Consider a Melanesian island nation in the South Pacific which had a population of 0.88 million in 2010.  The table below presents the nominal GDP and the GDP deflator (based on 2005 being the base year) for the years 2010, 2015, and 2020. 

Year	2010	2015	2020
Nominal GDP ($Billions)	17500	18222	18755
GDP Deflator	103.7	104.8	105.9
Over each 5-year period, there were no significant changes to government policies or capital investment, and the country experienced a net migration of 0%.  However, over the first five years (2010 to 2015), the growth rate of births was 12.5% while the growth rate of deaths was 7.5%.  Over the second five years (2015 to 2020), health care improved significantly such that the growth rate of births increased to 15% while the growth rate of deaths decreased to 5%.

The percentage change in real GDP per capita for the first five years is

To calculate the percentage change in **real GDP per capita** for the first five years (2010 to 2015), we'll follow these steps:

### Step 1: Calculate the Real GDP for 2010 and 2015
The formula for real GDP is:

\[
\text{Real GDP} = \frac{\text{Nominal GDP}}{\text{GDP Deflator}} \times 100
\]

- **2010**: 
\[
\text{Real GDP}_{2010} = \frac{17.5 \text{ billion}}{103.7} \times 100 = \frac{17.5}{1.037} \approx 16.87 \text{ billion}
\]
- **2015**:
\[
\text{Real GDP}_{2015} = \frac{18.222 \text{ billion}}{104.8} \times 100 = \frac{18.222}{1.048} \approx 17.38 \text{ billion}
\]

### Step 2: Calculate the Population Growth from 2010 to 2015
The initial population in 2010 is **0.88 million**.

Given the growth rates of births and deaths:
- Birth rate growth: 12.5%
- Death rate growth: 7.5%

The net population growth rate is:

\[
\text{Net Population Growth Rate} = 12.5\% - 7.5\% = 5\%
\]

Thus, the population in 2015 is:

\[
\text{Population}_{2015} = \text{Population}_{2010} \times (1 + 0.05) = 0.88 \times 1.05 = 0.924 \text{ million}
\]

### Step 3: Calculate Real GDP Per Capita for 2010 and 2015
Now, we calculate the **real GDP per capita** for 2010 and 2015.

- **2010**: 
\[
\text{Real GDP per Capita}_{2010} = \frac{\text{Real GDP}_{2010}}{\text{Population}_{2010}} = \frac{16.87 \text{ billion}}{0.88 \text{ million}} = \frac{16,870}{0.88} = 19,170.45 \text{ dollars}
\]
- **2015**:
\[
\text{Real GDP per Capita}_{2015} = \frac{\text{Real GDP}_{2015}}{\text{Population}_{2015}} = \frac{17.38 \text{ billion}}{0.924 \text{ million}} = \frac{17,380}{0.924} \approx 18,810.39 \text{ dollars}
\]

### Step 4: Calculate the Percentage Change in Real GDP Per Capita
The percentage change in real GDP per capita from 2010 to 2015 is given by:

\[
\text{Percentage Change} = \frac{\text{Real GDP per Capita}_{2015} - \text{Real GDP per Capita}_{2010}}{\text{Real GDP per Capita}_{2010}} \times 100
\]

\[
\text{Percentage Change} = \frac{18,810.39 - 19,170.45}{19,170.45} \times 100 \approx \frac{-360.06}{19,170.45} \times 100 \approx -1.88\%
\]

Thus, the **percentage change in real GDP per capita** from 2010 to 2015 is approximately **-1.88%**.

### Summary
The percentage change in real GDP per capita for the first five years (2010 to 2015) is approximately **-1.88%**.

---

Would you like further details on any part of this calculation?

Here are some related questions:
1. How is real GDP different from nominal GDP?
2. How does population growth impact GDP per capita?
3. What is the significance of the GDP deflator in economic analysis?
4. How can birth and death rates affect a country's economic performance?
5. How might changes in healthcare influence long-term economic growth?

**Tip**: When analyzing GDP data over time, always adjust for inflation using real GDP to get a clearer picture of economic growth.

Consider a Melanesian island nation in the South Pacific which had a population of 0.88 million in 2010. The table below presents the nominal GDP and the GDP deflator (based on 2005 being the base year) for the years 2010, 2015, and 2020.

Year	2010	2015	2020
Nominal GDP ($Billions)	17500	18222	18755
GDP Deflator	103.7	104.8	105.9
Over each 5-year period, there were no significant changes to government policies or capital investment, and the country experienced a net migration of 0%. However, over the first five years (2010 to 2015), the growth rate of births was 12.5% while the growth rate of deaths was 7.5%. Over the second five years (2015 to 2020), health care improved significantly such that the growth rate of births increased to 15% while the growth rate of deaths decreased to 5%.

The percentage change in real GDP per capita for the first five years is

Analyze the percentage change in real GDP per capita for a Melanesian island nation in the South Pacific from 2010 to 2015. This problem involves key economic concepts like population growth, real GDP, and GDP deflator. Suitable for college-level economics students.

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