Suppose an economy consists of the Coal, Electric, and Steel sectors. Denote the prices (that is, dollar values) of the total annual outputs of the Coal, Electric, and Steel sectors by pc PE, and ps, respectively. Suppose the general solution to find equilibrium prices that make each sector's income match its expenditures is pc = 0.89ps, PE = 0.88ps, and ps is free. One set of equilibrium prices for this economy is Pc = $89, pɛ = $88, and ps = $100. Find another set. Suppose the same economy used Japanese yen instead of dollars to measure the values of the various sector's output. Would this change the problem in any way? Discuss. If ps = $200, then pc = $ and pe = $ (Type integers or decimals.)
Suppose an economy consists of the Coal, Electric, and Steel sectors. Denote the prices (that is, dollar values) of the total annual outputs of the Coal, Electric, and Steel sectors by pc PE, and ps, respectively. Suppose the general solution to find equilibrium prices that make each sector's income match its expenditures is pc = 0.89ps, PE = 0.88ps, and ps is free. One set of equilibrium prices for this economy is Pc = $89, pɛ = $88, and ps = $100. Find another set. Suppose the same economy used Japanese yen instead of dollars to measure the values of the various sector's output. Would this change the problem in any way? Discuss. If ps = $200, then pc = $ and pe = $ (Type integers or decimals.)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Concept explainers
Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
Topic Video
Question
![### Equilibrium Prices in a Multi-Sector Economy
#### Problem Statement
Suppose an economy consists of the Coal, Electric, and Steel sectors. Denote the prices (that is, dollar values) of the total annual outputs of the Coal, Electric, and Steel sectors by \( p_C \), \( p_E \), and \( p_S \), respectively. Suppose the general solution to find equilibrium prices that make each sector's income match its expenditures is:
\[ p_C = 0.89p_S, \]
\[ p_E = 0.88p_S, \]
and \( p_S \) is free.
One set of equilibrium prices for this economy is:
\[ p_C = \$89, \]
\[ p_E = \$88, \]
\[ p_S = \$100. \]
Find another set of equilibrium prices. Suppose the same economy used Japanese yen instead of dollars to measure the values of the various sector's output. Would this change the problem in any way? Discuss.
#### Questions
1. If \( p_S = \$200 \), then \( p_C = \$ \) [type your answer here] and \( p_E = \$ \) [type your answer here]. (Type integers or decimals.)
#### Directions
- Solve for the equilibrium prices \( p_C \) and \( p_E \) given \( p_S = \$200 \).
- Discuss whether changing the currency to Japanese yen affects the economic analysis.
### Solution Steps:
1. **Finding New Equilibrium Prices:**
Given \( p_S = \$200 \):
Substitute \( p_S \) into the equilibrium equations:
\[
p_C = 0.89 \times 200 = 178
\]
\[
p_E = 0.88 \times 200 = 176
\]
So, \( p_C = \$178 \) and \( p_E = \$176 \).
2. **Discussion on Currency Change:**
Changing the currency from dollars to Japanese yen does not change the relative values or the equilibrium conditions. The equilibrium prices will be scaled by the exchange rate, but the equations and their solutions remain the same in terms of relative proportions.
### Summary
By substituting \( p_S = 200 \) into the given equations, we find that \( p_C = 178 \) and \( p_E = 176 \). Changing the measurement unit of the prices to Japanese yen](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa204cf79-6df4-4f25-af61-d4fca6ca5b9e%2F9e105ea7-0316-4b49-a5f1-07f5cad91e7a%2F7gvsd4b_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Equilibrium Prices in a Multi-Sector Economy
#### Problem Statement
Suppose an economy consists of the Coal, Electric, and Steel sectors. Denote the prices (that is, dollar values) of the total annual outputs of the Coal, Electric, and Steel sectors by \( p_C \), \( p_E \), and \( p_S \), respectively. Suppose the general solution to find equilibrium prices that make each sector's income match its expenditures is:
\[ p_C = 0.89p_S, \]
\[ p_E = 0.88p_S, \]
and \( p_S \) is free.
One set of equilibrium prices for this economy is:
\[ p_C = \$89, \]
\[ p_E = \$88, \]
\[ p_S = \$100. \]
Find another set of equilibrium prices. Suppose the same economy used Japanese yen instead of dollars to measure the values of the various sector's output. Would this change the problem in any way? Discuss.
#### Questions
1. If \( p_S = \$200 \), then \( p_C = \$ \) [type your answer here] and \( p_E = \$ \) [type your answer here]. (Type integers or decimals.)
#### Directions
- Solve for the equilibrium prices \( p_C \) and \( p_E \) given \( p_S = \$200 \).
- Discuss whether changing the currency to Japanese yen affects the economic analysis.
### Solution Steps:
1. **Finding New Equilibrium Prices:**
Given \( p_S = \$200 \):
Substitute \( p_S \) into the equilibrium equations:
\[
p_C = 0.89 \times 200 = 178
\]
\[
p_E = 0.88 \times 200 = 176
\]
So, \( p_C = \$178 \) and \( p_E = \$176 \).
2. **Discussion on Currency Change:**
Changing the currency from dollars to Japanese yen does not change the relative values or the equilibrium conditions. The equilibrium prices will be scaled by the exchange rate, but the equations and their solutions remain the same in terms of relative proportions.
### Summary
By substituting \( p_S = 200 \) into the given equations, we find that \( p_C = 178 \) and \( p_E = 176 \). Changing the measurement unit of the prices to Japanese yen
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 5 steps with 25 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
