Final answer:
The elasticity of supply is 1 for both price increases from 3 to 4 and from 7 to 8, which indicates unit elasticity. This is because the supply curve 4P = Q is linear, and thus, the elasticity remains constant along the curve.
Step-by-step explanation:
The question pertains to the calculation of the elasticity of supply for a given supply curve equation, which is 4P = Q. This equation represents a linear supply curve where P stands for price and Q stands for quantity supplied. To find the elasticity of supply as the price changes, we use the formula:
Elasticity of Supply = (Percentage Change in Quantity Supplied) / (Percentage Change in Price)
Let's calculate the elasticity of supply as the price rises from 3 to 4:
- When P = 3, Q = 4*3 = 12
- When P = 4, Q = 4*4 = 16
- The percentage change in quantity supplied = ((16-12)/12) * 100 = 33.33%
- The percentage change in price = ((4-3)/3) * 100 = 33.33%
- Elasticity of Supply = 33.33 / 33.33 = 1
Now let's calculate the elasticity of supply as the price rises from 7 to 8:
- When P = 7, Q = 4*7 = 28
- When P = 8, Q = 4*8 = 32
- The percentage change in quantity supplied = ((32-28)/28) * 100 = 14.29%
- The percentage change in price = ((8-7)/7) * 100 = 14.29%
- Elasticity of Supply = 14.29 / 14.29 = 1
The elasticity of supply is the same for both price increases because the supply curve is linear, meaning that the supply is unit elastic at all points along the curve.