Suppose Rhianna owns a business that sells potatoes. Her marginal cost curve is given by P = 9 + 2Q, where Q is in kilograms and she faces no fixed costs. At the quantity she is selling at, elasticity of supply is 9.5. How many kilograms of potatoes is she selling?

Question

BlackTom AI · Accepted Answer

We start from the given marginal cost (supply) relation: P = 9 + 2Q, where Q is kilograms.
From this, the slope dP/dQ = 2, so the inverse slope dQ/dP = 1/2.
Elasticity of supply Es is defined as Es = (dQ/dP) * (P/Q).
We are told Es = 9.5 at the quantity she is selling, so substitute: (1/2) * (P/Q) = 9.5.
This implies P/Q = 19, or P = 19Q.
We also have the price-quantity relation from the supply curve: P = 9 + 2Q.
Equating the two expressions for P in terms of Q gives 19Q = 9 + 2Q.
Solving for Q: 19Q − 2Q = 9 ⇒ 17Q = 9 ⇒ Q = 9/17.
Compute the numeric value: 9/17 ≈ 0.5294117647.
Rounding to two decimal places, Q ≈ 0.53 kilograms.

Suppose Rhianna owns a business that sells potatoes. Her marginal cost curve is given by P = 9 + 2Q, where Q is in kilograms and she faces no fixed costs. At the quantity she is selling at, elasticity of supply is 9.5. How many kilograms of potatoes is she selling?数值题

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