Question

the prices of consumer goods do not always exactly follow the cpi. the following chart shows several consumer items, along with their respective prices in 1983 and today.

item	price in 1983 ($)	current price ($)
hair dryer	15.25	29.95
box of tissues	1.15	2.25
toaster	22.85	44.25

using the prices shown on this chart, which of the following is a reasonable estimate of the current cpi?

a. 208
b. 195
c. 180
d. 173

Explanation:

Step1: Calculate the ratio of current price to 1983 price for each item

• For boots: $\frac{126.85}{67.45} \approx 1.88$
• For hair dryer: $\frac{29.95}{15.25} \approx 1.96$
• For tissues: $\frac{2.25}{1.15} \approx 1.96$
• For toaster: $\frac{44.25}{22.85} \approx 1.93$

Step2: Find the average of these ratios

First, sum the ratios: $1.88 + 1.96 + 1.96 + 1.93 = 7.73$
Then, divide by the number of items (4): $\frac{7.73}{4} \approx 1.93$

Step3: Convert the average ratio to CPI (CPI in 1983 is 100, so current CPI = ratio * 100)

$1.93 \times 100 = 193$ (closest to 195 among the options, considering possible rounding differences in calculations)

Answer:

b. 195