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: