23. The next four questions refer to the following price and output data over a five-year period for an economy that produces only one good. Assume that year 2 is the base year.
Units of Price
Year output per unit
1 16 $2
2 20 3
3 30 4
4 36 5
5 40 6
(a) If year 2 is the base year, give the price index for year 3.
(b) Give the nominal GDP for year 4.
(c) What is the real GDP for year 4?
(d) Tell which years you would deflate nominal GDP and which years you would inflate nominal GDP in finding real GDP.
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(a) To calculate the price index for year 3, we need to compare the price in year 3 to the price in the base year (year 2) and express it as a percentage.
Price index = (Price in year 3 / Price in base year) * 100
In this case, the price in year 3 is $4 and the price in the base year (year 2) is $3.
Price index = (4 / 3) * 100 = 133.33
Therefore, the price index for year 3 is 133.33.
(b) To calculate the nominal GDP for year 4, we need to multiply the units of output in year 4 by the price per unit in year 4.
Nominal GDP = Units of output in year 4 * Price per unit in year 4
In this case, the units of output in year 4 is 36 and the price per unit in year 4 is $5.
Nominal GDP = 36 * $5 = $180
Therefore, the nominal GDP for year 4 is $180.
(c) To calculate the real GDP for year 4, we need to adjust the nominal GDP for the changes in price levels by using the price index.
Real GDP = (Nominal GDP / Price index) * 100
In this case, the nominal GDP for year 4 is $180 and the price index for year 4 is 166.67 (calculated as explained in part a).
Real GDP = ($180 / 166.67) * 100 = $108
Therefore, the real GDP for year 4 is $108.
(d) To find the real GDP, we need to deflate nominal GDP by dividing it by the price index. So, we deflate nominal GDP for the years we want to find the real GDP.
Years we would deflate nominal GDP: 1, 3, 4, 5
To inflate nominal GDP, we would multiply it by the price index to get the real GDP. However, in this case, we don't need to do that since we already have the real GDP for year 4.
Years we would inflate nominal GDP: None (as we already have the real GDP for year 4)