1. Consider two consumption products, manufacturing (Ym) and services (Ys). Suppose individuals have the following preferences:...

 

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1. Consider two consumption products, manufacturing (Ym) and services (Ys). Suppose individuals have the following preferences: Ym = Ys GDP in the economy is the sum of GDPs in manufacturing and services, Y = pmYm psys The production functions of the respective sectors are, Ym = AmLm and, Ys = AsLs Lm Ls = L where L is the total stock of labor in the economy (assume that this is not growing over time). Labor is free to move between the two production sectorsand receives identical wages in both sectors. Answer the following (a) What is the relative price ratio (pm/ps) of the two goods as a function of relative technology values(Am and As)? (Hint: Use the fact that wages are equalized across sectors. Since wages are equalized, this means that the value of marginal product (p MPL) is also equalized.) (b) Whatistheshareofservicesexpendituresintheeconomy(psYS/Y)as a function of relative technology values. Suppose initially Am = As, what is the share? (c) What happens if the service technology doubles but manufacturing productivity remains the same, 2Am = As? (d) How would your answer to 1b change if they consumed in different proportions: Ym = 2Ys (e) Suppose instead of equal quantities, individuals spent equal amounts on both goods i.e. psS =1 pmM How would your answer to 1b change? Do you think this assumption is correct? 1. Consider two consumption products, manufacturing (Ym) and services (Ys). Suppose individuals have the following preferences: Ym = Ys GDP in the economy is the sum of GDPs in manufacturing and services, Y = pmYm psys The production functions of the respective sectors are, Ym = AmLm and, Ys = AsLs Lm Ls = L where L is the total stock of labor in the economy (assume that this is not growing over time). Labor is free to move between the two production sectorsand receives identical wages in both sectors. Answer the following (a) What is the relative price ratio (pm/ps) of the two goods as a function of relative technology values(Am and As)? (Hint: Use the fact that wages are equalized across sectors. Since wages are equalized, this means that the value of marginal product (p MPL) is also equalized.) (b) Whatistheshareofservicesexpendituresintheeconomy(psYS/Y)as a function of relative technology values. Suppose initially Am = As, what is the share? (c) What happens if the service technology doubles but manufacturing productivity remains the same, 2Am = As? (d) How would your answer to 1b change if they consumed in different proportions: Ym = 2Ys (e) Suppose instead of equal quantities, individuals spent equal amounts on both goods i.e. psS =1 pmM How would your answer to 1b change? Do you think this assumption is correct?