### Equilibrium Prices in a Multi-Sector Economy#### Problem StatementSuppose 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.#### Questions1. 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.### SummaryBy 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

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Description: ### Equilibrium Prices in a Multi-Sector Economy#### Problem StatementSuppose 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 secto

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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

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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.

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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

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