answerstohomework1spring2005

answerstohomework1spring2005 - Economics 302 Prof Kelly...

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Economics 302 Prof. Kelly Problem Set 1 Answer Key Exercise 1 a Total income is just the wage in Home times the number of workers: I H = w ¤ L b The percent of income spent on Home-produced goods is just the sum of the percentages from p 1 to p k : h ( k ) = p 1 + p 2 + ::: + p k = k X i =1 p i c In Foreign, they spend h ( k ) of their total income, w ¤ L ¤ ; on Home goods: E H;F = h ( k ) w ¤ L ¤ d In Home, they spend 1 ¡ h ( k ) of their total income, wL; on Foreign goods: E F;H = (1 ¡ h ( k )) wL e The total expenditure on Home goods is : E H = E H;F + E H;H = h ( k ) w ¤ L ¤ + h ( k ) wL = h ( k )[ w ¤ L ¤ + wL ] f Equating expressions, we have: w ¤ L = h ( k )[ w ¤ L ¤ + wL ] w ¤ L (1 ¡ h ( k )) = h ( k ) w ¤ L ¤ w w ¤ = μ h ( k ) 1 ¡ h ( k ) L ¤ L g For imports to equal exports, we need: h ( k ) w ¤ L ¤ = (1 ¡ h ( k )) wL w w ¤ = μ h ( k ) 1 ¡ h ( k ) L ¤ L h The expressions are the same. 1
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i We can rewrite (g) as: w C w U S = GDP C GDP U S = μ h ( k ) 1 ¡ h ( k ) L U S L C where GDP is GDP per capita. To solve for h ( k ) : h ( k ) L US GDP US = GDP C [1 ¡ h ( k )] L C h ( k ) L US GDP US + h ( k ) L C GDP C = GDP C L C h ( k ) =
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