Questions from Chapter 9:
1) Problem 4, page 271. (3 Marks)
The missing numbers for the Total product column are 180, 320, and 480. The
missing numbers for the Average product column are [– (not defined)], 160, and 140.
The missing numbers for the Marginal product column are 180, 100, and 60.
2) Problem 7, page 271 (5 marks)
7.
a) (1 mark)
b) Maximum production (Q = 9) occurs at L = 6. [Calculus trained students: To find
the maximum, take the first derivative and set it equal to zero and solve for L: dQ/dL
= 3 – (1/2)L = 0, which yields L = 6, Q = 9.] (2 Marks)
c) For 0 < L < 2, MP
L
[= (5/2)L] is increasing.
For 2 < L < 7, MP
L
[=3 – ½ L] is
decreasing. (1 mark)
d) MP
L
= 0 for L = 6, and MP
L
< 0 for L > 6. Past L = 6, adding L
lowers
output Q.
(1 mark)
Questions from Appendix Chapter 9:
3) Problem 2, page 648 (1 mark)
For K = 27, we have Q = 6L
1/3
, and so MP
L
= dQ/dL = 2L
–2/3
.
4) Problem 4, page 648 (2 marks)
We are given that Q = F(K, L) = min (2K, 3L) with K = 6 and L = 5.
Then Q = min (12, 15) = 12. MP
K
= F(7, 5) – F(6, 5) = 14 – 12 = 2.
MP
L
=F(6, 6) – F(6, 5) = 12 – 12 = 0.
Q
9
26
7
L