Question

The supply function and demand function for the sale of a certain type of DVD player are given by ​S(p)=130e0.004p and ​D(p)=416e−0.002p​, where​ S(p) is the number of DVD players that the company is willing to sell at price p and​ D(p) is the quantity that the public is willing to buy at price p. Find p such that ​D(p)=​S(p). This is called the equilibrium price.

Answer 1

Answer:

p=$193.86 (assuming we are talking about dollars)

Step-by-step explanation:

In order to solve this problem, we must set each function equal to each other, so we end up with the following equation we must solve for p:

$130e^{0.004p}=416e^{-0.002p}$

So next, we divide both sides of the equation by 130 and by $e^{-0.002p}$

So we get:

$\frac{e^{0.004p}}{e^{-0.002p}}=\frac{416}{130}$

and we simplify, so we get:

$e^{0.004p}e^{0.002p}=3.2$

which can be further simplified to:

$e^{0.006p}=3.2$

and next, we take the natural logarithm to both sides, so we get:

0.006p=ln(3.2)

and finally we divide both sides of the equation by 0.006 so we get:

$p=\frac{ln(3.2)}{0.006}$

and simplify so we get our answer:

p=$193.86  (in the case that p is given in dollars)