The short-term demand for crude oil in Country A in 2008 can be approximated by q equals f (p )equals 1 comma 782 comma 844 p Superscript negative 0.06, where p represents the price of crude oil in dollars per barrel and q represents the per capita consumption of crude oil. Calculate and interpret the elasticity of demand when the price is $42 per barrel.

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DeniceSandidge DeniceSandidge · Answer 1 · 2020-05-27T08:29:31+02:00

Answer:

elasticity = - 0.06

Explanation:

given data

q = 1,782,844 [tex]p^{-0.06}[/tex]

p = price of crude

q = per capita consumption

price = $42 per barrel

solution

we first differentiate the given equation with respect to p

q = 1,782,844 [tex]p^{-0.06}[/tex] .................1

[tex]\frac{dq}{dp}[/tex] = 1,782,844 × -0.06 × [tex]p^{-1.06}[/tex] ..............2

now put here price value $42 per barrel

[tex]\frac{dq}{dp}[/tex] = 1,782,844 × -0.06 × [tex]42^{-1.06}[/tex]

[tex]\frac{dq}{dp}[/tex] = - 2035.25

and

elasticity is express as here

elasticity = [tex]\frac{p}{q} \times \frac{dq}{dp}[/tex] ........................3

put here value and we get

elasticity = [tex]\frac{42}{1782844 \times 42^{-0.06} } \times - 2035.25[/tex]

solve it we get

elasticity = - 0.06