Answer:
The price elasticity of demand is: -2.625
Explanation:
Given
[tex]Q = 500000 - 700P +200I - 500S[/tex] --- the demand
[tex]I =\$13000[/tex] --- per capita income
[tex]S = \$400[/tex] --- average price of software
[tex]P = \$3000[/tex] --- price of computer
Required
The price elasticity of demand
Substitute values for I and S in: [tex]Q = 500000 - 700P +200I - 500S[/tex]
[tex]Q = 500000 - 700P +200*13000 - 500*400[/tex]
Collect like terms
[tex]Q = 500000 +200*13000 - 500*400- 700P[/tex]
[tex]Q = 2900000- 700P[/tex]
The price elasticity (n) is then calculated using:
[tex]n =\frac{P}{Q} * \frac{dQ}{dP}[/tex]
[tex]Q = 2900000- 700P[/tex]
Differentiate
[tex]\frac{dQ}{dP} = -700[/tex]
Calculate Q when [tex]P = \$3000[/tex]
[tex]Q = 2900000- 700*3000[/tex]
[tex]Q = 800000[/tex]
So, we have:
[tex]n =\frac{3000}{800000} * -700[/tex]
[tex]n =-\frac{3000* 700}{800000}[/tex]
[tex]n =-\frac{2100000}{800000}[/tex]
[tex]n =-\frac{21}{8}[/tex]
[tex]n =-2.625[/tex]
The price elasticity of demand is going to be –2.625.
The equation has
Q = 500,000 – 700P +200I - 500S.
p = $3,000
I = $13,000
S = $400
We have to put in these values in the equation that we have here:
Q = 500,000 – 700*3000 +200*13000 - 500*400
= 800000
= 500,000+200*13000 - 500*400 – 700P
= 2900000-700p
= -700p
The price elasticity =
-700*3000/800000
= -2.625
The price elasticity = -2.625
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