QUESTION ONE
a) Clearly distinguish between the following concepts and terms as used in Production Economics:
i. Iso-revenue line and Iso-cost line
ii. Rate of Technical Substitution and Rate of Product Transformation (6 marks)
b) Deborah has the following Marginal Physical Product (MPP) function in her milk production plant:
MPP = 4 + 8x – 0.3×2 where C = 0
At what level of input x does:
i. TPP reach its maximum
ii. APP reach its maximum
iii. MPP reach its maximum
iv. Stage 2 of production begin and end (8 marks)
c) Discuss the computational difficulties in Linear Programming as a farm firm optimization technique (3 marks)
d) Discuss the goals of Production Economics (5 marks)
e) Find the homogeneity of the following production function and state its returns to scale:
24X1/2Y3/2 – 2X3/Y (3 marks)
QUESTION TWO
a) State Euler’s Theorem as used in production economics (2 marks)
b) Briefly discuss the properties/characteristics of Cobb-Douglas Production Functions (7 marks)
c) Alamin has a coffee firm in Kiambu having the following functions:
Q= 0.8P – 20
TFC = 180
AVC = 4 + 2Q
Find Alamin’s profit maximizing level of output and his profit (6 marks)
QUESTION THREE
a) Using well labelled diagram distinguish between Competitive, Joint, Supplementary and Complementary products/enterprises (6 marks)
b) Edith has the following maize production function
Q = 2K0.5L0.3
Where Q is the quantity of maize produced while K and L are units of inputs capital and labour respectively. Supposing that a bag of maize sells at Ksh. 400, the prices of K and L are Ksh 16 and Ksh. 4 respectively, and that he has a total of Ksh. 5000 to spend on the two inputs:
i. Using Lagrangean optimization technique determine the quantities of K and L that Edith will need in order for him to maximize profit
ii. What will be Edith’s maximum profit (9 marks)
QUESTION FOUR
a) Discuss the steps which should be followed by a farm manager while making decisions in conditions of risk (6 marks)
b) Njoki has the following production relationship in her Irish Potato farm:
y = 2×1/2
Where y and x are quantities of inputs and outputs respectively. If the price of y is ksh. 8, price of x is ksh. 2 and Total Fixed Costs are ksh. 30, calculate:
i. The profit maximizing level of input
ii. The profit maximizing level of output (9 marks)
QUESTION FIVE
a) Briefly discuss the assumptions of linear programming as an optimization technique in scarce resource allocation (5 marks)
b) Given the following
Max Z = 4X1 – X2 + 2X3
Subject to:
2X1 + X2 + 2X3 ≤ 6
X1 – 4X2 + 2X3 ≤ 0
5X1 + 2X2 – 2X3 ≤ 4
X1,X2,X3 ≥ 0
Determine the optimal solutions (10 marks)