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 when the price is $66 per barrel.
To calculate the elasticity of demand, we can use the formula:
Elasticity of Demand = (% Change in Quantity Demanded) / (% Change in Price)
First, we need to find the quantity demanded at $66 per barrel:
q = 2,460,274(66)^-0.07
q ≈ 2,460,274(0.632455532)
q ≈ 1,556,108
Next, we need to find the quantity demanded at $67 per barrel:
q = 2,460,274(67)^-0.07
q ≈ 2,460,274(0.625730815)
q ≈ 1,539,458
Now we can calculate the percentage change in quantity demanded:
% Change in Quantity Demanded = [(1,539,458 - 1,556,108) / 1,556,108] * 100
% Change in Quantity Demanded = -1.06%
Next, we can calculate the percentage change in price:
% Change in Price = [(67 - 66) / 66] * 100
% Change in Price = 1.52%
Finally, we can calculate the elasticity of demand:
Elasticity of Demand = (-1.06% / 1.52%)
Elasticity of Demand ≈ -0.70
Interpretation: The elasticity of demand for crude oil in Country A at a price of $66 per barrel is -0.70. This means that demand for crude oil in Country A is inelastic at this price, as a 1% increase in price would result in only a 0.70% decrease in quantity demanded.