6005_Test_III_Summer2008_QandA

6005_Test_III_Summer2008_QandA - TEST III Q & A MANAGERIAL...

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MANAGERIAL ECONOMICS – MGNT 6005 Instructor: S. Davis Summer 2008 1. Continuous Compounding . Elizabeth Corday, a quality control supervisor for Surgery Products, Inc., is concerned about an increase in distribution costs for disposable syringes from $40 to $50 per case over the last five years. Corday feels that setting up a new direct-sales distribution network at a cost of $58.50 per unit may soon be desirable. A. Calculate the unit cost growth rate using the constant rate of change model with continuous compounding. B. Forecast when unit distribution costs will exceed the current cost of direct-sales distribution. ANS: A. C t = C 0 e gt $50 = $40e 5g 50/40 = e 5g 1.25 = e 5g ln(1.25) = 5g g = 0.22/5 = 0.04 or 4% B. Direct-sales cost = C 0 e gt $58.50 = $50e (0.04)t 58.5/50 = e (0.04)t 1.17 = e (0.04)t ln(1.17) = 0.04t t = 0.16/0.04 = 4 years 1
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2. Returns to Scale . Determine whether the following production functions exhibit constant, increasing, or decreasing returns to scale. A. Q = 25X + 0.5Y + 8Z B. Q = 9L + 5K – 400 C. Q = 10A + 7B + 4AB D. Q = 6L 2 + 3LK + 2K 2 E. Q = 2L 0.4 K 0.6 ANS: A. Initially, let X = Y = Z = 100, so output is: Q 1 = 25(100) + 0.5(100) + 8(100) = 3,350 Increasing all inputs by 4% leads to: Q 2 = 25(104) + 0.5(104) + 8(104) = 3,484 Because a 4% increase in all inputs results in a 4% increase in output (Q 2 /Q 1 = 3,484/3,350 = 1.04), the output elasticity is 1 and the production system exhibits constant returns to scale. B. Initially, let L = K = 100, so output is: Q 1 = 9(100) + 5(100) - 400 = 1,000 Increasing both inputs by 5% leads to Q 2 = 9(105) + 5(105) - 400 = 1,070 Because a 5% increase in both inputs results in a 7% increase in output (Q 2 /Q 1 = 1,070/1,000 = 1.07), the output elasticity is greater than 1 and the production system exhibits increasing returns to scale. C.
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This note was uploaded on 11/13/2011 for the course MIS 4100 taught by Professor Maxnorth during the Spring '11 term at Birmingham-Southern College.

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6005_Test_III_Summer2008_QandA - TEST III Q & A MANAGERIAL...

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