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

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

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:

`(e^(0.004p))/(e^(-0.002p))=(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=(ln(3.2))/(0.006)`

and simplify so we get our answer:

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