Question

The demand function for a certain commodity is given by , where p is the price per unit and q is the number of units. a. At what price per unit will the quantity b. If the price is $1.87 per unit, demanded equal 8 units

Answer 1

Answer:

(a) The price per unit is $1.83 when the quantity demanded is 8 units

(b) The quantity demanded is approximately 8 units when the price per unit is $1.87

Explanation:

Given

$p = 100e^{-q/2}$

$p \to$ price per unit

$q \to$ quantity demanded

Solving (a): Price per unit when quantity is 8

This means that we calculate p(8)

We have:

$p(q) = 100e^{-q/2}$

So:

$p(8) = 100e^{-8/2}$

$p(8) = 100e^{-4}$

$p(8) = 1.83$

Solving (b): Quantity demanded when price per unit is $1.87

This means that:

$p(q) = 1.87$ ---- find q

We have:

$p(q) = 100e^{-q/2}$

So:

$1.87 = 100e^{-q/2}$

Divide both sides by 100

$0.0187 = e^{-q/2}$

Take natural logarithm of both sides

$\ln(0.0187) = \ln(e^{-q/2})$

$-3.980 = \ln(e^{-q/2})$

Rewrite as:

$-3.980 = -q/2}*\ln(e)$

$-3.980 = -q/2$

Multiply by -2

$7.96 = q$

$q = 7.96$

Approximate

$q = 8$