Page 177 - DMTH201_Basic Mathematics-1

Basic Mathematics – I

Notes (iii) We have x = x in equilibrium
s d
300 + 20p = 1800 – 40p
1500
or p = = 25 (equilibrium price)
60
Further, equilibrium quantity is x = 300 + 20 × 25 = 800 units.

Break-Even Point

Profit of a firm is given by the difference of its total revenue and total cost. Thus, profit = TR –
TC.
In general, when a firm starts the production of a commodity it operates at loss when its output
is below a certain level, say x, because the total revenue is not large enough to cover fixed costs.
However, as the level of output becomes greater than x, the firm starts getting profits. The level
of output x is termed as the break-even point. Thus, break-even point is the lowest level of output
at which the loss of the firm gets eliminated. It is given by the equation TR - TC = 0 (or TR = TC).

Example
A company decides to set up a small production plant for manufacturing electronic clocks. The
cost for initial set up is 9 lakhs. The additional cost for producing each clock is 300. Each clock
is sold at 750. During the first month, 1,500 clocks are produced and sold:
(i) Determine the total cost function C(x) for the production of x clocks.

(ii) Determine the revenue function R(x).
(iii) Determine the profit function P(x).
(iv) How much profit or loss the company incurs during the first month when all the 1,500
clocks are sold?
(v) Determine the break-even point.
Solution:
(i) We are given TFC = 9,00,000 and TVC(x) = 300x
Total cost function, C(x) = 9,00,000 + 300x

(ii) Total revenue function, R(x) = p.x = 750x
(iii) Profit function, P(x) = TR - TC = 750x - 9,00,000 - 300x
= 450x - 9,00,000

(iv) Profit when x = 1,500, is given as
P(1,500) = 450 × 1,500 - 9,00,000 = 6,75,000 - 9,00,000 = - 2,25000
Note that profit is negative. Thus, the company incurs a loss of 2,25,000 during first
month.
(v) We know that TR = TC, at the break-even point
750x = 9,00,000 + 300x

9,00,000
or 450x = 9,00,000 or x = = 2,000 clocks.
450

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