Question

Abby consumes only apples. In year1, red apples cost $1 each, green apples cost $2 each, and Abby buys 10 red apples. In year 2, red apples cost $2, green apples cost $1, and Abby buys 10 green apples.a. Compute a consumer price index for apples for each year. Assume that year 1 is the base year in which the consumer basket is fixed. How does your index change from year 1 to year 2?b. Compute Abby’s nominal spending on apples in each year. How does it change from year 1 to year 2?c. Using year 1 as the base year, compute Abby’s real spending on apples in each year. How does it change from year 1 to year 2?d. Defining 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?e. Suppose that Abby is equally happy eating red or green apples. How much has the true cost of living increased for Abby? Compare this answer to your answers to parts (a) and (d). What does this example tell you about Laspeyres and Passche price indexes?

Answer 1

Part A)

Consumer price index is an amount of the average variation over time in the amounts paid by customers for a market basket of customer goods and services.

CPI= (Updated Cost/Base Period Cost) x 100

For multiple products, we have to ruminate the weights or proportion of expenditure of an item

CPI2= (P2Red xQ1Red) + (P2grn x Q1grn) / (P1Red xQ1Red) + (P1grn x Q1grn)

CPI2= (2 x 10) + (1x0)/ (1x10) + (2x0)

CPI2= 2

Based on the CPI in year 2, prices have doubled.

Part B)

Nominal expenditure is the total worth of outcome produced or expended in each year.

In year 1 and year 2, Abby buys

Year 1= $1 x 10= $10

Year 2= $1 x 10= $10

So, nominal expenditure remains constant at $10.

Part C)

Real expenditure is the quantity consumed or the basket in the current year calculated at the base year price.

Base year prices: Red $1& Green $2

Real expenditure in year 1 = (P1rQ1r) + (P1gQ1g)

=$1x10 + X2x0

= $10

Real expenditure in year 2 = (P1rQ2r) + (P1gQ2g)

= (1x 0) + (2 x 10)

= $20

So, real expenditure has increased from $10 to $20

Part D).

Implicit value deflator in year 1, it is the base year so it will be continuously 1 as the actual and nominal amounts are equal.

Implicit price deflator in year = nominal expenditure/real expenditure

Implicit price deflator in year 1 = 10/10

= 1

Implicit price deflator in year2 = 10/20

= 0.5

Thus, the implicit value deflator proposes that prices have dropped by half. The cause for this is that the deflator evaluations how much Abby standards her appeals using prices dominant in year 1.

We can perceive from this perception that the green apples are appreciated more .And when Abby consumes more green apples in year 2, it appears that her consumption has augmented as the price deflator standards green apples more than the red apples.

Part E)

Abby considers that red apples and green apples as perfect alternatives, then the cost of living in this budget has not changed in both year it costs $10 to eat 10 apples.

Permitting to the CPl, however, the cost of living has gathered. This is because it only takes into justification the detail that the red apple price has gathered; the CPl overlooks the fall in the price of green apples as they were not in the consumption package in year 1.

In difference to the CPI, the implicit value deflator approximations the cost of living has shared.

CPI is calculated based on the Laspreyers Index method, where the amount in the numerator is the amount in the base year. Where as in the Passche price index, the numerator is the Recent price calculated for current capacity of consumption.

The Laspeyres index inclines to exaggerate rise (in a cost of living framework), while the Paasche index tends to understate it, because the indices do not account for the fact that consumers typically react to value variations by changing the amounts that they buy. For example, if prices go up for good X then, at ceteris paribus, amounts of that good should go downcast.