Suppose that the residents of Veggieland spend all of their income on cauliflower, broccoli, and carrots. In 1998 they buy 100 heads of cauliflower for $200,50 bunches of broccoli for $75, and 500 carrots for $50. In 1999 they buy 75 heads of cauliflower for $225,80 bunches of broccoli for $120, and 500 carrots for $100. If the base year is 1998, what is the CPI in both years? What is the inflation rate in 1999?

As this is your third post....

First calculate the "weight" of each good. Total spending in the base year is cauliflower=200, broccoli=75, carrots=50, total=325. So, the weight for cauliflower is 200/325=.61538 Calculate the weights for broccoli and carrots.

Next, calculate prices in the base year and next year. In 1998 100 heads of cauliflower were purchased for $200. So, the price per head is $2. The price per head in 1999 is 225/75=$3. Calculate the prices for broccoli and carrots.

Now calculate the percentage change in prices. Cauliflower went from $2 to $3, a 50% increase. Multiply this by the cauliflower weight. I get .30769. Do the same for broccoli and carrots. Add up the weighted changes of the three goods. This is the overall weighted average increase in prices. I get .462

In CPI-speak, the base year is always 100.0 So, the CPI for 1999 is 146.2

Thank you so much for all your help!!!!!!!! :)

You're welcome! I'm glad I could help you with your question.

To calculate the CPI (Consumer Price Index) in both years, we need to follow these steps:

1. Calculate the weight of each good: The weights represent the proportion of total spending on each item. In this case, the total spending in the base year (1998) is $325, which consists of $200 for cauliflower, $75 for broccoli, and $50 for carrots. The weight for cauliflower is calculated by dividing its spending ($200) by the total spending ($325), which gives us 0.61538. Similarly, calculate the weights for broccoli and carrots.

2. Calculate the prices in the base year and the next year: In 1998, 100 heads of cauliflower were purchased for $200, so the price per head is $2. In 1999, 75 heads of cauliflower were purchased for $225, so the price per head is $3. Calculate the prices for broccoli and carrots in the same way.

3. Calculate the percentage change in prices: To calculate the inflation rate, we need to determine the percentage change in prices for each good. In this case, cauliflower's price increased from $2 to $3, which is a 50% increase. Multiply this by the weight of cauliflower. Repeat this step for broccoli and carrots to find their respective percentage changes.

4. Calculate the overall weighted average increase in prices: Add up the weighted changes of the three goods to get the overall weighted average increase in prices. This will give you the CPI for the following year (1999).

In CPI-speak, the base year always has a value of 100.0. So, if the CPI for 1998 is considered as the base year, the CPI for 1999 would be 146.2.

To calculate the inflation rate in 1999, we subtract 100 from the CPI of 1999 (146.2 - 100) and divide the result by 100. This gives us an inflation rate of 0.462, or 46.2%.

I hope this explanation helps you understand the process. Let me know if you have any further questions!