The linear break-even analysis helps to determine the least size of output that should be produced to avoid losses to a firm at initial stages of production. The analysis assumes that the total cost and the total revenue curves are both linear. Break-even refers to the condition of equality between TR and TC.
The general relationship between MR and AR of a monopoly firm involves the price elasticity of demand. It can be derived as below.
which is negative for normal goods. | e | represents the numerical value of e. Thus, | e | = -e, as e is already negative.
Thus, TR = TC at the point of the break-even. The equations of TR and linear TC curves are, respectively, given as
TR = PQ
(where, P is price and Q is quantity)
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and, TC = a + bQ
(where, a is total fixed cost, b is average variable cost and Q is quantity) For break-even,
Fig. 5.18: Break-even output (OQ) without profits (left panel) and break-even output (OQ) with profits (right panel): TR passes through the origin while TC (TC + π) makes an intercept on the vertical axis.
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Illustration 5.2
A firm has incurred a cost of Rs 200,000 on fixed factors. The variable cost per unit of output is Rs 20 and the selling price of the product is Rs 30.
(i) Determine the break-even output.
(ii) What would be your answer for (i) if the firm desires a profit of Rs 50,000?
Solution
(i) The break-even output from equation 5.20
Q = a/P-b
Substituting a = 200,000, P = 30 and b = 20 in the expression we have
Q = 200,000/30 – 20 = 20,000 units.
(ii) The break-even output with a profit of Rs 50,000 is given by equation 5.21. Thus
