Question

1. 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.

Answer 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