value of demand function when marginal revenue is given

Question

If the marginal revenue function is as follows $$\frac{dr}{dq}=2000-6(q+q^3).$$ Then what is the value of $p$ when $q=5$

What i try: $$\frac{dr}{dq}=2000-6(q+q^3)$$

$$\int dr=\int \bigg[2000-6(q+q^3)\bigg]dq$$

$$r=2000q-3q^2-1.5q^4+C$$

I did not understand How do i find value of $C$. Help me please.Thanks

The value of $p$? – Riemann'sPointyNose Jun 26 '20 at 17:37 — Riemann'sPointyNose, Jun 26 '20 at 17:37
actually here $p$ is demand function. – jacky Jun 26 '20 at 17:56 — jacky, Jun 26 '20 at 17:56

score 1 · Answer 1 · answered Jun 26 '20 at 18:49

1

Since the revenue is by definition $r = pq$ and $r= 2000q-3q^2-1.5q^4+C$, you conclude that $C=0$ and

$$r = q\underbrace{(2000-3q-\frac 32 q^3)}_{=p(q)}$$

Now, put $q=5$ into $p(q)$.

answered Jun 26 '20 at 18:49

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