Final answer:
Option D: The elasticity of supply as the price rises from 3 to 4 and from 7 to 8 is 1.00, and we would expect these answers to be the same.
Step-by-step explanation:
The elasticity of supply measures the responsiveness of the quantity supplied to changes in price. It is calculated by dividing the percentage change in quantity supplied by the percentage change in price. We can find the elasticity of supply as the price rises from 3 to 4 by using the formula:
Elasticity of Supply = (Percentage Change in Quantity Supplied) / (Percentage Change in Price)
Given the equation for the supply curve as 4P = Q, we can calculate the quantity supplied at price 3 and price 4: Q3 = 4(3) = 12 and Q4 = 4(4) = 16. Now let's calculate the percentage change in quantity supplied: % change in quantity supplied = ((Q4 - Q3) / Q3) x 100 = ((16 - 12) / 12) x 100 = (4 / 12) x 100 = 33.33%
Similarly, we can calculate the percentage change in price: % change in price = ((4 - 3) / 3) x 100 = (1 / 3) x 100 = 33.33%
Now let's plug the values into the formula:
Elasticity of Supply = (33.33% / 33.33%) = 1.00
Therefore, the elasticity of supply as the price rises from 3 to 4 is 1.00.
We can follow the same steps to calculate the elasticity of supply as the price rises from 7 to 8. Let's calculate the quantity supplied at price 7 and price 8: Q7 = 4(7) = 28 and Q8 = 4(8) = 32. Now let's calculate the percentage change in quantity supplied: % change in quantity supplied = ((Q8 - Q7) / Q7) x 100 = ((32 - 28) / 28) x 100 = (4 / 28) x 100 = 14.29%
Similarly, we can calculate the percentage change in price: % change in price = ((8 - 7) / 7) x 100 = (1 / 7) x 100 = 14.29%
Now let's plug the values into the formula:
Elasticity of Supply = (14.29% / 14.29%) = 1.00
Therefore, the elasticity of supply as the price rises from 7 to 8 is also 1.00.
Since both elasticities of supply are the same (1.00), we would expect these answers to be the same.