In: Economics
problem 3 (ii)
Michael consumes apples and pears. In year 1, apples cost $1 each, pears cost $2 each, Michael buys 4 apples and 2 pears in year 1. In year 2, apples cost $2 each and pears cost $1 each, and michael buys 2 apples and 4 pears.
Define the implicit price deflator as nominal spending divided by real spending; compute the deflator for each year. How does the deflator change from year 1 to year 2?
It is assumed that Year 1 is the base year.
Year 1
Nominal Spending = [Quantity of apples in Year 1 * Price of apples in Year 1] + [Quantity of pears in Year 1 * Price of pears in Year 1]
Nominal spending = [4 * $1] + [2 * $2] = $4 + $4 = $8
Real Spending = [Quantity of apples in Year 1 * Price of apples in Year 1] + [Quantity of pears in Year 1 * Price of pears in Year 1]
Real spending = [4 * $1] + [2 * $2] = $4 + $4 = $8
Calculate the implicit price deflator in Year 1 -
Implicit price deflator = [Nominal spending/Real spending] * 100 = [$8/$8] * 100 = 100
The implicit price deflator in Year 1 is 100.
Year 2
Nominal Spending = [Quantity of apples in Year 2 * Price of apples in Year 2] + [Quantity of pears in Year 2 * Price of pears in Year 2]
Nominal spending = [2 * $2] + [4 * $1] = $4 + $4 = $8
Real Spending = [Quantity of apples in Year 2 * Price of apples in Year 1] + [Quantity of pears in Year 2 * Price of pears in Year 1]
Real spending = [2 * $1] + [4 * $2] = $2 + $8 = $10
Calculate the implicit price deflator in Year 2 -
Implicit price deflator = [Nominal spending/Real spending] * 100 = [$8/$10] * 100 = 80
The implicit price deflator in Year 2 is 80.
Calculate change in deflator from year 1 to year 2 -
Change in deflator = [(Deflator in Year 2 - Deflator in Year 1)/Deflator in Year 1] * 100
Change in deflator = [(80 - 100)/100] * 100 = -20%
The deflator has decreased from year 1 to year 2 by 20 percent.