The short-term demand for crude oil in Country A in 2008 can be approximated by q=f(p)=2,460,274p^-0.07, 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.
To calculate the elasticity of demand, we can use the formula:
Elasticity of demand = (dq/dp) * (p/q)
First, let's take the derivative of the demand function with respect to p:
dq/dp = -0.07 * 2,460,274 * p^(-0.07 - 1)
dq/dp = -0.07 * 2,460,274 * p^(-1.07)
Now, let's plug in the values from the demand function:
dq/dp = -0.07 * 2,460,274 * p^(-1.07)
dq/dp = -172,218.18 * p^(-1.07)
Now, substitute this result and the demand function into the elasticity of demand formula:
Elasticity of demand = (-172,218.18 * p^(-1.07)) * p / (2,460,274 * p^(-0.07))
Elasticity of demand = -172,218.18 * p^(-0.07) / 2,460,274
Elasticity of demand = -0.07 * p^(-0.07) / 2,460,274
At any specific price, the elasticity will be different, but based on the calculation, we can see that the elasticity of demand for crude oil in Country A in 2008 is negative and very low, less than 1. This suggests that the demand for crude oil in Country A is relatively inelastic, meaning that changes in price have a small effect on the quantity demanded.