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Econ 100B: Economic Analysis – MacroeconomicsProblem Set #2 – SolutionsDue Date: July 10, 2020General Instructions:•Please upload a PDF of your problem set to Gradescope by 11:59 pm.•Late homework will not be accepted.•Please put your name and student ID at the upper right corner of the front page.1. Write out the steps need to show that the last equation on slide 21 of lecture 5 followsfrom the first equation on the same slide.Hint 1: A review of the first 2 pages ofthe memo1has some helpful hints.Hint 2: the expression forκcan be written asK=κEL.(8)1R.J. Hawkins (2020)The Solow-Swan and Romer Models.1
Taking the time derivative of Eq. (6) we have thatdKdt=dκdtEL+κdEdtL+κEdLdt(9)which, given thatE(t) =E(0egEt-→dEdt=gEE(10)andL(t) =L(0)egEt-→dLdt=gLL(11)yieldsdκdtEL+κgeEL+κEgLL=sκαEL-δκEL .(12)Dividing through byELand collecting terms, this becomesdκdt=sκα-(gE+gL+δ)κ .(13)2. The variableκis capital per worker per unit of worker efficiency, or capital per workermodified to reflect the difference in efficiency among workers. Consider two countries,A and B, with labor efficienciesEA= 1 andEB= 2, respectively.(a) If the size of the labor force is the same in each country andκ*is the same in eachcountry, which country will have a larger aggregate capitalKin steady state?2