The Consumer Price Index (CPI) for the year 2012 is 2.412 and the retail price per bushel for corn is $US12.06. Using 1992 as the base year (I.e CPI is 100) by how much would the real price for corn have risen or fallen if the retail price for corn in 1992 were $US7.66. Using the CPI and the given price in 1992 what should be the expected price for corn in 2000? What should have been the price in 1992 if the price in 2000 were considered reasonable?

To determine how much the real price for corn in 1992 would have risen or fallen, we need to adjust the price using the Consumer Price Index (CPI) for 2012. Here's how you can calculate it:

1. Calculate the inflation rate from 1992 to 2012:
Inflation rate = (CPI in 2012 - CPI in 1992) / CPI in 1992

In this case: Inflation rate = (2.412 - 1) / 1 = 1.412

2. Calculate the adjusted price for corn in 1992:
Adjusted price in 1992 = Price in 1992 * (1 + inflation rate)

Given: Price in 1992 = $US7.66
Adjusted price in 1992 = $US7.66 * (1 + 1.412) = $US16.10

So, the real price for corn in 1992 would have risen to $US16.10 if the retail price in 1992 were $US7.66.

Next, let's calculate the expected price for corn in 2000 using the CPI:

1. Calculate the inflation rate from 1992 to 2000:
Inflation rate = (CPI in 2000 - CPI in 1992) / CPI in 1992

We do not have the CPI for 2000, so we cannot perform this calculation directly.

2. Estimate the expected CPI for 2000:
One way to estimate the expected CPI for 2000 is by assuming a consistent inflation rate over the period. Based on the given CPI of 2.412 in 2012, we can approximate an average annual inflation rate.

Average annual inflation rate (approx.) = (CPI in 2012 - CPI in 1992) / (2012 - 1992)
Average annual inflation rate (approx.) = (2.412 - 1) / 20 = 0.0706

3. Calculate the estimated CPI for 2000:
CPI in 2000 = CPI in 1992 + (Inflation rate per year * Number of years)
CPI in 2000 = 1 + (0.0706 * 8) = 1.5648 (approx.)

4. Determine the expected price for corn in 2000:
Expected price in 2000 = Price in 1992 * (CPI in 2000 / CPI in 1992)
Expected price in 2000 = $US7.66 * (1.5648 / 1) = $US12.00 (approx.)

Therefore, based on the estimated CPI, the expected price for corn in 2000 would be around $US12.00.

Lastly, let's calculate the price in 1992 if the price in 2000 were considered reasonable:

1. Calculate the inflation rate from 2000 to 1992:
Inflation rate = (CPI in 1992 - CPI in 2000) / CPI in 2000

We do not have the CPI for 2000, so we cannot perform this calculation directly.

2. Estimate the expected CPI for 2000 based on the given price of $US12.00:
Estimated CPI in 2000 = (Price in 2000 / Price in 1992) * CPI in 1992
Estimated CPI in 2000 = ($US12.00 / $US7.66) * 1 = 1.563 (approx.)

3. Calculate the estimated inflation rate from 2000 to 1992:
Estimated inflation rate = (CPI in 1992 - Estimated CPI in 2000) / Estimated CPI in 2000
Estimated inflation rate = (1 - 1.563) / 1.563 = -0.360 (approx.)

4. Calculate the price in 1992:
Price in 1992 = Price in 2000 / (1 + inflation rate)
Price in 1992 = $US12.00 / (1 + (-0.360)) = $US8.75 (approx.)

Therefore, if the price in 2000 were considered reasonable, the price for corn in 1992 would have been around $US8.75.