Revenue functions from marginal revenue functions - class-XII

The rate of change of price with respect to demand is the derivative dp/dD. Differentiating p = 60 + 2D - 10D² term by term gives dp/dD = 0 + 2 - 20D = 2 - 20D. Option A incorrectly divides 60 by D, and Option C has an incorrect coefficient.

$\Rightarrow$  We have $TC=a+bQ+cQ^2+dQ^3$

$MC = \dfrac{\mathrm{d} TC}{\mathrm{d} x}$

$\Rightarrow$  We have given, $y=48x-2x^2$

Suppose: $y = ax^n$
Then, $dy = nax^{n-1}$

Remember

$\dfrac{x^4}{4} = \dfrac{1}{4}x^4$

So differentiating both terms in the expression for using the formula gives:

$\dfrac{dy}{dx} = x^3+4x$

The cost function equation is expressed as C(x)= FC + V(x), where C equals total production cost, FC is total fixed costs, V is variable cost and x is the number of units.

$4500$ =fixed expenditures

$10x$ = variable cost

C(X)= $4500+10x$

$\Rightarrow$  Here, price per unit $(p)=Rs.6$

R(x)= ( price per unit)*(number of units produced or sold)

Revenue function = $25 \times x$ (number of units)

Revenue function =$25x$

$\Rightarrow$  Here, price per unit $(p)=Rs.6$ and fix cost is $Rs.4500$.

$\Rightarrow$  Here, price per unit $(p)=Rs.6$