Question

Year	Bill's Nominal Income	CPI
2010	$40,000	80
2011	$43,000	90
2012	$45,000	110

(a) Using the base year as the comparison year, calculate the Real Value of Bill’s Income for 2010 measured in base year dollars. Please show the work done to get your answer.

(b) Using the base year as the comparison year, calculate the Real Value of Bill’s Income for 2011 measured in base year dollars. Please show the work done to get your answer.

(c) Using the base year as the comparison year, calculate the Real Value of Bill’s Income for 2012 measured in base year dollars. Please show the work done to get your answer.

(d) Explain what happened to Bill's real income from 2010 to 2011.  

(e) Explain what was the cause for your answer in (d) above.

(f) Using the information above, calculate the inflation rate from 2010 to 2011.   Please show the work done to get your answer. Give your answer to the second decimal (hundredths place).

(g) In one factual sentence, state what information your answer for the inflation rate in (f) above tells us. I do not want an opinion as to whether this number is high or low. Please use your answer in (f) above in your answer for (g).

(h) If Sue lent Bill $20,000 at the start of 2010 for 1 year and charged Bill a nominal interest rate of 12.00%, then please calculate the real interest rate that Sue earned for this 1 year loan. Please show how you got your answer. Please be clear what your answer is and calculate your answer to the second decimal place (hundredths place).

(i) If Sue wanted to earn a real interest rate (return) of 12.00% for the loan mentioned in (h) above, then what nominal interest rate should she have charged Bill? Please show how you got your answer. Please be clear what your answer is and calculate your answer to the second decimal place (hundredths place)

Answer 1

a. Nominal income of Bill in 2010 = $40,000

CPI in 2010 = 80

Real income of Bill in 2010 = (Nominal Income in 2010/CPI in 2010) * 100 = ($40,000/80) * 100 = $50,000

b. Nominal income of Bill in 2011 = $43,000

CPI in 2010 = 90

Real income of Bill in 2011 = (Nominal Income in 2011/CPI in 2011) * 100 = ($43,000/90) * 100 = $47,777.78

c. Nominal income of Bill in 2012 = $45,000

CPI in 2012 = 110

Real income of Bill in 2012 = (Nominal Income in 2012/CPI in 2012) * 100 = ($45,000/110) * 100 = $40,909.09

d. It can be observed that the real income of Bill decreased from $47,778 to $40,909 between 2011 and 2012. This decrease in the real income of Bill can be attributed to a relatively smaller increase in the nominal income of Bill compared to increase in CPI. This led to a fall in the real income between 2011 and 2012.

The higher increase in the price level eroded the purchasing power of Bill between 2011-12.