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?Numerical

Similar Questions

The supply of a good will be more elastic, the

A new technology dramatically speeds up the production process for widgets, allowing manufacturers to increase their output more easily in response to price changes. Given this development, what can we most likely conclude about the price elasticity of supply for widgets?

Let’s consider the supply curve S(P)=8+2P, where P is the price of the good. As the price of the good decreases, the absolute value of the price elasticity of supply:

What is the shape of the supply curve when it is perfectly elastic?

The supply of a good will be more elastic, the

The supply of a good will be more elastic, the

The supply of a good will be more elastic, the

The supply of a good to a market is likely to be more elastic when ____________________

More Practical Tools for Students Powered by AI Study Helper

Homework AI Solver

Stylized AI Paper Writer

Plagiarism Checker Assistant

Citation AI Academic Writing Tool

In-Class Translation Assistant

AI Note Generator

AI Quiz Answers

Past Exam Questions from University Test Bank

Smart Practice Assistant

Adaptive Practice

Making Your Study Simpler