Suppose the economy of a large nation has a defense industry, a banking industry, and a pharmaceutical industry. 1-unit output of defense requires 0.6 inputs of defense, O0.2 inputs of banking, and 0.2 inputs of pharmaceuticals. 1-unit output of banking requires 0.1 inputs of defense, 0.4 inputs of banking, and 0.5 inputs of pharmaceuticals. 1-unit output of pharmaceuticals requires 0.1 inputs of defense, 0.2 inputs of banking, and 0.2 inputs of pharmaceuticals. If the nation wants to have surpluses of 106 units of defense production, 243 units of banking production, and 216 units of pharmaceutical production, find the gross production of each industry.
Suppose the economy of a large nation has a defense industry, a banking industry, and a pharmaceutical industry. 1-unit output of defense requires 0.6 inputs of defense, O0.2 inputs of banking, and 0.2 inputs of pharmaceuticals. 1-unit output of banking requires 0.1 inputs of defense, 0.4 inputs of banking, and 0.5 inputs of pharmaceuticals. 1-unit output of pharmaceuticals requires 0.1 inputs of defense, 0.2 inputs of banking, and 0.2 inputs of pharmaceuticals. If the nation wants to have surpluses of 106 units of defense production, 243 units of banking production, and 216 units of pharmaceutical production, find the gross production of each industry.
Chapter1: Financial Statements And Business Decisions
Section: Chapter Questions
Problem 1Q
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Question
Transcribed Image Text:**Economic Interdependence in a Multi-Industry Nation**
**Problem Statement:**
Consider an economy with three major industries: defense, banking, and pharmaceuticals. The production dynamics between these industries are interdependent, with specific input requirements as follows:
- **Defense Industry:** To produce 1 unit, the defense industry needs 0.6 units of its own output, 0.2 units of banking, and 0.2 units of pharmaceuticals.
- **Banking Industry:** To produce 1 unit, the banking industry requires 0.1 units of defense, 0.4 units of its own output, and 0.5 units of pharmaceuticals.
- **Pharmaceutical Industry:** To produce 1 unit, the pharmaceutical industry requires 0.1 units of defense, 0.2 units of banking, and 0.2 units of its own output.
**Objective:**
The nation aims to achieve surpluses across these industries, specifically:
- 106 units in defense
- 243 units in banking
- 216 units in pharmaceuticals
The challenge is to determine the gross production required by each industry to meet these surplus goals, given the interdependent nature of the production processes.
**Explanation:**
This problem involves setting up a system of linear equations that captures the inputs required for production in each industry, taking into account the desired surpluses. Solving this system will provide the gross production levels needed to satisfy the economic goals.
Expert Solution
Step 1
Given,
Defense industry :
1 unit output = 0.6 units of defense + 0.2 units of banking + 0.2 units of pharmaceuticals
Required for 106 units of output
= 0.6 x 106 + 0.2 x 106 + 0.2 x 106
= 63.6 units + 21.2 units + 21.2 units
Banking industry :
1 unit output = 0.1 units of defense + 0.4 units of banking + 05 units of pharmaceuticals
Required for 243 units of output
= 0.1 x 243 + 0.4 x 243 +0.5 x 243
= 24.3 units + 97.2 units + 121.5 units
Pharmaceuticals industry :
1 unit output = 0.1 units of defense + 0.2 units of banking + 0.2 units of pharmaceuticals
Required for 216 units of output
= 0.1 x 216 +0.2 x 216 + 0.2 x 216
= 21.6 units + 43.2 units + 43.2 units
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