To calculate the GDP using the expenditure approach, we need to sum up all the expenditures made in the economy. The general formula for GDP using the expenditure approach is:

$\text{GDP} = C + I + G + (X - M)$

Where:

• C = Consumption expenditures
• I = Investment expenditures (includes business investment and construction of new homes)
• G = Government purchases of goods and services
• X = Exports
• M = Imports

Breakdown of the given data:

1. Consumption Expenditures (C): $90
2. Imports (M): $10
3. Government Purchases (G): $60
4. Construction of new homes and apartments: $50 (This is included in Investment)
5. Sales of homes and apartments: $40 (This is a transfer, so it doesn't affect GDP directly)
6. Exports (X): $0
7. Government stimulus checks to households: $30 (This is a transfer, so it doesn't affect GDP directly)
8. Household purchases of durable goods: $60 (This is part of Consumption Expenditures, so it's already included)
9. Beginning-of-year inventory: $10 (This is used to calculate investment in inventory)
10. End-of-year inventory: $20 (This is used to calculate investment in inventory)
11. Business Fixed Investment (I): $70

Additional Considerations:

The inventory change is calculated as the difference between the end-of-year inventory and beginning-of-year inventory: $\text{Change in inventory} = \text{End-of-year inventory} - \text{Beginning-of-year inventory} = 20 - 10 = 10$ So, this change in inventory contributes $10 to Investment.

Now, let’s calculate GDP:

$\text{GDP} = C + I + G + (X - M)$

Substituting the known values:

$\text{GDP} = 90 + (70 + 10) + 60 + (0 - 10)$

$\text{GDP} = 90 + 80 + 60 - 10$

$\text{GDP} = 220$

Final GDP Value:

The value of GDP is $220.

Let me know if you would like further clarification or more details! Here are some related questions to explore:

1. How does inventory change affect GDP?
2. What is the difference between government purchases and government transfers in GDP calculation?
3. How do exports and imports influence GDP?
4. How would GDP change if government purchases increased by $20?
5. What role does business fixed investment play in the GDP calculation?

Tip: Always remember that GDP counts only final goods and services, so sales of used goods (like homes) do not directly contribute to GDP unless they involve new production.