Question

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.

Answer 1

The elasticity of demand for crude oil when the price is $42 per barrel is -0.06, indicating that the demand is inelastic in the short term in Country A.

Step-by-step explanation:

To calculate the elasticity of demand for crude oil when the price is $42 per barrel, we use the given demand function q = f(p) = 1,782,844 * p-0.06. The elasticity of demand (E) at a given price point is calculated by multiplying the derivative of the demand function with respect to price (p) by the price (p) and dividing by the demand (q). The derivative of the given demand function with respect to price is -0.06 * 1,782,844 * p-1.06, so when p = $42, the derivative is approximately -106,970.64. Now, E = (-106,970.64 * 42) / (1,782,844 * 42-0.06), which simplifies to E = -106,970.64 / 1,782,844 = -0.06.

The interpretation of this elasticity of demand is that it is inelastic, as the absolute value of E is less than 1. This means that for a 1% increase in the price of crude oil, there would be less than a 1% decrease in the quantity demanded in the short term. This is similar to how the short-term demand for oil in the United States was inelastic in 1973 following the OPEC oil export cut-off.

Answer 2

elasticity = - 0.06

Step-by-step explanation:

given data

q = 1,782,844
`p^(-0.06)`

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
`p^(-0.06)` .................1

`(dq)/(dp)` = 1,782,844 × -0.06 ×
`p^(-1.06)` ..............2

now put here price value $42 per barrel

`(dq)/(dp)` = 1,782,844 × -0.06 ×
`42^(-1.06)`

`(dq)/(dp)` = - 2035.25

and

elasticity is express as here

elasticity =
`(p)/(q) * (dq)/(dp)` ........................3

put here value and we get

elasticity =
`(42)/(1782844 * 42^(-0.06) ) * - 2035.25`

solve it we get

elasticity = - 0.06