The quantity demanded each week x (in units of a hundred) of the Mikado miniature camera is related to the unit price p (in dollars) by the demand equation . When is demand unitary?
Hint: Solve E(p)=1 for p.
A) p=51.38
B) p=26.67
C) p= 59.19
D) p= 61.07

Question

The quantity demanded each week x (in units of a hundred) of the Mikado miniature camera is related to the unit price p (in dollars) by the demand equation  . ​ When is demand unitary?
Hint: Solve E(p)=1 for p. 
A) p=51.38 
B) p=26.67 
C) p= 59.19 
D) p= 61.07

Quizplus · Accepted Answer

To find when demand is unitary, we need to solve E(p)=1 for p.
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Rewriting the equation in terms of p, we get:

p = 100(60.5 - 0.5x)/x

Setting E(p) = 1, we get:

1 = -60.5/x^2 + 0.5/x

Multiplying both sides by x^2, we get:

x^2 = 0.5(60.5) = 30.25

Taking the square root of both sides, we get:

x = 5.5

Substituting x = 5.5 back into our demand equation, we get:

p = 100(60.5 - 0.5(5.5))/5.5 = 100(56.75/5.5) = 26.67

Therefore, the unit price at which demand is unitary is $26.67. The best choice is B.

The Quantity Demanded Each Week X (In Units of a Hundred)