Final answer:
The student inquired about the price elasticity of supply, which is calculated using the percentage changes in quantity supplied and price. With a supply equation of 4P = Q, the elasticity of supply is found to be 1 when the price rises from 3 to 4 and also when the price rises from 7 to 8; this is due to the constant elasticity along a straight-line supply curve.
Step-by-step explanation:
The student is asking about the price elasticity of supply, which measures how the quantity supplied of a good responds to a change in price. To find the elasticity of supply between two price points, we use the formula:
Elasticity of Supply = (Percentage Change in Quantity Supplied) ÷ (Percentage Change in Price)
In the given example, with a supply curve equation of 4P = Q, we first find the quantity supplied at each price level:
- When price rises from 3 to 4, initial quantity Q1 = 4 * 3 = 12, and final quantity Q2 = 4 * 4 = 16.
- When price rises from 7 to 8, initial quantity Q3 = 4 * 7 = 28, and final quantity Q4 = 4 * 8 = 32.
Now we calculate the percentage changes and the elasticity for each case:
- From a price of 3 to 4, the percentage change in quantity is ((16 - 12) ÷ 12) * 100 = 33.33%, and the percentage change in price is ((4 - 3) ÷ 3) * 100 = 33.33%. Thus, the elasticity of supply is 33.33% ÷ 33.33% = 1.
- From a price of 7 to 8, the percentage change in quantity is ((32 - 28) ÷ 28) * 100 = 14.29%, and the percentage change in price is ((8 - 7) ÷ 7) * 100 = 14.29%. Thus, the elasticity of supply is 14.29% ÷ 14.29% = 1.
We would expect these answers to be the same because the supply curve is a straight line, which means the elasticity of supply is constant along the curve.