A car dealer offers three types of cars: Audi, Skoda, and Seat. In 2014 Audis cost 35,000 EUR, Skodas cost 24,450 EUR, and Seats cost 27,860 EUR. In that year, 43% of the turnover came from the sales of Skodas and 23% derived from selling Seats. In 2019 Audis were offered for 36,550 EUR, Skodas for 23,770 EUR and Seats for 28,110 EUR. Turnover grew in all brands by 12.5% in 2019 compared to 2014.

1. Calculate and interpret the Laspeyres Price index for 2019 with 2014 as the base year. 
2. Calculate and interpret the Paasche Price index for 2019 with 2014 as the base year. 
3. Calculate and interpret the Fisher Price index for 2019 with 2014 as the base year. 

Answer:

According to the text provided, I consider that the answers are as follows:

a)

SKODA: 0.9722

AUDI: 1.0443

SEAT: 1.0090

b)

SKODA: 0.9722

AUDI: 1.0443

SEAT: 1.0090

c)

SKODA: 0.9586

AUDI: 1.0672

SEAT: 1.0135

Step-by-step explanation

Both work by dividing the spending of a specific basket in the current time (the operation of p * q for each product in the basket is considered to calculate the index) by how much the same basket would cost in the base period (period 0). The main difference is the quantities used: the Laspeyres index uses q0 quantities, while the Paasche index uses period n quantities.

This means that a Laspeyres index of 1 implies that since the numerator equals the denominator, an individual can afford to buy a basket of goods in the current period, just as he did in the base period. Since the quantities are the same, this leaves the price as a variable, which must remain unchanged.

The main disadvantage of these indices is the fact that they do not take substitution effects into account. When the price of something goes up, we tend to consume less of it. Since the Laspeyres index uses base period quantities, it tends to overestimate inflation by assuming that individuals' spending continues to be distributed in the same way. The same goes for the Paasche index: By using current period amounts, you underestimate inflation.

Fisher's price index is a geometric average, defined as the square root of the product of the Laspeyres index by that of the Paashe.

The Fisher index tries to solve the problems of overvaluation of inflation calculated with the Laspeyres index and of undervaluation obtained with the Paasche index. To do this, it calculates the geometric mean of the Laspeyres and Paasche price indices.

PFA