Question

If marginal revenue is shown by the equation MR= 100-10q, what is the corresponding demand curve?
1) p= 100-5Q
2) P= 50-10Q
3) P=100-20Q
4) P=50-50Q

Answer 1

The correct answer is (1) p= 100-5Q

The demand function will be derived through integration of marginal revenue function.

The marginal revenue is given as:

$\text{MR}=100-10Q$

The total revenue function will be:

$\text{Total revenue}=\dfrac{100Q}{1}-\dfrac{10Q^2}{2}=100Q-5Q^2$

Total revenue is derived by multi[lying the demand function by the quantity. Therefore, the demand function will be derived as follows:

$\text{demand function}=\dfrac{\text{Total revenue function}}{\text{Quantity}}$

$\text{demand fucnction}=\dfrac{100Q-5Q^2}{Q}=100-5Q$

The demand function must be P=100-5Q