work out the connection between the three ways to measure GDP growth: A) As a percentage change holding prices constant. B) Expressing growth in terms of a common item (converting everything into a particular good (e.g. apples). And C) as the weighted average of the growth in each of the goods weighted by their corresponding expenditure shares.

Work out the algebraic steps that:

1. take you from the first to the second equation in slide 14;
2. take you from that same top equation in slide 14 to the one in slide 15; and
3. prove the relationship in slide 16.

Your task is to write up a two page 'study guide' that compiles the derivations of points (1)-(3) above.

14 Real GDP Growth 1. Fix a base year price, real GDPt+1_ _ Pat * at+1 + Pbt * be+1 _ 1 real GDPt Pat * at + Pb,t * bt 2. Or in terms of one good, say, apples (divide numerator and denominator by Pa,t) real GDP++1 at+1 + Pb.z * bt+1 real GDPt - 1 = Pat at + Pb.t * bt Pat In the first, real GDP is in constant year t dollars, in the second, real GDP is measured in units of apples. 15 Real GDP Growth An equivalent representation is a weighted average of the growth in each of the goods based on their expenditure shares. real GDP +1 -1 =0t at+ 1 + (1 - 0.) bt+1 real GDPt at bt 1 where 0 is the fraction of nominal GDP accounted for by purchases of apples, and (1 -0.) the share accounted for by purchases of bananas. 16 Real GDP Growth Why does real GDP growth matter? Well, suppose that households get utility from apples and bananas every period f: ut = 0ln(a,) + (1-0)In(b;) Ut+1 = 0ln(at+1) + (1-0)In(b:+1) Then, Ut+1 - Wt =0 -t+1\\ (b+ + 1 ) - 1 1 + (1 - 0) 2+ So, if @ = 0, then utility increases whenever real GDP growth is positive