9) The following data show nominal GDP and the appropriate price index for four

Question

9) The following data show nominal GDP and the appropriate price index for four years. Compute real GDP for each year. All GDP are in billions. Year Nominal GDP Price index Real GDP 25 2A 1 $125 2 130 3 127 4 132 120 104 96 real GDP Real GOP growth rote nital real aur a) Calculate growth rate in real GDP between year 2 and 3. X looo drowback: doesn't account for b) What is the average annual real GDP growth rate based on the four years of data? Population growth. c) Suppose the economy grows at this average annual rate, how long it takes for the initial real GDP to double?

Explanation / Answer

Real GDP ($ billion) = (Nominal GDP / Price index) x 100

Year 1: (125/120) x 100 = 104.17

Year 2: (130/104) x 100 = 125

Year 3: (127/85) x 100 = 149.11

Year 4: (132/96) x 100 = 137.5

(a)

Real GDP growth rate = (149.11/125) - 1 = 1.1929 - 1 = 0.1929 = 19.29%

(b)

If average annual growth rate be r% per year, then

104.17 x (1 + r)3 = 137.5

(1 + r)3 = 1.320

Taking cube root,

1 + r = 1.0969

r = 0.0969

r = 9.69%

(c)

Let initial real GDP be $G and number of years to double be N. Then

$G x (1.0969)N = $G x 2

(1.0969)N = 2

Taking natural logarithm on both sides,

N x ln 1.0969 = ln 2

N x 0.0925 = 0.6931

N = 7.49 years

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