Marginal Cost and Revenue - Class XII Economics
Calculus-based applications in economics covering marginal cost, marginal revenue, average cost, and related cost function calculations using differentiation techniques
Questions
Marginal cost is defined as the instantaneous rate of change of total cost at any level of output.
- True
- False
If both average cost (AC) and marginal cost (MC) are U shaped, then
- AC will reach a minimum at a level of output that is less than that at which MC reaches a minimum.
- the total cost curve will be a straight line.
- AC will reach a minimum at a level of output that is greater than that at which MC reaches a minimum.
- both AC and MC will reach a minimum at the same level of output.
If average cost is at a minimum, then
- it is equal to marginal cost.
- total cost is also at a minimum.
- profit is at a maximum.
- all of the above are true.
If the amount of taxes paid $(T)$ depends on income $(x)$, how would you use calculus notation to describe the marginal tax rate? If taxes and income are both measured in dollars per year, what are the units of the marginal tax rate?
- Same as units of $T$
- Same as units of $x$
- Unit - less
- None of these
Differentiation refers to the process whereby we
- Calculate the area underneath a curve
- Calculate the intercept of a curve with the horizontal axis
- Calculate the gradient to a curve at any point on the curve
- Calculate the intercept of a curve with the vertical axis
The cost function for x units of a commodity is given by $C(x)=\dfrac{x^3}{3}+x^2-15x+3$. Find marginal cost function.
- $x^2+2x-15$
- $x^2-2x-15$
- $x^2+2x+15$
- None of these
If a function $p = 50 3x$, find $TR$.
- $50x-3x^2$
- $50x+3x^2$
- $50+3x^2$
- $50-3x^2$
When we differentiate an expression with respect to one of a number of independent variables, we are engaged in
- Finding definite integrals
- Total differentiation
- Partial differentiation
- Integration
The cost function of a firm $C(x)=2x^2-4x+5$. Find the average cost when $x=2$.
- $\dfrac{5}{2}$
- $\dfrac{1}{4}$
- $\dfrac{3}{4}$
- $\dfrac{5}{7}$
The cost function of a firm $C(x)=2x^2-4x+5$. Find the average cost when $x=10$.
- $16.5$
- $15.5$
- $12.5$
- None of these
The cost function of a firm $C(x)=4x^2-x+70$. Find the marginal cost when $x=3$.
- 23
- 24
- 25
- 26
The cost function of a firm $C(x)=2x^2-4x+5$. Find the marginal cost when $x=10$.
- 34
- 35
- 36
- None of these
The cost function of a firm $C(x)=2x^2-4x+5$. Find the marginal cost when $x=2$.
- 4
- 5
- 6
- 7
The cost function of a firm $C(x)=3x^2-2x+3$. Find the marginal cost when $x=3$.
- 19
- 18
- 16
- 17
The cost function for x units of a commodity is given by $C(x)=3x^3-6x+5$. Find marginal cost function , when $x=2$.
- $6$
- $4$
- $2$
- None of these
The cost function of a firm $C(x)=4x^2-x+70$. Find the average cost when $x=3$.
- $\dfrac{104}{3}$
- $\dfrac{103}{3}$
- $\dfrac{105}{3}$
- $\dfrac{103}{4}$
The demand function of a monopolist is given by $p=1500-2x-x^2$. Find the marginal revenue when $x=10$.
- $1170$
- $1160$
- $1150$
- None of these
Given the marginal cost function $\dfrac{2x}{3}+3-\dfrac{16}{x^2}$, find average cost function.
- $\dfrac{1}{3}x^2+3x-7+\dfrac{16}{x}$
- $\dfrac{1}{2}x^2+3x-7+\dfrac{16}{x}$
- $\dfrac{1}{4}x^2+3x-7+\dfrac{16}{x}$
- None of these
The cost function of a firm $C(x)=3x^2-2x+3$. Find the average cost when $x=3$.
- 8
- 9
- 10
- 12
If the total cost function for a manufacturer is given by $C =\dfrac{5x^2}{\sqrt(x^2+3)}+5000$, find marginal cost function.
- $\dfrac{3x(x^2+6)}{(x^2+3)^{(3/2)}}$
- $\dfrac{4x(x^2+6)}{(x^2+3)^{(3/2)}}$
- $\dfrac{5x(x^2+6)}{(x^2+3)^{(3/2)}}$
- None of these