101.0520 'Sketches of Answers to Problems Set 1Chapter 2 (4)(a) Look at footnote 7 on page 17 in the book and make sure you understand the details. Using this formula, a country growing at 10% per year will double its income in seven years, a country growing at 5% will take 14 years to do so. Now try a direct argumentusing a calculator. If a country has income x today and is growing at 10%, it will have an income of x (1 + 1/10)next year. If you understand this, you can see that thinking of this number as the “newx”,income the year after will be scaled up by the same formula. This means that i n c o m e the day after is just x + 1/10)2. Plodding on in this vein, we see that income after t years is x (1 + 1/10)t. Now think of as an unknown, and we wish to know: for what value of t is x (1 +1/10)t equal to 2 xs? How would you solve this using a calculator?while (1 t (4)(B) If we are comparing to the counterfactual outcome, then thecountry would be 1.0620−1.0520= 20.9% richer. (4)(c) Compounding monthly, we get (1 + 0.3)12 =23.3; hence the equivalentannualinflation rate would be approximately (23.3−1)×100 = 2230%. (Compare with the without-compounding case and feel the power of exponential growth!)

(9)(a) Open-ended question. It is possible that instead of looking only at the number of children, parents also care about the quality of their children. A (probably inappropriate) analogy would be, when you get richer, instead of purchasing two low-end cell phones, you mightwantto simply purchase a trendy high-end model.(9)(b) Higher population growth rates are usually the results of higher rates of newborn children, who are and will remain under 15 for 15 years. Accumulating overtime, they can make up a rather large proportion of the overall population.(9)(c) Open-ended question. Poorer countries may be more likely to be rural because it requires a certain level of trade and productivity (either industrial or agricultural) urbanization. On the other hand, rural countries face many challenges to grow rich; for instance, rural areas are usually less densely populated, rendering it harder for the governmentto provide education and health services to the local residen(9)(d) As we have seen, prices of primary goods typically fluctuates more than those of manufactured goods. One possible explanation is that primary goods are more susceptible to factors largely beyond human control (such as rainfall). Manufactured goods are less likely to experience large price fluctuation since price fluctuations in a few of its inputs can only affect its price to a certain degree, if not cancelling out each other completelyChapter 3 (2)(a) δ= 0, hence s/θ = g. When θ= 4, s = 4g, and hence the savings rate should 0.32 and 0.4 when g = 0.08 and 0.1, respectively. Similarly, when s = 0.2, θ= s/g = 0therefore θneeds to be 2.5 and 2 when g is 0.08 and

often

to induce

ts.

.

be

.2/g, and