Question

Suppose a simple economy produces only two goods, pillows and rugs. In the first year, 50 pillows are produced, and sold at $5 each; 11 rugs are produced, and sold at $50 each. In the second year, 54 pillows are produced, and sold for $6 each; 12 rugs are produced, and sold at $52 each. In the third year, 60 pillows are produced and sell for $7.00 dollars each; 14 rugs are produced and sold for 64 dollars each. Calculate real GDP for each year and the growth rate of real GDP from year 1 to year 2 and from year 2 to year 3. Next, construct a constant weight price index for the three years. Use the first year as the base year for both calculations.

Answer 1

Question 1

First year has to be taken as base year.

Calculate the real GDP in first year -

Real GDP = (Pillows produced in Year 1 * Price of pillows in Year 1) + (Rugs produced in Year 1 * Price of rugs in Year 1)

Real GDP = (50 * $5) + (11 * $50) = $250 + $550 = $800

The real GDP in Year 1 is $800.

Calculate the real GDP in second year -

Real GDP = (Pillows produced in Year 2 * Price of pillows in Year 1) + (Rugs produced in Year 2 * Price of rugs in Year 1)

Real GDP = (54 * $5) + (12 * $50) = $270 + $600 = $870

The real GDP in Year 2 is $870.

Calculate the real GDP in third year -

Real GDP = (Pillows produced in Year 3 * Price of pillows in Year 1) + (Rugs produced in Year 3 * Price of rugs in Year 1)

Real GDP = (60 * $5) + (14 * $50) = $300 + $700 = $1,000

The real GDP in Year 3 is $1,000.

Question 2

Calculate the growth rate of real GDP from year 1 to year 2 -

Growth rate = [(Real GDP in Year 2 - Real GDP in Year 1)/Real GDP in Year 1] * 100

Growth rate = [($870 - $800)/$800] * 100

Growth rate = 8.75%

The growth rate of real GDP from year 1 to year 2 is 8.75 percent.

Calculate the growth rate of real GDP from year 2 to year 3 -

Growth rate = [(Real GDP in Year 3 - Real GDP in Year 2)/Real GDP in Year 2] * 100

Growth rate = [($1,000 - $870)/$870] * 100

Growth rate = 14.94%

The growth rate of real GDP from year 2 to year 3 is 14.94 percent.

Question 3

In case of construction of constant weight price index, production of base year is taken.

Base year is Year 1.

So, market basket will be contain production of Year 1 that is 50 pillows and 11 rugs.

Value of market basket at Year 1 price = (50 * $5) + (11 * $50) = $250 + $550 = $800

Value of market basket at Year 2 price = (50 * $6) + (11 * $52) = $300 + $572 = $872

Value of market basket at Year 3 price = (50 * $7) + (11 * $64) = $350 + $704 = $1,054

Calculate constant weight price index for Year 1 -

Price index = [Vaue of market basket at Year 1 price/Value of Market basket at Year 1 price] * 100

Price index = [$800/$800] * 100 = 100

The constant weight price index for Year 1 is 100.

Calculate constant weight price index for Year 2 -

Price index = [Vaue of market basket at Year 2 price/Value of Market basket at Year 1 price] * 100

Price index = [$872/$800] * 100 = 109

The constant weight price index for Year 2 is 109.

Calculate constant weight price index for Year 3 -

Price index = [Vaue of market basket at Year 3 price/Value of Market basket at Year 1 price] * 100

Price index = [$1,054/$800] * 100 = 100

The constant weight price index for Year 3 is 131.75.