1. Production Theory and Analysis

2. Creation of utility Production
Production refers to the transformation of inputs or resources into outputs of goods and services
Creation of utility

3. Created by human labor and capital
Characteristics of goods & services to be classified as Production are:
Created by human labor and capital
Satisfy human wants directly or indirectly
Are comparatively scarce and have economic value
Have a definite monetary price/cost

4. Factors of Production INPUTS Land Labor Capital Enterprise Immobile
Passive
Heterogeneous
Active
Mobile
Variable
productivity
Structures
Equipment
Cap.goods
Money
Innovative function
Risk
Decision making

5. INPUTS CAPITAL LABOR Land & Natural Entrepreneur Workers Structures
Resources
Entrepreneur
Workers
Machinery
plant &
equipment

6. Factors of Production Inputs Short Run- At least one input is fixed
Fixed Inputs
Variable Inputs
Short Run- At least one input is fixed
Long Run - All inputs are variable
The length of long run depends on industry.

7. Level & Scale of Production
Level of production can be altered changing the proportion of variable inputs
Output = Fixed inputs + Variable inputs
Scale of production can be altered by changing the supply of all the inputs only in the long run
Output = Total inputs(variable inputs)

8. Concept of Product
Total Product - total volume of goods produced during a specific period of time
Average Product - the per unit product of a variable factor
Marginal Product - the rate at which total product increases / addition to total product resulting from a unit increase in the quantity of the variable factor

9. Production Function With Two InputsK Q 6 10 24 31 36 40 39 5 12 28 42 4 3 23 33 2 7 18 30 1 8 14 L
Q = f(L, K)
Input & output are measured in physical units
Assumption- Technology is constant the during analysis period
- All units of L & K are homogenous

10. Production Function with Two Inputs
Discrete Production Surface

11. Production Function with One Variable Input
Total Product
TP = Q = f(L)
Marginal Product
MPL =
TP L
Average Product
APL =
TP L
Production or Output Elasticity
Q/Q
L/L
Q/ L
Q/L = EL
MPL
APL

12. Production Function with One Variable Input
Total, Marginal, and Average Product of Labor, and Output Elasticity

13. Production Function with One Variable Input
Total, Marginal, and Average Product of Labor, and Output Elasticity L Q MP AP E - 1 3 2 8 5 4
1.25 12 14
3.5
0.57
2.8 6 -2 -1

14. Production Function with One Variable Input

15. Production Function with One Variable Input
Total
Product 2 4 6 8 10 12 14 16 1 3 5 7 A B C D E F
Law of Diminishing Returns states that when increasing amounts of Variable inputs are combined with a fixed level of another input, a point will be reached where MP will decline. TP
Marginal
& Average
Product
Labor -3 -2 -1 1 2 3 4 5 6 7 6 A’ B’ C’ D’ E’ F’ AP
Labor MP

16. The Law of Diminishing Returns & Stages of Production
Total
Product 2 4 6 8 10 12 14 16 1 3 5 7 A B C D E F TP I
Inflection pt. G
Marginal
& Average
Product
Labor -3 -2 -1 1 2 3 4 5 6 7 6
Stage I of Labor
Stage II of Labor
Stage III of Labor B’ C’ A’ D’ E’ F’ AP MP
Labor

17. The Law of Diminishing Returns & Stages of Production
Total
Product 2 4 6 8 10 12 14 16 1 3 5 7 A B C D E F TP I G
Marginal
& Average
Product
Labor -3 -2 -1 1 2 3 4 5 6 7 6
Stage I of Labor
Stage II of Labor
Stage III of Labor B’ C’ A’ D’ E’ F’
MPL is increasing
MPK is negative AP
MPL & MPK Positive
MPL is negative MP
Labor

18. Optimal Use of the Variable Input
Marginal Revenue Product of Labor
MRPL = (MPL)(MR)
Marginal Resource Cost of Labor
TC L
MRCL =
Optimal Use of Labor
MRPL = MRCL

19. Optimal Use of the Variable InputMP
MR = P L
2.50 4
$10
3.00 3 10
3.50 2 10
4.00 1 10
4.50 10
Assumption : Firm hires additional units of labor at constant
wage rate = $20

20. Use of Labor is Optimal When L = 3.50
Optimal Use of the Variable Input L MP
MR = P
MRP
MRC L L L
2.50 4
$10
$40
$20
3.00 3 10 30 20
3.50 2 10 20 20
4.00 1 10 10 20
4.50 10 20
Assumption : Firm hires additional units of labor at constant
wage rate
Use of Labor is Optimal When L = 3.50

21. Optimal Use of the Variable Input$ 40 30 20 10
MRCL = w = $20
dL = MRPL
Units of Labor Used

22. Exercise
The marginal product of labor equation for a firm is given by: MPL = 10(K/L)0.5
Currently the firm is using 49 units of capital and 100 units of labor. Capital usage is fixed, but labor can be varied. If the price of labor is $20 per unit and the firms' output sells for $4, is the firm producing efficiently in the short run? If not, explain and determine the optimal rate of labor input.

23. MRPL = MRCL = w
 28 ≠ 20 Not efficient
L = 196

24. Production With Two Variable Inputs
Isoquants show combinations of two inputs that can produce the same level of output. K 6 10 24 31 36 40 39 5 12 28 36 40 42 40 Q 4 12 28 36 40 40 36 3 10 23 33 36 36 33 2 7 18 28 30 30 28 1 3 8 12 14 14 12 1 2 3 4 5 6 L

25. Isoquants

26. Economic Region of Production
Firms will only use combinations of two inputs that are in the economic region of production.
Ridge line W

27. dQ=Q/ L *dL + Q/ K *dK= 0
Marginal Rate of Technical Substitution
Q = f(L,K)
dQ=Q/ L *dL + Q/ K *dK= 0
dK= (-) Q/ L
dL Q/ K
Q/ L = MPL and Q/ K = MPK
dK MPL = MRTS
dL MPK =
(L) MPL = -(K) MPK

28. Marginal Rate of Technical SubstitutionK
Absolute value of the slope of isoquant is called the MRTS
MRTS = -(-2.5/1) = 2.5

29. Production With Two Variable Inputs
Perfect Substitutes
Perfect Complements 2K 1L
Capital
Capital 6 4 2 6 4 2 B C
-1K 2L A
Labor
Labor

30. Optimal Combination of Inputs
Isocost lines represent all combinations of two inputs that a firm can purchase with the same total cost.

31. Isocost Lines Capital 10 8 6 4 2 Labor 2 4 6 8 10
AB C = $100, w = r = $10 10 8 6 4 2 A
slope = -w/r = -1
vertical intercept = 10 1K 1L B
Labor

32. Isocost Lines A’ 14 10 8 4 A A” B” B B’ B* 4 8 10 12 14 16 20 Capital
AB C = $100, w = r = $10
A’B’ C = $140, w = r = $10
A’’B’’ C = $80, w = r = $10
AB* C = $100, w = $5, r = $10 A A” B” B B’ B*
Labor

33. Optimal Combination of Inputs for Minimizing costs or Maximizing output
Isocost Lines
AB C = $100, w = r = $10
A’B’ C = $140, w = r = $10
A’’B’’ C = $80, w = r = $10
MRTS = w/r

34. Optimal input combinations: Slope of isoquant = Slope of isocost line
(absolute)Slope of isoquant = (absolute) Slope of isocost line
MRTS = w r
Since MRTS = MPL/ MPK
MPL = w
MPK r
MPL = MPK
w r
If MPL = 5, MPK =4, and w = r
MPL > MPK
w r

35. Profit Maximization MPL = w MPL = MPK w r MPK r
MRP(input) = MRC(input)
with constant input prices
MRP(input) = input price
To maximize Profits:
MRPL = w = (MPL)(MR)
MRPK = r = (MPK)(MR)
MPL = w
MPK r
MPL = MPK
w r

36. Returns to Scale
Returns to scale refers to the degree by which output changes as a result of a given change in the quantity of all inputs used in production.
Long run function
Both L & K are changing

37. Production Function Q = f(L, K)
Returns to Scale
Production Function Q = f(L, K)
Q = f(hL, hK)
If  = h, constant returns to scale.
If  > h, increasing returns to scale.
If  < h, decreasing returns to scale.

38. Constant Returns to Scale Increasing Returns to Scale
Decreasing Returns to Scale

39. Empirical Production Functions
Cobb-Douglas Production Function
Q = AKaLb
For example: the inputs are doubled i.e. instead of K & L, we are using 2K & 2L, then by how much the production will increase.
New Q = A(2K)a(2L)b
= A(2)a+bKaLb
= 2a+bAKaLb
= 2a+bQ

40. Now Q = 2a+bQ
If a + b = 1, constant returns to scale.
If a + b > 1, increasing returns to scale.
If a + b <1, decreasing returns to scale.

41. Exercise
Do the following production functions have constant, increasing or decreasing returns of scale? ( K, L, M are inputs)
a. Q = 0.5X + 2Y + 40Z
b. Q = 3L + 10K + 500
c. Q = K/L
d. Q = 4A + 6B + 8AB
e. Q = 10L 0.5 K 0.6

42. A. constant returns to scale.
B. diminishing returns to scale.
C. Decreasing returns to scale
D. increasing returns to scale.
E. increasing returns to scale

43. Economies of scale Diseconomies of scale
Technology – cost effective at high level of production
Specialization of labour
Diseconomies of scale
Transportation cost
Difficult to manage

44. Exercise
Medical Testing Labs, Inc., provides routine testing services for blood banks in the Los Angeles area. Tests are supervised by skilled technicians using equipment produced by two leading competitors in the medical equipment industry. Records for the current year show an average of 27 tests per hour being performed on the Testlogic-1 and 48 tests per hour on a new machine, the Accutest-3. The Testlogic-1 is leased for $18,000 per month, and the Accutest-3 is leased at $32,000 per month. On average, each machine is operated 25 eight-hour days per month.
a. Does Medical Testing Lab usage reflect an optimal mix of testing equipment?
b. If tests are conducted at a price of $6 each while labor and all other costs are fixed, should the company lease more machines?

45. a) (27*25*8)/ = (48*25*8) / = 0.3
In both instances, the last dollar spent on each machine increased output by the same 0.3 units, indicating an optimal mix of testing machines.
b) For each machine hour, the relevant question is Testlogic-1
27 ×(25×8)× $6 > $18,000 or $32,400 > $18,000.
Accutest-3
48 ×(25×8)× $6 > $32,000 or $57,600 > $32,000.
In both cases, each machine returns more than its marginal cost (price) of employment, and expansion would be profitable.

46. Exercise
The marginal product of labor for international trading is given by the equation
MPL = 10K0.5/L0.5
Currently the firm is using 100 units of capital and 121 units of labor. The capital stock is constant but the labor can be varied. If the price of labor is 10/- and price of output is Rs. 2/- per unit, is the firm operating efficiently in the short run? If not, determine the optimal rate of labor input.

47. Answer: not optimally, L = 400

48. The production function is : Q = 20K0.5L0.5
With marginal product functions
MPK = 10L0.5/K MPL = 10K0.5/L0.5
If the price of capital is Rs. 5/- and price of labor is Rs. 4/- per unit, determine the expansion path for the firm.
The firm currently is producing 200 units of output per period using input rates of L = 4 and K =25. is this an efficient input combination? Why or why not? If not, determine the efficient input combination for producing an output rate of 200.
If the price of labor increases from Rs 4 to Rs 8 per unit, determine the efficient input combination for an output rate of 200. What is the capital –labor ratio now?

49. Answer: K= 0.8L,
L= and K= 8.94,
L = and K = 12.65

50. Suppose the price of one unit of labor is $10 and price of one unit of capital is $2.50.
Use this information to determine the isocost equations corresponding to a total cost of $200 and $500.
Plot these two isocost lines on a graph
If the price of labor falls from $10 per unit to $8 per unit, determine the new $500 isocost line and plot it on the same diagram used in part (b)
Answer: K = 80- 4L and K = 200 – 4L,
K = 200 – 3.2L

51. 4. Given the production function Q = 30K0.7L0.5
and input prices r = 20 and w = 30.
Determine an equation for the expansion path
What is the efficient input combination for an output rate of Q = 200? For 500?
Answer: K = 2.1L, for 200: L = 3.15 and K = 6.62, for 500: L = and K =

52. Answer: CPAs – 1.67 and bookkeepers – 2.29
The revenue dept. of a state govt. employs certified public accountants (CPAs) to audit corporate tax returns and book keepers to audit individual returns. CPAs are paid $31200 per yr, while the annual salary of a bookkeeper is $ Given the current staff of CPAs and bookkeepers, a study made by the dept’s economist shows that adding one year of a CPA’s time to audit corporate returns results in an additional tax collection of $ In contrast, an additional bookkeeper adds $41600 per year in additional tax revenue.
If the dept’s objective is to maximize tax revenue collected, is the present mix of CPAs and bookkeepers optimal? Explain
If the present mix of CPAs and bookkeepers is not optimal, explain what re-allocation should be made. That is, should the department hire more CPAs and fewer bookkeepers or vice versa.
Answer: CPAs – 1.67 and bookkeepers – 2.29