Question

In: Economics

problem 3 (ii) Michael consumes apples and pears. In year 1, apples cost $1 each, pears...

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?

Solutions

Expert Solution

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.


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