# answerstooptionalhomework6spring2007 - Economics 102 Spring...

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Economics 102 Spring 2007 Answers to Homework #6 (optional homework) 1. (a) We need to assume that this is a closed economy (X-M=0). Using Y=AE=C+I+G, we have Y=100+0.7Y+440. Solving this for Y gives Y=1800. (b) Plug Y=1800 into the aggregate production function to get L= 810,000. Meanwhile, we can find the full employment level by equating the demand and supply functions for labor. This gives us L=1,000,000. The equilibrium employment is smaller than the full employment. (c) When L=1,000,000, Y=2,000 (you can solve for this using the production function). So we need to increase Y by 200. The multiplier equals 10/3. Then: Change in Y=(10/3)*(Change in G) This tells us that G needs to increase by 60, resulting in a new G=300. Figure 1 AE Line 2 Line 1 Y1 Y2 Y L L D S L2 L2 L1 Aggregate L1 Production S D Function w/P Y Figure 3 Figure 2

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(d) The situation we analyzed above is described by the three graphs above. Before the change in G, the equilibrium output is determined by the intersection of Line 1 and the 45 degree line (Y1). Figure 2 is a “flipped” aggregate demand function and Figure 3 is flipped graph for the labor market. As is easily seen, the full employment L2 is larger
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