Suppose that large oil reserves are discovered off the coast of Cuba, and these reserves will increase the world's supply of oil by 2.5%. If the elasticities of demand and supply of oil are 0.50 and 0.40, respectively, what happens to the price of oil?
It falls by 25%.
It falls by 2.78%.
It falls by 36%.
It falls by 2.5%.
To determine the effect on the price of oil due to the increase in supply, we can use the concept of elasticity of demand and supply. The formula to find the percentage change in price due to a change in supply is given by:
[ \frac{\Delta P}{P} = \frac{E_s}{E_s + E_d} \cdot \frac{\Delta Q}{Q} ]
Where:
Given:
Now, we can plug in the values into the formula:
[ \frac{\Delta P}{P} = \frac{0.40}{0.40 + 0.50} \cdot 0.025 ]
Calculating the denominator:
[ 0.40 + 0.50 = 0.90 ]
Now substituting back into the equation:
[ \frac{\Delta P}{P} = \frac{0.40}{0.90} \cdot 0.025 ]
Calculating (\frac{0.40}{0.90}):
[ \frac{0.40}{0.90} \approx 0.4444 ]
Now, multiplying by 0.025:
[ \frac{\Delta P}{P} \approx 0.4444 \cdot 0.025 \approx 0.0111 ]
This means that the percentage change in price is approximately 1.11%. Since this is a decrease in price, we can express it as:
[ \Delta P \approx -1.11% ]
Now, we can compare this with the options provided. The closest option to our calculated decrease of approximately 1.11% is:
It falls by 2.5%.
However, since our calculation shows a decrease of about 1.11%, none of the options perfectly match. The closest option is It falls by 2.5%, but it is important to note that