This document discusses economic principles of rural land resource management, including efficiency, optimization, and input-output relationships. It defines efficiency as either physical efficiency, when output is produced on the production possibility frontier at lowest cost, or economic efficiency, when marginal costs equal marginal revenues. Optimization means producing at the point where marginal rate of technical substitution equals 1. Input-output relationships refer to how specific resources like land and water are used to produce outputs like crops. The document explores concepts like production functions, laws of diminishing returns, and how optimal production is where marginal revenue equals marginal cost.

1. Economic & Management Aspects of
Rural Land Resources 1
Economic & Management
Aspects of Rural Land
Resources
SGH 2573

2. Economic & Management Aspects of
Rural Land Resources 2
Basic Economic Principles of Land Resources
♦ Introduction
♦ Efficiency
♦ Optimisation
♦ Input-output relationship
♦ The economic optimum

3. Economic & Management Aspects of
Rural Land Resources 3
Basic Economic Principles of Land Resources
 Two main economic principles of land resource
management are efficiency and optimization.
 Both are critical to sustainable rural land
resources management at least for three reasons,
namely to:
* increase output without increasing land area
(increase productivity)
* ensure full employment of resources to the
extent whereby each of them is equally
productive
* attain cost effectiveness in production

4. Economic & Management Aspects of
Rural Land Resources 4
Efficiency
 Efficiency is one of the basic tenets of land resource
management
 Two categories:
(1) Physical efficiency: when output is produced
exactly on the production possibility frontier
(PPF) or at lowest possible cost. Also called
productive or technical efficiency.
(2) Economic efficiency: when each additional input
cost incurred equals each additional output
revenue. Also called allocative efficiency.

5. Economic & Management Aspects of
Rural Land Resources 5
• PPF is a concave
curve due to disparity
in factors’ levels of
intensities and
technologies of the
two sectors
• Higher marginal
costs become
inevitable due to
diminishing marginal
returns in the
production of each
good
Productive or technical efficiency

6. Economic & Management Aspects of
Rural Land Resources 6
▪ PPF is based on the
concept of opportunity
cost – amount of one
output forsaken to
increase amount of
another
▪ Rate at which opportunity
cost changes is called
marginal rate of technical
substitution (MRTS)
Productive or technical efficiency

7. Economic & Management Aspects of
Rural Land Resources 7
E.g. Minimize TC = 188*goat + 206*Sheep
s.t. TC  6,800
Productive or technical efficiency
0
5
10
15
20
25
30
35
40
0 5 10 15 20 25 30 35
No. of sheep (heads)
No.
of
goats
(heads)
A
B
(Inefficient
budget)
(Infeasible
budget)
Combination of products exactly on the budget
line is technically efficient. Output production
does not exceed the budget line (RM 6,800)

8. Economic & Management Aspects of
Rural Land Resources 8
Economic or Allocative Efficiency
 Market condition whereby resources are allocated
in a way that maximizes the net benefit attained
through their use
 A situation in which the limited resources of a
country are allocated in accordance with the
wishes of consumers
 Allocatively efficient economy produces an
"optimal mix" of commodities
 A firm is allocatively efficient when its price is equal
to its marginal costs (that is, P = MC).

9. Economic & Management Aspects of
Rural Land Resources 9
 Production process that satisfies both technical and
economic efficiency
 When output is produced where:
(1) MR = MC
Additionally, in case of multi-output, say A and
B:
(2) MVPA= MVPB
(3) MRTSA,B = 1
where MR = marginal revenue, MC = marginal cost,
MVP = marginal value product, and MRTS =
marginal rate of technical substitution (A/B)
 May be reflected through production that maximises
revenue or profit
Optimality

10. Economic & Management Aspects of
Rural Land Resources 10
Optimum production – maximising revenue/profit
• Budget constraints
(FA and FB) are
imposed on PPF
• FB is budget use in
case of under-
production
• FA is budget use in
case of efficient
production
• However, only point
A yields optimum
production
F Two-output case

11. Economic & Management Aspects of
Rural Land Resources 11
4
Optimum production – maximising revenue/profit
Two-output case (cont.)

12. Economic & Management Aspects of
Rural Land Resources 12
Goat = 30 + 0.4*Sheep - 0.094*Sheep2 (PPF)
Goat = 36.17 - 1.096*Sheep (Budget line)
From PPF : dPPF(Goat)/dPPF(Sheep) = 0.4 - 0.188*Sheep
From Budget line: dBL(Goat)/dBL(Sheep) = -1.096
At tangential point, dPPF(Goat)/dPPF(Sheep) = dBL(Goat)/dBL(Sheep)
Thus, 0.4 - 0.188*Sheep = -1.096
Sheep = (0.4+1.096)/0.188
= 7.96
≈ 8
From PPF: Goat = 30 + 0.4*8 - 0.094*82
= 30 + 3.2 - 6.016
≈ 27
Total cost = 188 x 27 + 206 x 8
= 5,076 + 1,648
= 6,724
Total revenue = 350 x 27 + 400 x 8
= 9,450 + 3,200
= 12,650
Total profit = 12,650 - 6,724 = 5,926
Optimum production – maximising revenue/profit
Two-output case (cont.)

13. Economic & Management Aspects of
Rural Land Resources 13
-743
-408
3945
8140
4195
-3.27
0
20
-677
-373
4280
8883
4603
-3.08
4
19
-611
-337
4585
9560
4976
-2.89
7
18
-546
-302
4859
10172
5313
-2.70
10
17
-480
-267
5102
10718
5615
-2.51
12
16
-414
-231
5316
11198
5882
-2.33
15
15
-348
-196
5499
11612
6113
-2.14
17
14
-282
-161
5651
11960
6309
-1.95
19
13
-217
-125
5773
12242
6470
-1.76
21
12
-151
-90
5864
12459
6595
-1.57
23
11
-85
-55
5925
12610
6685
-1.39
25
10
-19
-19
5956
12695
6739
-1.20
26
9
47
16
5956
12714
6759
-1.01
27
8
112
51
5925
12668
6742
-0.82
28
7
178
87
5865
12556
6691
-0.63
29
6
244
122
5773
12378
6604
-0.45
30
5
310
157
5652
12134
6482
-0.26
30
4
376
193
5499
11824
6325
-0.07
30
3
441
228
5317
11448
6132
0.12
30
2
507
264
5104
11007
5904
0.31
30
1
0
0
4860
10500
5640
0.00
30
0
MR
MC
Profit
Total
revenue
Total cost
MRTS
Goat
Sheep
 Goat /  Sheep = MRTS = 1
MR = MC
Optimum
production –
maximising
revenue/profit
Price:
Goat:RM350/
head
Sheep: RM
400/head
Cost:
Goat: RM
188/head
Sheep: RM
206/head
Two-output case
(cont.)

14. Economic & Management Aspects of
Rural Land Resources 14
Two-output case (cont.)
Total cost
Total revenue
Profit
MC
MR
-2000
0
2000
4000
6000
8000
10000
12000
14000
0 5 10 15 20 25
No. of sheep (heads)
Revenue,
cost,
profit
(RM)
Optimality
region
Maximum
profit
Optimum production – maximising revenue/profit
MR = MC

15. Economic & Management Aspects of
Rural Land Resources 15
Effect of N on paddy
production
Single-output
case
Physical Productivity & Law of Diminishing Returns

16. Economic & Management Aspects of
Rural Land Resources 16
All biologically-oriented
resource productions
are subjected to the Law
of Diminishing Return
Physical Productivity & Law of Diminishing Returns
Technical efficiency
guides in the use of
input at different stages
of production
X = maximum MPP
Y = maximum APP
Z = maximum yield
Full
employment
of input
Over
employment
of input
Irrational Rational Irrational
Under
employment
of input
Single-output case (cont.)

17. Economic & Management Aspects of
Rural Land Resources 17
Nitrogen (kg)
200
195
190
185
180
160
140
120
100
80
60
40
20
0
R
e
v
e
n
u
e/
c
o
s
t
(RM)
700
600
500
400
300
200
100
0
TR
TVC
TAN
Economic Productivity & Law of Diminishing Returns
Single-output case (cont.)
▪ Considers physical
output, output price,
and cost of input.
▪ Enterprise aims at
optimal production.
▪ Basically where
MR = MC, i.e.
d(TR) = d(TVC).
▪ Optimal point is
where TVC curve
is tangential to TR
curve.

18. Economic & Management Aspects of
Rural Land Resources 18
Revenue and Cost function
TR = Total revenue
TVC1 = constant
marginal
cost
TVC2 = diminishing
marginal
cost
TVC3 = increasing
marginal
cost
TVC4 = decreasing
& increasing
marginal
cost
2
1
3
4
Different relationships of production
function → different optimality
implications

19. Economic & Management Aspects of
Rural Land Resources 19
Optimality and Production Decisions
Case of constant marginal cost A = Point of maximum 
B = Point of maximum
revenue
C = Point of terminal
production cycle
▪ Points of maximum profit
and maximum revenue
may not be the same.
▪ Enterprise gains maximum
profit first before maximum
revenue.
▪ Production should stop
when profit is zero
▪ Firm must set output and/or
cost strategies. E.g.
reduce expenditure or
increase yield
MR=0
MR=MC
TR-TC=0
Reduced TC
Longer cycle
Increased yield

20. Economic & Management Aspects of
Rural Land Resources 20
 Some resources are specifically used in the
production of economic goods or services
 E.g. land (L) and water (W) are used to grow
paddy
 This is called input-output relationship
 Mathematically P = f(L, W)
 Three categories of input-output relationship:
Example of Production Decisions
Input
L, W P
Output

21. Economic & Management Aspects of
Rural Land Resources 21
Y = f(x) (single-input production)
Y = f(x1, x2) (two-input production)
Y = f(x1, x2,…,xm) (multi-input production)
 Most economic production is multi-input: an output
is produced via a combination of resources, e.g.
land, capital, labour, fertilizer, water, temperature,
labour, etc.
 Input-output relationship of most production differ
according the form of function
Example of Production Decisions: Production
Function

22. Economic & Management Aspects of
Rural Land Resources 22
Forms of function (cont.)
Output, Y
0
Y = c + mX
c
Y
X
Input, X
m
(1) Linear function
Y = c + mX
dY/dX = m
c = intercept
(3) Quadratic function
Y = a + bX – b1X2
dY/dX = b – 2b1X
a = intercept
Output, Y
Input, X
Y = a + bX – b1X2
1Y
2X
2Y
1X
a

23. Economic & Management Aspects of
Rural Land Resources 23
Forms of function (cont.)
(3) Cobb-Douglas function
0 Input, X
Output, Y log Y = a + b1log X1 + b2logX2
log Y = a + b1log X1 + b2logX2
y/X1 = b1(Y/X1)
y/X2 = b2(Y/X2)
a = intercept

24. Economic & Management Aspects of
Rural Land Resources 24
 Physical & economic productivity of land
resources can be analyzed using a specific
production function
 Different enterprises may have different
productivity and thus production functions
 Most production functions are rather non-
linear
 Non-linear functions can be transformed into
somewhat linear, through logarithmic
transformation for estimation purposes
Production function (cont.)

25. Economic & Management Aspects of
Rural Land Resources 25
Total
value
of grain
(RM/ha)
NPK
(kg/ha)
60
20
150
40
290
60
380
80
440
100
485
120
520
140
546
160
565
180
569
185
570
190
569
195
505
200
Production function (cont.)
Total cost
Total value of
grain (RM/ha)
0
100
200
300
400
500
600
0 50 100 150 200 250
NPK (kg/ha)
Revenue,
cost
(RM)

26. Economic & Management Aspects of
Rural Land Resources 26
Ln of total
value of
grain
(RM/ha)
Log of total
value
of grain
(RM/ha)
NPK
(kg/ha)
4.094345
1.778151
20
5.010635
2.176091
40
5.669881
2.462398
60
5.940171
2.579784
80
6.086775
2.643453
100
6.184149
2.685742
120
6.253829
2.716003
140
6.302619
2.737193
160
6.336826
2.752048
180
6.343880
2.755112
185
6.345636
2.755875
190
6.343880
2.755112
195
6.224558
2.703291
200
Production function (cont.)
0
1
2
3
4
5
6
7
0 50 100 150 200 250
NPK (kg/ha)
Value
of
grain
(RM/ha)
in
logarithm
Using regresion method
ln (Grain value) = a1 + b1(NPK)
Ln (Grain value) = 4.791444+0.008891*NPK
log (Grain value) = ao + b0(NPK)

27. Economic & Management Aspects of
Rural Land Resources 27
Production function (cont.)
Example: Rubber production
0
500
1000
1500
2000
2500
0 5 10 15 20 25 30
Years of production
Revenue,
Cost
(RM)
TR = 1,200 + 0.75*Year + 10.5*Year2 – 1.5*Year3/3.543
TC = 500 + 1.5*Year
Maximum  Maximum TR
Terminal cycle

28. Economic & Management Aspects of
Rural Land Resources 28
Production function: Maximum profit
TR = 1,200 + 0.75*Year + 10.5*Year2 – 1.5*Year3/3.543… (1)
TC = 500 +15*Year ………………………………………......(2)
d(TR)/d(Year) = 0.75 + 21*Year – 4.5*Year2/3.543……….………(3)
d(TR)/d(Year) =15 …………………………………………….……...(4)
Solve for (3) and (4) at maximum level of TR curve:
1.27*Year2 – 21*Year + 14.25 = 0
Year = {-(-21) ± √[(-21)2 – 4(1.27)(14.25)]}/2(1.27)
= {21 ± √(441 – 72.39)}/2.54
= 21 ± √(368.61)}/2.54
= (21 ± 19.2)/2.54
= 0.71 and 15.83 years
 Logical answer = 15.83 years
 = TR-TC
At Year = 15.83, TR = 1,200 + 0.75*15.83 + 10.5*15.832 – 1.5*15.833/3.543
= 1,200 + 11.87 + 2,631.18 – 1,679.43 = 2,163.62
At Year 15.83, TC = 500 +15*15.83 = 737.45
 = 2,163.62 -737.45 = 1,426.17
Use this formula:

29. Economic & Management Aspects of
Rural Land Resources 29
Production function: Maximum revenue
TR = 1,200 + 0.75*Year + 10.5*Year2 – 1.5*Year3/3.543
MR = d(TR)/d(Year) = 0.75 + 21*Year – 4.5*Year2/3.543
At maximum level of revenue curve, MR = 0
0.75 + 21*Year – 4.5*Year2/3.543 = 0
1.27*Year2 – 21*Year – 0.75 = 0
Year = {-(-21) ± √[(-21)2 – 4(1.27)(-0.75)]}/2(1.27)
= {21 ± √(441 + 3.81)}/2.54
= 21 ± √(444.81)}/2.54
= (21 ± 21.09)/2.54
= 0.37 and 16.57 years
 Logical answer = 16.57 years
At Year = 16.57, TR = 1,200 + 0.75*16.57 + 10.5*16.572 – 1.5*16.573/3.543
= 1,200 + 12.43 + 2,882.93 – 1,926.14 = 2,169.22
At Year 16.57, TC = 500 +15*16.57 = 748.55
 = 2,169.22 -748.55 = 1,420.67

30. Economic & Management Aspects of
Rural Land Resources 30
Production function: Terminal cycle
TR = 1,200 + 0.75*Year + 10.5*Year2 – 1.5*Year3/3.543… (1)
TC = 500 +15*Year ………………………..……………….....(2)
At terminal period, TR – TC = 0:
1,200 + 0.75*Year + 10.5*Year2 – 1.5*Year3/3.543 – 500 – 15*Year = 0
700 – 14.25*Year + 10.5*Year2 – 1.5*Year3/3.543 = 0
1.5*Year3/3.543 – 10.5*Year2 + 14.25*Year – 700 = 0
(1.5*Year2/3.543 – 10.5*Year + 14.25)Year – 700 = 0
Solving for the logical component equation:
1.5*Year2/3.543 – 10.5*Year + 14.25 = 0
Year = {-(-10.5) ± √[(-10.5)2 – 4(1.5/3.543)(14.25)]}/2(1.5/3.543)
= {10.5 ± √[(110.25 – 24.13)]}/0.846
= (10.5 ± 9.28)/0.846
= 1.44 and 23.35 years
Use of graph may
be more accurate!

31. Economic & Management Aspects of
Rural Land Resources 31
Production function: Example of rubber production
Highest profit
Highest revenue
Terminal cycle
See previous
graph

32. Economic & Management Aspects of
Rural Land Resources 32
Production function: Example of fish production
TC
TR
0
2000
4000
6000
8000
10000
12000
14000
16000
18000
20000
0 50 100 150 200 250
No. of bags of fertlisers
Fish
Revenue,
Cost
(RM)
MR
MC
-6000
-5000
-4000
-3000
-2000
-1000
0
1000
2000
3000
0 50 100 150 200 250
No. of bags of fertilisers
Fish
Revenue,
Cost
(RM)
A’
B’ C’
D’
A B C D
AA’ = Break-even point
BB’ = Point of maximum 
CC’ = Point of maximum
revenue
DD’ = Point of terminal
production
Estimate the amount of
input, cost, and revenue at
each of these points!

33. Economic & Management Aspects of
Rural Land Resources 33
Production function (further example)
 FFB = 6.205 + 2.0548*YEAR – 0.0622*YEAR2
 APP = FFB/YEAR
= 2.0548 – 0.0622X + 6.205X-1
 MPP = dY/ dX
= 2.0548 – 0.1244X
Case of Tabung Haji’s Lawiang Estate, Kluang.
TP
AP
MP
-10
-5
0
5
10
15
20
25
0 5 10 15 20 25 30
Age of production (years)
FFB
output
(m.t./ha/year)
Stage 1
Stage 2
Stage 3
APP=MPP MPP=0
▪ Compare this graph
with that on page 15.
▪ When management
becomes rather
complicated
economic stages of
production overlap.

34. Economic & Management Aspects of
Rural Land Resources 34
 Maximum APP = (Y/X)d/dX = 0
= -0.0622 – 6.205X-2 = 0
-0.0622 = 6.205X-2
X-2 = -0.0622/6.205 = -0.01
1/X2 = -0.01
X2 = -1/0.01 = -100
(X2)2 = (-100)2 = 10,000
X = (10,000)0.4 = 10 years
 Maximum MPP = (dY/dX)d/dX = 0
= -0.1244 = 0
 No feasible solution (no maximum MPP)
Production function (cont.)

35. Economic & Management Aspects of
Rural Land Resources 35
TR = p.Y
= p(6.205 + 2.0548X – 0.0622X2)
Let TC = 150X; and p = 250
MR = (p.Y)d/dX
= p(2.0548 – 0.1244X)
MC = 150
At point A, MR = MC
Thus, p(2.0548 – 0.1244X) – 150 = 0
2.0548 – 0.1244X = 150/p
X = (2.0548 – 150/p)/0.1244
= 11.7 years
Production function (cont.)
 Point of allocative efficiency of
production is where output’s
marginal revenue equals
resource’s marginal cost:
MR = MC
At this point, slope of the total
cost of land resource is
tangential to the slope of the
output’s revenue curve
 Profit is maximized if total
output’s revenue is greater
than total resource’s cost:
 TR > TC

36. Economic & Management Aspects of
Rural Land Resources 36
Given that:
MR = (p.Y)d/dX
= p(2.0548 – 0.1244X)
At point B, MR = 0, thus:
p(2.0548 – 0.1244X) = 0
X = 2.0548/0.1244
≈ 16.8 years
Production function (cont.)
 Point of maximum
output’s revenue is
when MR = 0
 Production curve is
stationary
 It normally occurs after
the point of maximum
profit
 Beyond that point,
economic efficiency
declines

37. Economic & Management Aspects of
Rural Land Resources 37
Given that:
TR = p.Y
= p(6.205 + 2.0548X – 0.0622X2)
TC = 150X; p = 250
At point C, TR = TC, thus:
TR-TC = 0
p(6.205 + 2.0548X – 0.0622X2) – 150X
1551.25 + 513.7X – 15.55X2 – 150X = 0
1551.25 + 363.7X – 15.55X2 = 0
Production function (cont.)
X= -(363.7)± [(363.7)2 – 4(-15.55)(1551.5)]0.5
2(-15.55)
= -363.7±(132,277.69+96,487.75)0.5
-31.1
-363.7± 478.29
-31.1
-3.68 years and
Use
27.07 years

38. Economic & Management Aspects of
Rural Land Resources 38
Thank you!