Final answer:
The elasticity of supply for the given supply curve equation when price rises from 3 to 4 and from 7 to 8 is calculated to be 1 in both cases, indicating unitary elasticity.
Step-by-step explanation:
To calculate the price elasticity of supply using the given supply curve equation 4P = Q, we apply changes in price and calculate the corresponding changes in quantity. The formula for elasticity of supply is the percentage change in quantity supplied divided by the percentage change in price.
Price from 3 to 4
Original quantity when P=3: Q = 4*3 = 12
New quantity when P=4: Q = 4*4 = 16
Change in quantity: 16 - 12 = 4
Percentage change in quantity supplied: (4/12) x 100 = 33.33%
Percentage change in price: (4-3)/3 x 100 = 33.33%
Elasticity of supply: 33.33% / 33.33% = 1
Price from 7 to 8
Original quantity when P=7: Q = 4*7 = 28
New quantity when P=8: Q = 4*8 = 32
Change in quantity: 32 - 28 = 4
Percentage change in quantity supplied: (4/28) x 100 = 14.29%
Percentage change in price: (8-7)/7 x 100 = 14.29%
Elasticity of supply: 14.29% / 14.29% = 1
The elasticity of supply as price rises from 3 to 4 and from 7 to 8 would both be 1, indicating unitary elasticity. Therefore, despite different price levels, the elasticities are the same due to the linear nature of the supply curve.