Math Problem Statement

Suppose there is an economy that produces only four goods in one year. Paper: $8,000 Books: $15,000 Toner: $4,000 Envelopes: $5,000 The production of books requires the following amount of intermediate goods: Paper: $4,000 Toner: $2,500 The production of envelopes requires the following amount of intermediate goods: Paper: $2,500 (i) Find the total GDP for the economy

Solution

To calculate the total Gross Domestic Product (GDP) for this economy, we use the expenditure approach, which considers the value of final goods and services produced within the economy. The formula is:

GDP=(Value of Final Goods)GDP = \sum (\text{Value of Final Goods})

Step 1: Identify Final and Intermediate Goods

Final goods are those that are not used as inputs in production and are directly consumed. Intermediate goods are those used in the production of other goods.

Given data:

  • Paper: $8,000
  • Books: $15,000
  • Toner: $4,000
  • Envelopes: $5,000

However, not all goods are final goods because some are used as inputs in production.

Intermediate Goods Used in Production:

  • Paper used in books: $4,000
  • Toner used in books: $2,500
  • Paper used in envelopes: $2,500

Step 2: Use the Value-Added Approach

Since intermediate goods should not be double-counted in GDP, we exclude them. The value-added approach considers only the contribution of each sector:

GDP=(Paper OutputPaper Used)+(Books Output)+(Toner OutputToner Used)+(Envelopes Output)GDP = (\text{Paper Output} - \text{Paper Used}) + (\text{Books Output}) + (\text{Toner Output} - \text{Toner Used}) + (\text{Envelopes Output})

Substituting values:

GDP=(8,0006,500)+15,000+(4,0002,500)+5,000GDP = (8,000 - 6,500) + 15,000 + (4,000 - 2,500) + 5,000

GDP=1,500+15,000+1,500+5,000GDP = 1,500 + 15,000 + 1,500 + 5,000

GDP=23,000GDP = 23,000

Final Answer:

The total GDP for the economy is $23,000.


Would you like further explanation or an alternative method for calculating GDP?

Here are some related questions to expand your understanding:

  1. What are the three main approaches to calculating GDP?
  2. How does the value-added approach prevent double counting?
  3. What would happen to GDP if book production increased by 20%?
  4. How do intermediate goods differ from final goods in GDP calculation?
  5. What role does the production of capital goods play in GDP?

Tip: Always ensure that intermediate goods are not double-counted in GDP to avoid overestimating economic output.

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Math Problem Analysis

Mathematical Concepts

Macroeconomics
Gross Domestic Product (GDP)
Value-Added Approach
Expenditure Approach

Formulas

GDP = Sum(Value of Final Goods)
GDP = (Paper Output - Paper Used) + (Books Output) + (Toner Output - Toner Used) + (Envelopes Output)

Theorems

GDP Calculation using Value-Added Approach

Suitable Grade Level

Undergraduate Economics / High School AP Economics