Two companies, Lawnman Inc. and Tauro Co., are competing in the manufacture and

Question

Two companies, Lawnman Inc. and Tauro Co., are competing in the manufacture and sale of a new type of kryptonite-powered lawnmowers. Lawnman has a somewhat older plant and requires a variable cost of $150 per lawnmower; its fixed costs are $200,000 per year. Tauro's plant is more automated and thus has lower unit variable costs of $100; its fixed cost is $400,000.

Since the two companies are close competitors, they both sell their product at $250 per unit.

What is the break-even quantity for each?

At which quantity would the two companies have equal profits?

If sales of each company were to reach 4,500 units per year, which company would be more profitable? Why?

Explanation / Answer

For firm 1,

C1 = 200 + 150x

TR1 = 250x, where x is the number of units sold.

In eq, 200 + 150x = 250x or 100x=200 or x=2

For firm 2,

C2 = 400 + 100y

TR2 = 250y, where y is the number of units sold.

In eq, 400 + 100y = 250y or 150y=400 or x=2.67

250x – (200 + 150x) = 250x – (400 +100x)

100x – 200 = 150x – 400

200 = 50x or x=4

Profit 1 = 250x – (200 + 150x) = 100x – 200 =450000-200

Profit 2 = 250x – (400 +100x) = 150x – 400 = 625000-400

Profit 2>1, at such high levels of output firm 2 is more efficient.

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