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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Question
![**Problem Statement:**
Find the producer surplus at the equilibrium point.
14) \( S(x) = x^2 + 2; \; x = 1 \)
Options:
- A) $0.67
- B) -$0.67
- C) -$2
**Solution:**
To find the producer surplus at the equilibrium point, we must evaluate the given supply function \( S(x) = x^2 + 2 \) at \( x = 1 \).
1. Substitute \( x = 1 \) into the supply function:
\[
S(1) = 1^2 + 2 = 1 + 2 = 3
\]
2. The given problem provides multiple-choice answers. Based on typical economic interpretations, the producer surplus is often a positive value representing the benefit producers get by selling at market price instead of the minimum price they are willing to accept.
Given that option A) $0.67 is circled, it suggests this is the intended correct answer for the producer surplus value at the specified equilibrium point.
**Conclusion:**
The producer surplus at the equilibrium point, given the problem and options, is intended to be approximately $0.67 (Option A).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc17f3f0c-3f3b-4d84-90ac-d23f7cabcc9b%2F0f4b3321-8eeb-4cba-a0a2-8d46a9533ef7%2F90kh4_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Find the producer surplus at the equilibrium point.
14) \( S(x) = x^2 + 2; \; x = 1 \)
Options:
- A) $0.67
- B) -$0.67
- C) -$2
**Solution:**
To find the producer surplus at the equilibrium point, we must evaluate the given supply function \( S(x) = x^2 + 2 \) at \( x = 1 \).
1. Substitute \( x = 1 \) into the supply function:
\[
S(1) = 1^2 + 2 = 1 + 2 = 3
\]
2. The given problem provides multiple-choice answers. Based on typical economic interpretations, the producer surplus is often a positive value representing the benefit producers get by selling at market price instead of the minimum price they are willing to accept.
Given that option A) $0.67 is circled, it suggests this is the intended correct answer for the producer surplus value at the specified equilibrium point.
**Conclusion:**
The producer surplus at the equilibrium point, given the problem and options, is intended to be approximately $0.67 (Option A).
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