Final answer:
GDP is calculated using the formula GDP = C + I + G + (X - M). Adjusting GDP to Personal Income involves accounting for depreciation, net foreign factor income, and differences between income earned/received. The calculation confirms the provided Personal Income value of $16.8M.
Step-by-step explanation:
To show mathematically how Gross Domestic Product (GDP) relates to Personal Income, we need to start with the basic GDP calculation method and then make appropriate adjustments to derive the Personal Income.
GDP can be calculated using the expenditure approach: GDP = Consumption + Investment + Government spending + (Exports – Imports). This formula is often represented as GDP = C + I + G + (X - M). Plugging in the given values we get:
GDP = $13.3M (Consumption) + $3.3M (Gross Private Investment) + $3.8M (Government purchases) + ($3.4M (Exports) - $3.8M (Imports))
GDP = $13.3M + $3.3M + $3.8M + ($3.4M - $3.8M)
GDP = $13.3M + $3.3M + $3.8M - $0.4M
GDP = $20M
To adjust GDP to Personal Income, we subtract Depreciation and adjustments, add Net Foreign Factor Income, subtract Income earned/not received, and add Income received/not earned:
Personal Income = GDP + Net Foreign Factor Income - Depreciation and adjustments (CCA) - Income earned/not received + Income received/not earned
Personal Income = $20M + $0.6M - $2.2M - $5.6M + $4.0M
Personal Income = $16.8M
This matches the given Personal Income value, confirming the relationship between GDP and Personal Income.