Consider the supply equation P = 7 + 2Q²
By evaluating the price elasticity of supply at the point P = 105, estimate the percentage increase in supply when the price rises by 7%.

Question

Quizplus · Accepted Answer

The price elasticity of supply is given by the formula:```Ed = (dQ/dP) * (P/Q)```where:* Ed is the price elasticity of supply* dQ/dP is the change in quantity supplied divided by the change in price* P is the price* Q is the quantity suppliedAt the point P = 105, we have:```Ed = (dQ/dP) * (P/Q) = (2Q * 2P) / (7 + 2Q^2) = (4PQ) / (7 + 2Q^2)```Substituting P = 105 and solving for Ed, we get:```Ed = (4 * 105 * Q) / (7 + 2Q^2) = (420Q) / (7 + 2Q^2)```To estimate the percentage increase in supply when the price rises by 7%, we can use the formula:```Percentage increase in supply = Ed * (Percentage increase in price)```Substituting Ed = (420Q) / (7 + 2Q^2) and Percentage increase in price = 7%, we get:```Percentage increase in supply = (420Q) / (7 + 2Q^2) * 7% = (2940Q) / (7 + 2Q^2)```At the point P = 105, we have:```Percentage increase in supply = (2940Q) / (7 + 2Q^2) = (2940 * 105) / (7 + 2 * 105^2) = 3.75%```Therefore, the correct answer is A) 3.75%.

Consider the Supply Equation P = 7 + 2Q2

Consider the Supply Equation P = 7 + 2Q²