Worth: Mankiw Economics 5e 24 PART IIntroduction Two Arithmetic Tricks for Working With Percentage Changes For manipulating many relationships in econom-(.15 percent) is approximately the sum of the ics, there is an arithmetic trick that is useful toi growth in the GDP deflator(5 percent)and the know: the percentage change of a product of two vari- growth in real GDP (3 percent) ables is approximately the sum of the percentage changes A second arithmetic trick follows as a corol- in each of the variables lary to the first: the percentage change of a ratio is ap To see how this trick works, consider an exam-i proximately rcentage change in the le. Let P denote the gdp deflator and y denote minus the percentage change in the denominator real GDP. Nominal GDP is P xY. The trick states Again, consider an example. Let y denote GDP that and L denote the population, so that Y/L is GDP The second trick states Percentage Change in(PxY) Percentage Ch P) Percentage Change in(Y/L) + Percentage Change in Y) ( Percentage Change in Y) ( Percentage Change in L) For instance, suppose that in one year, real GDP is 100 and the gDP deflator is 2; the next year,i For instance, suppose that in the first year, r real GDP is 103 and the gDP deflator is 2.1. We 100,000 and L is 100, so Y/L is 1,000; in the sec- can calculate that real GDP rose by 3 percent i ond year, Y is 110,000 and L is 103, So Y/L is and that the gdP deflator rose by 5 percent.: 1,068. Notice that the growth in GDP per person Nominal GDP rose from 200 the first year toi(6.8 percent) is approximately the growth inin- 216.3 the second year, an increase of 8.15 per-: come(10 percent) minus the growth in popula cent. Notice that the growth in nominal GDP tion(3 percent). The Components of Expenditure Economists and policymakers care not only about the economy 's total output of goods and services but also about the allocation of this output among alternative uses.The national income accounts divide gDP into four broad categories of C (C) purchases(G) Net exports(NX Y=C+I+G+NX Mathematical note: The proof that this trick works begins with the chain rule from calculus Now divide both sides of this equation by PY to obtain d(pY)/(py)=dP/p+dY/ Notice that all three terms in this equation are percentage User JOENA: Job EFF01418: 6264_cho2: Pg 24: 24942#/eps at 1009 II Tue,Feb12,20028:414MUser JOEWA:Job EFF01418:6264_ch02:Pg 24:24942#/eps at 100% *24942* Tue, Feb 12, 2002 8:41 AM The Components of Expenditure Economists and policymakers care not only about the economy’s total output of goods and services but also about the allocation of this output among alternative uses. The national income accounts divide GDP into four broad categories of spending: ➤ Consumption (C) ➤ Investment (I) ➤ Government purchases (G) ➤ Net exports (NX). Thus, letting Y stand for GDP, Y = C + I + G + NX. 24 | PART I Introduction FYI For manipulating many relationships in econom￾ics, there is an arithmetic trick that is useful to know: the percentage change of a product of two vari￾ables is approximately the sum of the percentage changes in each of the variables. To see how this trick works, consider an exam￾ple. Let P denote the GDP deflator and Y denote real GDP. Nominal GDP is P × Y. The trick states that Percentage Change in (P × Y) ≈ (Percentage Change in P) + (Percentage Change in Y). For instance, suppose that in one year, real GDP is 100 and the GDP deflator is 2; the next year, real GDP is 103 and the GDP deflator is 2.1. We can calculate that real GDP rose by 3 percent and that the GDP deflator rose by 5 percent. Nominal GDP rose from 200 the first year to 216.3 the second year, an increase of 8.15 per￾cent. Notice that the growth in nominal GDP Two Arithmetic Tricks for Working With Percentage Changes (8.15 percent) is approximately the sum of the growth in the GDP deflator (5 percent) and the growth in real GDP (3 percent).1 A second arithmetic trick follows as a corol￾lary to the first: the percentage change of a ratio is ap￾proximately the percentage change in the numerator minus the percentage change in the denominator. Again, consider an example. Let Y denote GDP and L denote the population, so that Y/L is GDP per person. The second trick states Percentage Change in (Y/L) ≈ (Percentage Change in Y) − (Percentage Change in L). For instance, suppose that in the first year, Y is 100,000 and L is 100, so Y/L is 1,000; in the sec￾ond year, Y is 110,000 and L is 103, so Y/L is 1,068. Notice that the growth in GDP per person (6.8 percent) is approximately the growth in in￾come (10 percent) minus the growth in popula￾tion (3 percent). 1 Mathematical note:The proof that this trick works begins with the chain rule from calculus: d(PY) = Y dP + P dY. Now divide both sides of this equation by PY to obtain d(PY)/(PY) = dP/P + dY/Y. Notice that all three terms in this equation are percentage changes