Small differences in the rate of economic growth can lead to

Small differences in the rate of economic growth can lead to large differences in living standards. Consider two countries, Fritolaysia and Ghersey. Currently, real GDP per person (average income) is $35,000 in Fritolaysia and $12,000 in Ghersey. Over the past decade, real GDP per person grew at a rate of 1.4% in Fritolaysia and 2.6% in Ghersey. Suppose you want to project what the real GDP per person will be in each country 100 years from now. You can use a simple formula to do so: Average Income in n years = (Current Average Income) Times (1 + g)^n In this formula, g represents the growth rate (in decimal form) of real GDP per person and n represents the number of years. If Fritolaysia experiences average income growth of 1.4% per year for the next 100 years, its average income will rise to: Average Income in 100 years = ($35,000) Times (1 + 0.014)^100 = $140,561 Use the growth formula to fill in the following table. (Recall that average income is initially $12,000 in Ghersey.) Round your answers to the nearest dollar. If average income continues to grow at 1.4% per year in Fritolaysia and 2.6% in Ghersey, real GDP per person in Fritolaysia will be than real GDP per person in Ghersey after 100 years. Suppose the growth of average income falls slightly to 1.1% per year in Fritolaysia and falls slightly to 2.1% per year in Ghersey. In this case, real GDP per person in Fritolaysia will be than real GDP per person in Ghersey after 100 years.

Solution

(a) Fritolaysia

If growth is 1.1%, average income after 100 years = $35,000 x (1.011)¹⁰⁰ = $35,000 x 2.9862 = $104,516

(b) Ghersey

If growth is 2.6%, average income after 100 years = $12,000 x (1.026)¹⁰⁰ = $12,000 x 13.0238 = $156,286

If growth is 2.1%, average income after 100 years = $12,000 x (1.021)¹⁰⁰ = $12,000 x 7.9905 = $95,886

(c) Fill in the blanks:

(1) Real GDP in Frito will be lower than real GDP in Ghersey after 100 years.

(2) Real GDP in Frito will be higher than real GDP in Ghersey after 100 years.