This document provides an overview of concepts to be covered in an economics lecture, including:
1) Unconstrained and constrained optimization
2) Linear programming involving primal problems, shadow prices, and profit/cost minimization
3) An example of a corner point combination showing the lowest cost production requires 5/3 cases of good A and 2/3 cases of good B
4) Determining shadow prices by setting up and simultaneously solving equations involving labor, material, and production capital constraints
3. Concepts to be covered in
lecture
1) Unconstrained optimisation.
2) Constrained optimisation.
3) Linear programming.
Primal problem.
Shadow prices.
Profit maximisation.
Cost minimisation.
10. Corner Point Combination Cost
a 2.5A +0B 鐃 1250
b 5/3A + 2/3B 鐃 1233
c 0A + 4B 鐃 2400
The lowest cost is 鐃 1233 and it requires 5/3 cases of
type A and 2/3 cases of type B per production run to be
produced.
Contribution per one unit of constraint (shadow prices)
10 VHR + 20 VM + 10VC (HR = labour component, M =
material, C = production capital
and V = shadow price)
and 4VHR + 10VM + 5VC = 500
5VHR + 5VM + 4VC = 600
The slack variable is production capital
4 VHR + 10VM = 500
and 5 VHR + 5VM = 600
Simultaneous solving for two unknowns result in:
VHR = 116 2/3
& VM = 3 1/3
Every one additional HR input will add 鐃 116.66 to
total cost and one additional unit of material will add
鐃 3.33 to total cost.
