A company has determined their demand curve is d(q) = 196 - q² and their supply curve is s(q) = 3q², where q is the quantity produced. A) Find the equilibrium quantity q= B) Find the producer surplus at the equilibrium quantity.
A company has determined their demand curve is d(q) = 196 - q² and their supply curve is s(q) = 3q², where q is the quantity produced. A) Find the equilibrium quantity q= B) Find the producer surplus at the equilibrium quantity.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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**Equilibrium Quantity and Producer Surplus**
A company has determined their demand curve is \( d(q) = 196 - q^2 \) and their supply curve is \( s(q) = 3q^2 \), where \( q \) is the quantity produced.
### A) Find the equilibrium quantity
\[ q = \quad \boxed{} \]
### B) Find the producer surplus at the equilibrium quantity.
\[ S = \quad \boxed{} \]
---
In this problem, you are tasked with finding the equilibrium quantity and the producer surplus. The supply and demand curves are given, and they help determine the market behavior under equilibrium conditions. The equilibrium quantity is found where the supply curve intersects the demand curve. The producer surplus is the difference between what producers are willing to accept and what they actually receive at the equilibrium quantity.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa532d6c3-fc4a-4c4d-b082-7cb1920e9739%2F63f13ecf-a49a-434e-b8db-0e59f58e2c6f%2Fv4k6vhu_processed.png&w=3840&q=75)
Transcribed Image Text:---
**Equilibrium Quantity and Producer Surplus**
A company has determined their demand curve is \( d(q) = 196 - q^2 \) and their supply curve is \( s(q) = 3q^2 \), where \( q \) is the quantity produced.
### A) Find the equilibrium quantity
\[ q = \quad \boxed{} \]
### B) Find the producer surplus at the equilibrium quantity.
\[ S = \quad \boxed{} \]
---
In this problem, you are tasked with finding the equilibrium quantity and the producer surplus. The supply and demand curves are given, and they help determine the market behavior under equilibrium conditions. The equilibrium quantity is found where the supply curve intersects the demand curve. The producer surplus is the difference between what producers are willing to accept and what they actually receive at the equilibrium quantity.
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