Consider the following data for a hypothetical economy that manufactures engines (the only intermediate good), motorcycles and cars.
Year Commodity Price Quantity
2009 Engines $2 150
2009 Cars $15 100
2009 Motorcycles $10 50
2010 Engines $6 154
2010 Cars $50 99
2010 Motorcycles $9 55
2011 Engines $10 160
2011 Cars $90 90
2011 Motorcycles $8 70
Calculate a real GDP index for each year using the chain-weighted method with real GDP in 2009 equal to 1.
Price | Quantity | ||
2009 | Engine | 2 | 150 |
2009 | Car | 15 | 100 |
2009 | Motorcycle | 10 | 50 |
2010 | Engine | 6 | 154 |
2010 | Car | 50 | 99 |
2010 | Motorcycle | 9 | 55 |
2011 | Engine | 10 | 160 |
2011 | Car | 90 | 90 |
2011 | Motorcycle | 8 | 70 |
To calculate real GDP of 2010 using chain weighted method:
We need,
2009 quantity at 2009 prices which is 2 * 150 + 15 * 100 + 10 * 50 = 300 + 1,500 + 500 = 2,300
2010 quantity at 2009 prices which is 2 * 154 + 15 * 99 + 10 * 55 = 308 + 1,485 + 550 = 2,343
2009 quantity at 2010 prices which is 6 * 150 + 50 * 100 + 9 * 50 = 900 + 5,000 + 450 = 6,350
2010 quantity at 2010 prices which is 6 * 154 + 50 * 99 + 9 * 55 = 924 + 4,950 + 495 = 6,369
Growth rate in 2009 prices = [(2,343 - 2,300) / 2,300] * 100 = 1.86%
Growth rate in 2010 prices = [(6,369 - 6,350) / 6,350] * 100 = 0.29%
Average of both growth rate = (1.86% + 0.29%) / 2 = 1.075%
Thus using chain weighted method, real GDP in 2010 = 2,300 * 1.075% = 2,324.725
To calculate real GDP of 2011 using chain weighted method:
We need,
2010 quantity at 2010 prices which is 6 * 154 + 50 * 99 + 9 * 55 = 924 + 4,950 + 495 = 6,369
2011 quantity at 2010 prices which is 6 * 160 + 50 * 90 + 9 * 70 = 960 + 4,500 + 630 = 6,090
2010 quantity at 2011 prices which is 10 * 154 + 90 * 99 + 8 * 55 = 1,540 + 8,910 + 440 = 10,890
2011 quantity at 2011 prices which is 10 * 160 + 90 * 90 + 8 * 70 = 1,600 + 8,100 + 560 = 10,260
Growth rate in 2010 prices = [(6,090 - 6,369) / 6,369] * 100 = -4.38%
Growth rate in 2011 prices = [(10,260 - 10,890) / 10,890] * 100 = -5.78%
Average of both growth rate = (-4.38 - 5.78) / 2 = -5.08
Thus using chain weighted method, real GDP in 2011 = 6,369 * [6,369 * -5.78%] = 6,000.87
Consider the following data for a hypothetical economy that manufactures engines (the only intermediate good), motorcycles...
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