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solutions_EC201midterm2[1]

solutions_EC201midterm2[1] - EC201 Fall 2007 Prof Jordi...

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EC201, Fall 2007, Prof. Jordi Jaumandreu Solutions midterm 2 There are four problems which you have to solve. The problems have fi ve questions each and the number of points that each question is worth is detailed. Take these numbers as a guide to how long you should spend on a question. Be sure that you write everything (diagrams, calculations and explanations) in the allocated space. A solution without the corresponding calculations will not be given any credit. Graphs without the associated explanations will only be given partial credit. Answers should be precise and concise. Clarity of exposition will be taken into account. 1
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1. (25 pts) Suppose a fi rm has a fi xed-proportions production function, in which one unit of output is produced using two workers and one unit of capital. a. (2pts) Draw the isoquants for this production function, representing labor on the x -axis and capital on the y -axis. Isoquants with right angles on a ray with slope 1 2 . b. (3 pts) De fi ne and show the expansion path of the fi rm. The expansion path of the fi m is the set of combinations ( l, K ) that will be chosen to produce the di ff erent output levels. In this case the expansion path is the ray with slope 1 2 . c. (6 pts) Suppose capital is fi xed at three units. Show, by means of a line on the diagram, the short run possibilities of combining workers and capital when workers go from zero to 12. Explain. The ray up to the point (6 , 3) and an horizontal line at the level of K = 3 from there on. Along this horizontal line we are in the same level of production q = 3 . d. (8 pts) Draw the total product of labor (short run production function), the average product of labor and the marginal product of labor when workers go from zero to 12 and capital is fi xed at 3. Explain a little the diagrams.
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