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Unformatted text preview: 1 Midterm Exam Solutions Economics 100B, Fall 2008 Section A00 The following exam should be completed in 1 hour and 20 minutes. Notes, calculators, cell phones, electronic devices, etc. are not permitted. We will give partial credit in some cases, so it is best to show your work. There are 100 points distributed over 3 questions. Question 3 is longer than the others. Work carefully, relax, and good luck! 1. (25 points) Answer the following questions for the production function: q = L + L 1/2 K (a) (4 points) What is the marginal product of labor? ( 1/2) / 1 (1/ 2) MPL q L L K ! = " " = + (b) (4 points) What is the marginal product of capital? MPK = ! q / ! K = L 1/ 2 (c) (3 points) Can q be produced without labor? No q = (0) + (0) 1/ 2 K = (d) (3 points) Can q be produced without capital? Yes q = L + L 1/ 2 (0) = L 2 (e) (3 points) Are there diminishing returns to labor (does MP L fall as L gets larger)? Consider cases with and without capital. ( 3/2) If 0, there are diminishing returns to labor: / ( 1/ 4) If 0, there are constant returns to labor (not diminishing returns): / K MPL L L K K MPL L ! > " " = ! < = " " = (f) (3 points) Are there diminishing returns to capital (does MP K fall as K gets larger)? Consider cases with and without labor. For 0 or 0, the returns to capital are constant. Therefore, there are no diminishing returns to capital. / K K MPK K > = ! ! = (g) (5 points) Does production have constant, increasing, or decreasing returns to scale? Show how you arrive at your answer. (1/2) (1/2) (1/2) (1/2) The production function has increasing returns to scale. To prove this, we need to show: ( , ) ( , ) where ( , ) ( , ) ( ) ( ) ( ) f L K f L K f L K L L K f L K L L K L L K ! ! ! ! ! ! ! ! ! ! ! > = + = + = + (3/2) (1/2) (1/2) (1/2) (1/2) (1/2) (1/2) (1/2) (1/2) (1/2) ( ) Since (for 1), ( , ) ( ) ( ) ( , ) L L K L L K L K L K f L K L L K L L K f L K ! ! ! ! ! ! ! ! ! ! ! !...
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