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# Book solutions - Rose-Hulman Institute of Technology /...

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Rose-Hulman Institute of Technology / Department of Humanities & Social Sciences / K. Christ Fall Quarter, 2009 – 2010 / SL 351, Managerial Economics; EMGT 531, Economics for Technical Managers Problem Set 3 - Solutions Textbook Problems: Hirschey, Chapter 7: P7.4, P7.7, P7.8, P7.10 Hirschey, Chapter 8: P8.7, P8.8, P8.9, P8.10 Hirschey, Chapter 9: P9.2, P9.6, P9.8, P9.10 Hirschey, Chapter 10: P10.4, P10.5, P10.6, P10.7, P10.8 Hirschey, Chapter 11: P11.4, P11.7, P11.8, P11.10 Hirschey, Chapter 12: P12.5, P12.6, P12.7, P12.8 P7.4 A. Initially, let X = Y = Z = 100, so output is: Q = 0.5(100) + 2(100) + 40(100) = 4,250 Increasing all inputs by an arbitrary percentage, say 2 percent, leads to: Q = 0.5(102) + 2(102) + 40(102) = 4,335 Because a 2 percent increase in all inputs results in a 2 percent increase in output (Q 2 /Q 1 = 4,335/4,250 = 1.02), the output elasticity is 1 and the production system exhibits constant returns to scale. B. Initially, let L = K = 100, so output is: Q = 3(100) + 10(100) + 500 = 1,800 Increasing both inputs by an arbitrary percentage, say 3 percent, leads to: Q = 3(103) + 10(103) + 500 = 1,839 Because a 3 percent increase in both inputs results in a 2.2 percent increase in output (Q 2 /Q 1 = 1,839/1,800 = 1.022), the output elasticity is less than 1 and the production system exhibits diminishing returns to scale. C. Initially, let A = B = 100, so output is:

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Q = 4(100) + 6(100) + 8(100)(100) = 81,000 Increasing both inputs by an arbitrary percentage, say, 1 percent, leads to: Q = 4(101) + 6(101) + 8(101)(101) = 82,618 Because a 1 percent increase in both inputs results in a 2 percent increase in output (Q 2 /Q 1 = 82,618/81,000 = 1.02), the output elasticity is greater than 1 and the production system exhibits increasing returns to scale. D. Initially, let L = K = 100, so output is: Q = 7(100 2 ) + 5(100)(100) + 2(100 2 ) = 140,000 Increasing both inputs by an arbitrary percentage, say, 2 percent, leads to: Q = 7(102 2 ) + 5(102)(102) + 2(102 2 ) = 145,656 Because a 2 percent increase in both inputs results in a 4 percent increase in output (Q 2 /Q 1 = 145,656/140,000 = 1.04), the output elasticity is greater than 1 and the production system exhibits increasing returns to scale. E. Initially, let L = K = 100, so output is: Q = 10(100 0.5 )(100 0.3 ) = 398 Increasing both inputs by an arbitrary percentage, say, 4 percent, leads to: Q = 10(104 0.5 )(104 0.3 ) = 411 Because a 4 percent increase in both inputs results in a 3.3 percent increase in output (Q 2 /Q 1 = 411/398 = 1.033), the output elasticity is less than 1 and the production system exhibits decreasing returns to scale.
P7.6 SOLUTION A. No. The rule for an optimal combination of newspaper (N) and magazine (M) ads is: Here, the question is \$500 3,000 ? \$125

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## This note was uploaded on 09/25/2011 for the course BSAD 314 taught by Professor Staff during the Spring '10 term at SUNY Canton.

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Book solutions - Rose-Hulman Institute of Technology /...

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