Economic Growth 3rd Edition by David Weil Solution manual

(Y_{U.S., 2009 – t}) ´ (1 + g)^t = Y_{U.S., 2009}.

        Since Y_{U.S., 2009 – t} = Y_{Sri Lanka, 2009} = $4,034, Y_{U.S., 2009} = $41,099, and g = 0.018, we then substitute in these values and solve for t.

($4,034) ´ (1 + 0.018)^t = $41,099.

                                                                      (1 + 0.018)^t = ($41,099/$4,034).

        One can solve for t by simply trying out different values on a calculator. Alternatively, taking the natural log of both sides, and noting that ln(x^y) = yln(x), we get

tln(1 + 0.018) = ln($41,099/$4,034)

                                                                        t = 130.11.

        That is, 130.11 years ago, the income per capita of the United States equaled that of Sri Lanka’s income in the year 2009. This year was roughly 2009 – t, i.e., the year 1879.

7.     In order to calculate the year in which income per capita in China will overtake the income per capita in the United States, we first need to find t, the number of years it will take for the income per
capita in the two countries to be equal. That is,

(Y_{U.S., 2009}) ´ (1 + .018)^t = (Y_{China, 2009}) ´ (1 + .079)^t.

Since Y_{U.S., 2009} = $41,099, Y_{China, 2005} = $7,634, we then substitute in these values and solve for t.

(1 + 0.079/1 + .018)^t = ($41,099/$7,634).

We can solve for t by trying out different values on a calculator. Alternatively, taking the Natural Log of both sides, and noting that ln(x^y) = yln(x), we get

tln(1.06) = ln($41,099/$7,634)

                                                                    t = 28.89.

        That is, in 28.89 years, assuming they grow at the current growth rates, the income per capita of China will surpass that of the United States. This year will roughly be 2009 + t, i.e., the year 2038.

n Solutions to Appendix Problems

A.1.    The number of people living on less than a dollar a day will be larger if we calculate it using market exchange rates instead of purchasing power exchange rates because market exchange rates only take into account the relative value of traded goods, which are relatively more expensive in poorer countries. Individuals in these countries will have low purchasing power for traded goods. By using the market exchange rate, we are assuming that traded goods and non-traded goods are the same price, and therefore individuals in poor countries will have low purchasing power for non-traded goods as well, which will make them appear poorer than they actually are.