Managerial Economics Foundation

OPEN UNIVERSITY MALAYSIA
Managerial Economics Assignment

QUESTION 1

A certain production process employs two inputs labor (L) and raw materials (R). Output (Q) is a function of these two inputs and is given by the following relationship:

Q = 6L2 R2 - 0.10L3 R3

Assume that raw materials (input R) are fixed at 10 units.

(a) Determine the total product function (TPL) for input L. (2 marks)
(b) Determine the marginal product function for input L. (2 marks)
(c) Determine the average product function for input L. (2 marks)
(d) Find the number of units of input L that maximizes the total product function. (2 marks)
(e) Find the number of units of input L that maximizes the marginal product function. (2 marks)
(f) Find the number of units of input L that maximizes the average product function. (2 marks)
(g) Determine the boundaries for the three stages of production. (3 marks) [TOTAL: 15 MARKS]
ANSWER 1
Q = 6L R2 - 0.10L3 R3 Whereas : R = 10 (a) TPL For Input = 6L (10) – 0.1L (10) = 6L (100) – 0.1L (1000) = 600L - 100 L b) MP For Input = d(TPL)/dL = 600L – 100L = 1200L – 300L c) AP For Input = TPL / L = (600L -100L )/ L = 600L – 100L

d) Maximise Total Product Function For Input L [ d(TPL) ]/dl = 0 1200L -300L = 0 0 = L / L = 1200/300 L = 4 e) [ d(MPL) ] / dl = 0 (Condition for max point on MPL) [ d(MPL) ] / dl = 1200L – 300L = 1200 – 600L When [ d(MPL) ] / dL = 0 1200-600L = 0 -600L = -1200 L = -1200/-600 L = 2 f) [ d(APL)]/dL = 0 (Condition for max point on MPL) [ d(APL)]/dL = 600L – 100L = 600 – 200L When [ d(APL) ]/dL = 0 600 – 200L = 0 L = -600/-200 L = 3 g)

QUESTION 2
Consolidated Salt Company sells table salt to both retail grocery chains and commercial users (e.g., bakeries, snack food