Price Index Food 41Cec5
1. Problem: Compute various price indices using the given food basket prices for years 1985, 1990, and 1995.
2. Formula: The simple price index for an item is given by
$$\text{Simple Price Index} = \frac{\text{Price in current year}}{\text{Price in base year}} \times 100$$
The unweighted aggregate price index is the average of the simple price indices of all items.
3. a) Simple price index of sugar in 1990 with base year 1985:
$$\frac{28}{22} \times 100 = 127.27$$
Interpretation: Sugar price increased by 27.27% from 1985 to 1990.
4. b) Unweighted aggregate price index for 1985 (base year):
Since 1985 is base year, index = 100.
5. c) Unweighted aggregate price index for 1990 using 1985 as base:
Calculate simple price indices for all items:
Eggs: $\frac{30}{25} \times 100 = 120$
Milk: $\frac{40}{32} \times 100 = 125$
Banana: $\frac{25}{20} \times 100 = 125$
Potatoes: $\frac{20}{10} \times 100 = 200$
Sugar: $\frac{28}{22} \times 100 = 127.27$
Average:
$$\frac{120 + 125 + 125 + 200 + 127.27}{5} = 139.45$$
Interpretation: Overall food basket price increased by 39.45% in 1990 compared to 1985.
6. d) Unweighted aggregate price index for 1995 using 1985 as base:
Eggs: $\frac{36}{25} \times 100 = 144$
Milk: $\frac{55}{32} \times 100 = 171.88$
Banana: $\frac{28}{20} \times 100 = 140$
Potatoes: $\frac{28}{10} \times 100 = 280$
Sugar: $\frac{32}{22} \times 100 = 145.45$
Average:
$$\frac{144 + 171.88 + 140 + 280 + 145.45}{5} = 176.67$$
Interpretation: Food basket price increased by 76.67% in 1995 compared to 1985.
q_count is 4 because four subproblems were solved from the first question.