Question

Answer the following short questions about macroeconomic data.

a) In 1970, a hot dog, soda, and chips at Top Dog cost $1; today it costs $5.75. The consumer price index was 38.842 in 1970 and is 260.209 now. What is the 1970 price of a Top Dog meal expressed in today’s dollars? Has the price risen by more or less than the overall price level since 1970?

b) If the CPI was 253 in December 2018 and 258 in December 2019, what was the rate of inflation over that twelve-month period?

c) Explain why if real GDP per person in a country grows at 6% each year for a decade, after 10 years it will have risen by more than 60%. By about how much will it in fact have risen over the decade?

Answer 1

CPs in 1970 = 38.842 CPI is today 260.209 Inflation over this period = 260.209-38.842 XLOO 38.842 569.92) so, overall prices have risen by 569.92 % over this enod: So, if 1970 porce u $1 todo this price in today's dollars $ 16+ $1 (569.92:14) $1 + $5.6992 $6.6992 ~ $6.7 1970 pouce egpareved in today's dollars is $6.7 price today = $5.75. This is less than the 1970 price expressed in today's dollars. Therefore, the price of top dog meal has risen by LESS them the overall price level.

b) CPI 2018 = 253, CPI 2019 = 258 Inflation rate 258-253 X100 = 1.976 ~ 1-98 4. 253 Therefore inflat rate over this twelve month penod is 198) c) In coease in GDP per person per year = 61.50-06 Increase after 10 years (1+0.06)'0-16 = 0.7908 = 79-08-1 So, GDP per person after 10 years will have risen by 19.08./
c) The real GDP per person will have risen by more than 60% after 10 years because the growth rate of GDP per person is compounded each year.

If real GDP per person initially is 1, then after 10 years it will equal 1(1+0.06)¹⁰ = 1.7908.

So, the real GDP per person will have risen by 0.7908 that is 79.08%.

It happens because of compounding of the annual growth rate over this 10 year period.