For problems 1 – 4: The Dolan Corporation, a maker of small engines, determines that in 2019 the demand curve for its product is P = 2,000 - 50Q where P is the price (in dollars) of an engine and Q is the number of engines sold per month. At what price, if any, will the demand for Dolan’s engines be of unitary elasticity? a.$500 b.$1000 c.$250 d.$750

Question
Asked Sep 4, 2019
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For problems 1 – 4: The Dolan Corporation, a maker of small engines, determines that in 2019 the demand curve for its product is

 

= 2,000 - 50Q

 

where is the price (in dollars) of an engine and is the number of engines sold per month.

 

At what price, if any, will the demand for Dolan’s engines be of unitary elasticity?

  a.

$500

  b.

$1000

  c.

$250

  d.

$750

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Expert Answer

Step 1

Solution- 

Given in the question
There is a unitary elasticity of demand
elasticity of demand = -1.
P= 2,000 -50Q....2)
P
price in dollars
Q = No. of Engine Sold
At Price P= $750
From equation (1)
P 2,000-50Q
Q =40 0.02P
help_outline

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Given in the question There is a unitary elasticity of demand elasticity of demand = -1. P= 2,000 -50Q....2) P price in dollars Q = No. of Engine Sold At Price P= $750 From equation (1) P 2,000-50Q Q =40 0.02P

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Step 2
Differentiating w.r.t "p"
dO
0-0.02
dP
dQ
-0.02
..(3)
dP
Change in Quantity Demanded
Original quantity Demanded
Change in Price
Price elasticity of demand
Original price
Price elasticity of demnd
dp Q
From equation (1)
help_outline

Image Transcriptionclose

Differentiating w.r.t "p" dO 0-0.02 dP dQ -0.02 ..(3) dP Change in Quantity Demanded Original quantity Demanded Change in Price Price elasticity of demand Original price Price elasticity of demnd dp Q From equation (1)

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Step 3
-1-0.02*
P
0.02
P
= 50
P 50Q..4)
putting value of "p"in equation(2)
500 2,000 50Q
50Q 50Q 2,000
100Q 2,000
Q =20.(5)
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-1-0.02* P 0.02 P = 50 P 50Q..4) putting value of "p"in equation(2) 500 2,000 50Q 50Q 50Q 2,000 100Q 2,000 Q =20.(5)

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