit) is more in response to sales and also since these firms have higher break-even output.

The second firm is more elastic to sales than the 1 st firm so it more leveraged.

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