Page 373 - DMTH201_Basic Mathematics-1

Basic Mathematics – I

Notes 14.5 Summary

We can write total revenue as TR = p.x, where p is price and x is quantity. Total revenue
2
d TR d TR
will be maximum at a level of output where = 0 (or MR = 0) and < 0. The first
dx dx 2
d TR dp p dx
order condition implies that = p x 0 or 1 i.e. h = 1. Thus maxima of
dx dx x dp
total revenue occurs at a level of output where elasticity of demand is unity.
Let p = f(x) and p = g(x) be the market demand and supply of a commodity and a specific tax
of t per unit be imposed. Then under equilibrium, we can write f(x) = g(x) + t.

Let x be the equilibrium quantity obtained by solving the above equation for x. We can
t
write the expression for tax revenue T as T = t.x (note that x is a function of t).
t t
TP L f L
The average product of labour is AP = , the marginal product of labour is MP
L L L L
dx d TP L dx
L
= f ( ) and necessary condition for maximum output is MP L 0
dL dL dL
x
C F ( ) dC
If total cost C = F(x), then we can define AC , and MC = F ( ).
x
x x dx
14.6 Keywords

Derivative: The rate at which a function changes with respect to its independent variable.
Geometrically, this is equivalent to the slope of the tangent to the graph of the function.

Domain: The set, or collection, of all the first elements of the ordered pairs of a function is called
the domain of the function.
Function: A set of ordered pairs. It results from pairing the elements of one set with those of
another, based on a specific relationship. The statement of the relationship is often expressed in
the form of an equation.
Range: The set containing all the values of the function.

14.7 Self Assessment

2
2
3
1. Total number of parallel tangents of f (x) = x – x + 1 and f (x) = x – x –2x + 1 is equal to
1 2
(a) 2
(b) 3
(c) 4
(d) None of these
3
2
2. The function 2tan x – 3tan x + 12tanx + 3, x is
(a) increasing
(b) decreasing

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