Economic Growth 3rd Edition by David Weil Solution manual

In Country A, Alfred earns 1,000 while Doris earns 4,000, making it an income disparity of 3,000.
In Country B, the income disparity is 1,000. Therefore, we see within-country income inequality in
both Country A and Country B. Because there is no between-country inequality, world inequality
can be entirely attributed to within-country inequality.

 

5.     We can solve for the average annual growth rate, g, by substituting the appropriate values into the equation:

(Y₁₉₀₀) ´ (1 + g)¹⁰⁰ = Y₂₀₀₀.

        Letting Y₁₉₀₀ = $1,617, Y₂₀₀₀ = $23,639, and rearranging to solve for g, we get:

g = ($23,639/$1,617)^(1/100) – 1,

                                                        g 0.0272.

        Converting g into a percent, we conclude that the growth rate of income per capita in Japan over this period was approximately 2.72 percent per year.

        To find the income per capita of Japan 100 years from now, in 2100, we solve

(Y₂₀₀₀) ´ (1 + g)¹⁰⁰ = Y₂₁₀₀.

        Letting Y₂₀₀₀ = $23,639 and g = 0.0272,

($23,971) ´ (1 + 0.0272)¹⁰⁰ = Y₂₁₀₀,

                                                                                       Y₂₁₀₀ = $346,043.09.

        That is, if Japan grew at the average growth rate of 2.72 percent per year, we would find the income per capita of Japan in 2100 to be about $346,043.09.

6.     In order to calculate the year in which income per capita in the United States was equal to income per capita in Sri Lanka, we need to find t, the number of years that passed between the year 2009 and the year U.S. income per capita equaled that of 2009 Sri Lanka income per capita. Equating income per capita of Sri Lanka in year 2009 to income per capita of the United States in year 2009 – t, we now write an equation for the United States as