Question

Assume that a demand equation is giben by q = 7000-100p. Find the marginal revenue for the given production levels (levels of q). (Hint: Solve the demand equation for p and use R(q) = qp)

A. 1500 units (simplify answer)

B. 3500 units (simplify answer)

C. 6500 units (simplify answer)

Answer 1

Answer:

Option B.

Step-by-step explanation:

The demand function is

$q=7000-100p$

where p is price.

Solve the demand equation for p.

$100p=7000-q$

$p=\dfrac{7000-q}{100}$

The revenue function is

$R(q)=qp$

Substitute the value of p in the above function.

$R(q)=q(\dfrac{7000-q}{100})$

$R(q)=\dfrac{7000q-q^2}{100}$

Differentiate with respect to q.

$R'(q)=\dfrac{7000-2q}{100}$

Equate R'(q)=0,

$\dfrac{7000-2q}{100}=0$

$7000=2q$

Divide both sides by 2.

$3500=q$

Therefore, the correct option is B.