Question

An island economy produces only fish and crabs. $$\begin{array}{lcc} \text { Quantities } & 2013 & 2014 \\ \hline \text { Fish } & 1,000 \text { tons } & 1,100 \text { tons } \\ \text { Crabs } & 500 \text { tons } & 525 \text { tons } \\ \text { Prices } & 2013 & 2014 \\ \hline \text { Fish } & \$ 20 \text { a ton } & \$ 30 \text { a ton } \\ \text { Crabs } & \$ 10 \text { a ton } & \$ 8 \text { a ton } \end{array}$$ Calculate the island's chained-dollar real GDP in 2014 expressed in 2013 dollars.

Short answer

The island's chained-dollar real GDP in 2014 expressed in 2013 dollars is 27250 dollars.

Step-by-step solution

- Calculate Nominal GDP for 2013

The nominal GDP for 2013 is calculated by multiplying the quantities produced by their respective prices for that year. \[ \text{Nominal GDP}_{2013} = (1000 \text{ tons of Fish} \times 20 \text{ dollars/ton}) + (500 \text{ tons of Crabs} \times 10 \text{ dollars/ton}) \] \[ \text{Nominal GDP}_{2013} = 20000 + 5000 = 25000 \text{ dollars} \]

- Calculate Nominal GDP for 2014

The nominal GDP for 2014 is calculated similarly by multiplying the quantities produced by their respective prices for that year. \[ \text{Nominal GDP}_{2014} = (1100 \text{ tons of Fish} \times 30 \text{ dollars/ton}) + (525 \text{ tons of Crabs} \times 8 \text{ dollars/ton}) \] \[ \text{Nominal GDP}_{2014} = 33000 + 4200 = 37200 \text{ dollars} \]

- Calculate Real GDP for 2014 Using 2013 Prices

To find the real GDP for 2014 expressed in 2013 dollars, multiply the 2014 quantities by the 2013 prices. \[ \text{Real GDP}_{2014 \text{ (in 2013 dollars)}} = (1100 \text{ tons of Fish} \times 20 \text{ dollars/ton}) + (525 \text{ tons of Crabs} \times 10 \text{ dollars/ton}) \] \[ \text{Real GDP}_{2014 \text{ (in 2013 dollars)}} = 22000 + 5250 = 27250 \text{ dollars} \]

- Calculate the Growth Factor

The growth factor needed to chain the real GDP calculation can be found by dividing the real GDP of 2014 (in 2013 dollars) by the nominal GDP of 2013. \[ \text{Growth Factor} = \frac{ \text{Real GDP}_{2014 \text{ (in 2013 dollars)}} }{ \text{Nominal GDP}_{2013} } = \frac{27250}{25000} = 1.09 \]

- Calculate Chained-Dollar Real GDP for 2014

Use the growth factor found in Step 4 to chain the 2013 nominal GDP. \[ \text{Chained-Dollar Real GDP}_{2014} = \text{Nominal GDP}_{2013} \times \text{Growth Factor} \] \[ \text{Chained-Dollar Real GDP}_{2014} = 25000 \times 1.09 = 27250 \text{ dollars} \]

Key concepts

Nominal GDP

Nominal GDP is a measure of the market value of all finished goods and services produced within a country in a specific time period. It is measured using current prices, without adjusting for inflation. To calculate nominal GDP, you multiply the quantity of goods and services produced by their current prices. For example, in 2013, the island produced 1,000 tons of fish at \(20 per ton and 500 tons of crabs at \)10 per ton. Thus, the nominal GDP for 2013 is \[ \text{Nominal GDP}_{2013} = (1000 \text{ tons of Fish} \times 20 \text{ dollars/ton}) + (500 \text{ tons of Crabs} \times 10 \text{ dollars/ton}) = 25000 \text{ dollars} \] The same formula applies for 2014, using that year's quantities and prices.\[ \text{Nominal GDP}_{2014} = (1100 \text{ tons of Fish} \times 30 \text{ dollars/ton}) + (525 \text{ tons of Crabs} \times 8 \text{ dollars/ton}) = 37200 \text{ dollars} \] As you can see, nominal GDP can change due to variations in price or quantity produced.

Real GDP

Real GDP measures the value of all goods and services produced in an economy but adjusts for changes in price or inflation. This helps to compare economic output across different years more accurately. For calculating real GDP, we use the quantities from the current year but prices from a base year. In this case, to calculate the 2014 real GDP using 2013 prices, we multiply the 2014 quantities by the 2013 prices. This results in the following calculation: \[ \text{Real GDP}_{2014 \text{ (in 2013 dollars)}} = (1100 \text{ tons of Fish} \times 20 \text{ dollars/ton}) + (525 \text{ tons of Crabs} \times 10 \text{ dollars/ton}) = 27250 \text{ dollars} \] This method neutralizes the effect of inflation and provides a clearer picture of economic growth.

Economic Growth

Economic growth refers to the increase in the market value of the goods and services produced by an economy over time. It is often measured as the percentage increase in real GDP from one period to another. Positive growth indicates a thriving economy, while negative growth may suggest economic troubles. By examining changes in real GDP, economists can assess whether an economy is expanding or contracting. In the given example, calculating the island’s real GDP for 2014 using 2013 prices showcases the growth in physical quantities of fish and crabs produced, independent of price changes. Understanding real GDP is crucial for making long-term economic comparisons and formulating policy decisions.

2013 Prices

To understand the true growth of an economy, it's essential to use constant prices from a base year, such as 2013 in this case. This eliminates the effects of inflation and price changes over time. When economic analysts use 2013 prices to calculate real GDP for subsequent years, they can determine whether there’s genuine growth in the quantity of goods and services produced. Here, the 2013 prices for fish (\(20 per ton) and crabs (\)10 per ton) serve as the baseline to calculate real GDP in 2014, leading to the following adjustment: \[ \text{Real GDP}_{2014 \text{ (in 2013 dollars)}} = 27250 \text{ dollars} \] Hence, using base-year prices offers a stable comparison ground.

Growth Factor

The growth factor is a multiplier that shows the rate of economic growth between two time periods. It is calculated by dividing the real GDP of the latter year by the nominal GDP of the base year. In this case, the growth factor is calculated as: \[ \text{Growth Factor} = \frac{ \text{Real GDP}_{2014 \text{ (in 2013 dollars)}} }{ \text{Nominal GDP}_{2013} } = \frac{27250}{25000} = 1.09 \] This growth factor indicates a 9% increase in economic output in real terms. To find the chained-dollar real GDP, we apply this growth factor to the nominal GDP of the base year, thereby adjusting it for true growth: \[ \text{Chained-Dollar Real GDP}_{2014} = 25000 \times 1.09 = 27250 \text{ dollars} \] Understanding the growth factor helps in comprehending the true scale of economic growth after adjusting for price changes.