Suppose there are two types of labor - routine (think factory worker) and non-routine (think manager or product designer). Production combines these two types of labor and capital. Production in the economy is described by the following production function: Yt = At (Kt + LN)\" Lilia- (1) Here, Yt is GDP, At is TFP, Kt is capital, List is routine labor, and Ln,t is non-routine labor (all in year t) and o: is a parameter with O 0 is a number. Suppose in year t = 2, K2 = 2K , L32 = 0 and Ln; = K so that rms have fully substituted away from routine workers to capital. Finally, assume TFP is constant with A1 = A2 = A. Using the production function in equation (1) above, compute GDP in years t = 1 and t = 2. Your answer should depend only on the parameters oz, A and K (and the number 2!). This is the simulation step. Yes the simulation is only two periods! (B) (4 points) (Measuring TFP) Suppose a new class of Principles of Macro students were to look at the data we simulated for Yt, Kt, and L; = L13: + LN in each year t = 1, 2 and were asked to measure TFP in this economy as the Solow residual implied by the production function K; = fithLia. Show that they would nd: 141 = A22a_1 and 12 = A (C) (2 points) (TFP MisMeasurement) Given our results in part (B), if 220'1 > 1, then our TFP measurement exercise would imply TFP (A) is falling even though from our assumption in part (A) we know according to the \"true\" production function TFP (A) is constant. In one or two sentences, explain why our measurement approach gives the \"wrong\" answer. Can this help us understand why automation may not be causing growth in Total Factor Productivity