this to affect short run output when defined as (i) output gap, and (ii) percent-age change? Provide economic intuition for each definition.Now consider the case of capital augmenting technology, so that the produc-tion function becomes,Yt=L1-αt(AKt)α,(2)How does this change your analysis?1A function exhibits constant returns to scale if scaling up the inputs by factorλleads toan equivalent increase in output1
3Log-DifferencesIn the lecture notes it is claimed that,Yt-YtYt≈lnYt-lnYt=yt-yt(3)The Taylor expansion of a functionf() around a pointais given by,f(x) =f(a) +∂f∂x|a(x-a) +12!∂2f∂x2|a(x-a)2+...+1n!∂nf∂xn|a(x-a)n+...(4)where∂nf∂xn|astands for the partial derivative evaluated at the pointa.1. Find the Taylor Series expansion of ln (x) around the pointx2. Hence, or otherwise, show that to the first order (i.e.cut the series offafter the first partial derivative) thatYt-YtYt≈lnYt-lnYt4IS Curve Intuition - THIS QUESTION TOBE SUBMITTED FRIDAY WEEK 1Consider the following macroeconomic changes.