1. Section 3 – Theory of the Firm
Thus far we have focused on the individual consumer’s decisions:
Choosing consumption and leisure to:
Maximize Utility
Minimize Income
Section 3 deals with another economic agent, the producer, and their decisions:
Choose inputs, production in order to:
Minimize Costs (to hopefully maximize profits) 6

2. Section 3 – Theory of the Firm
In this section we will cover:
Chapter 6: Inputs and Production Functions
Chapter 7: Costs and Cost Minimization
Chapter 8: Cost Curves 6

3. Chapter 6: Inputs and Production Functions
Consumer Theory
Theory of the Firm
Goods
Utility
Inputs
Production
Profits 6

4. Chapter 6: Inputs and Production Functions
In this chapter we will cover:
6.1 Inputs and Production
6.2 Marginal Product (similar to marginal utility)
6.3 Average Product
6.4 Isoquants (similar to indifference curves)
6.5 Marginal rate of technical substitution (MRTS, similar to MRS)
6.6 Special production functions (similar to special utility functions)
6.7 Technological Progress 6

5. 6.1 Inputs and Production
Inputs: Productive resources, such as labor and capital, that firms use to manufacture goods and services (also called factors of production)
Output: The amount of goods and services produced by the firm
Production: transforms inputs into outputs
Technology: determines the quantity of output possible for a given set of inputs.

6. More Terms
Production function: tells us the maximum possible output that can be attained by the firm for any given quantity of inputs.
Q = f(L,K,M)
Q = f(P,F,L,A)
Computer Chips = f1(L,K,M)
Econ Mark = f2(Intellect, Study, Bribe)

7. Production and Utility Functions
In Consumer Theory, consumption of GOODS lead to UTILITY:
U=f(kraft dinner, wieners)
In Production Theory, use of INPUTS causes PRODUCTION:
Q=f(Labour, Capital, Technology) 6

8. Production Function Notes
A technically efficient firm is attaining the maximum possible output from its inputs (using whatever technology is appropriate)
A technically inefficient firm is attaining less than the maximum possible output from its inputs (using whatever technology is appropriate)

9. Notes on the Production Function
production set : all points on or below the production function
Note: Capital refers to physical capital
(goods that are themselves produced goods) and not financial capital (the money required to start or maintain production).

10. • • • Q Example: The Production Function and Technical Efficiency
Q = f(L) D • C • •
Inefficient point B
Production Set L

11. Causes of technical inefficiency:
Shirking
-Workers don’t work as hard as they can
-Can be due to laziness or a union strategy
2) Strategic reasons for technical inefficiency
-Poor production may get government grants
-Low profits may prevent competition
3) Imperfect information on “best practices”
-inferior technology

12. Example: Acme medical equipment faces the production function:
Q=K1/2L1/2
Given labour of 10 and capital of 20, is Acme producing efficiently by producing 12 units?
What level of production is technically efficient?

13. Example:
Q =K1/2L1/2 =201/2101/2 =14.14
Acme is not operating efficiently by producing 12 units. Given labour of 10 and capital of 20, Acme should be producing units in order to be technically efficient.

14. 6.2 Marginal Product The production function calculates TOTAL PRODUCT
Marginal Product of an input: the change in output that results from a small change in an input holding the levels of all other inputs constant.
MPL = Q/L (holding constant all other inputs)
MPK = Q/K (holding constant all other inputs) 6

15. Marginal Utility and Marginal Product
In Consumer Theory, marginal utility was the slope of the total utility curve
In Production Theory, marginal product is the slope of the total product curve: 6

16. Q L
MPL increasing
MPL becomes negative
MPL
MPL decreasing L

17. Law of Diminishing Returns
Law of diminishing marginal utility: marginal utility (eventually) declines as the quantity consumed of a single good increases.
Law of diminishing marginal returns states that marginal products (eventually) decline as the quantity used of a single input increases.
Generally the first few inputs are highly productive, but additional units are less productive (ie: computer programmers working in a small room) 6

18. Example: Production as workers increaseQ
Example: Production as workers increase
Each
Additional
worker
Is less
productive
Each
Additional
worker
Decreases
Production
Each
Additional
worker
Is equally
productive
Each
Additional
worker
Is more
productive
Total Product L

19. 6.3 Average Product
Average product: total output that is to be produced divided by the quantity of the input that is used in its production:
APL = Q/L
APK = Q/K
Example:
Q=K1/2L1/2
APL = [K1/2L1/2]/L = (K/L)1/2
APK = [K1/2L1/2]/K = (L/K)1/2

20. Marginal, and Average Product
When Marginal Product is greater than average product, average product is increasing
-ie: When you get an assignment mark higher than your average, your average increases
When Marginal Product is less than average product, average product is decreasing
-ie: When you get an assignment mark lower than your average, your average decreases
Therefore Average Product is maximized when it equals marginal product 6

21. Q L
APL increasing
APL decreasing
APL
MPL
APL maximized
APL L
MPL

22. 6.4 Isoquants Example: Q = 4K1/2L1/2
Isoquant: traces out all the combinations of inputs (labor and capital) that allow that firm to produce the same quantity of output.
Example: Q = 4K1/2L1/2
What is the equation of the isoquant for Q = 40?
40 = 4K1/2L1/2
=> 100 = KL
=> K = 100/L

23. …and the isoquant for Q = Q*?
Q* = 4K1/2L1/2
Q*2 = 16KL
K = Q*2/16L

24. K
Example: Isoquants
All combinations of (L,K) along the
isoquant produce 40 units of output.
Q = 40
Slope=K/L
Q = 20 L

25. Indifference and Isoquant Curves
In Consumer Theory, the indifference curve showed combinations of goods giving the same utility
The slope of the indifference curve was the marginal rate of substitution
In Production Theory, the isoquant curve shows combinations of inputs giving the same product
The slope of the isoquant curve is the marginal rate of technical substitution: 6

26. MPL/MPK = -K/L = MRTSL,K
6.5 Marginal Rate of Technical Substitution (MRS)
Marginal rate of technical substitution (labor for capital): measures the amount of K the firm the firm could give up in exchange for an additional L, in order to just be able to produce the same output as before.
Marginal products and the MRTS are related:
MPL/MPK = -K/L = MRTSL,K

27. Marginal Rate of Technical Substitution (MRS)

28. The marginal rate of technical substitution, MRTSL,K tells us:
The amount capital can be decreased for every increase in labour, holding output constant OR
The amount capital must be increased for every decrease in labour, holding output constant
-as we move down the isoquant, the slope decreases, decreasing the MRTSL,K
-this is diminishing marginal rate of technical substitution
-as you focus more on one input, the other input becomes more productive

29. MRTS Example MRTSL,K = MPL/MPK MRTSL,K =4K/4L MRTSL,K =K/L Let Q=4LK
MPL=4K
MPK=4L
Find MRTSL,K
MRTSL,K = MPL/MPK
MRTSL,K =4K/4L
MRTSL,K =K/L

30. Isoquants – Regions of Production
Due to the law of diminishing marginal returns, increasing one input will eventually decrease total output (ie: 50 workers in a small room)
When this occurs, in order to maintain a level of output (stay on the same isoquant), the other input will have to increase
This type of production is not economical, and results in backward-bending and upward sloping sections of the isoquant: 6

31. K
Example: The Economic and the Uneconomic Regions of Production
Isoquants
MPK < 0
Uneconomic region
Q = 20
MPL < 0
Economic region
Q = 10 L

32. Isoquants and Substitution
Different industries have different production functions resulting in different substitution possibilities:
ie: In mowing lawns, hard to substitute away from lawn mowers
In general, it is easier to substitute away from an input when it is abundant
This is shown on the isoquant curve 6

33. MRTSL,K is high; labour is scarce so a little more labour frees up a lot of capital
MRTSL,K is low; labour is abundant so a little more labour barely affects the need for capital • • L

34. MRTS Example Let Q=4LK MPL=4K MPK=4L MRTSL,K =K/L
Show diminishing MRTS when Q=16.
When Q=16, (L,K)=(1,4), (2,2), (4,1)
MRTS(1,4)=4/1=4
MRTS(2,2)=2/2=1
MRTS(4,1)=1/4

35. K
MRTSL,K =4 • 4
MRTSL,K =1
MRTSL,K =1/4 • 2 • 1
Q=16 L 1 2 4

36. When input substitution is easy, isoquants are nearly straight linesK
When input substitution is hard when inputs are scarce, isoquants are more L-shaped
170
130
100 55
100 L

37. Returns To Scale
How much will output increase when ALL inputs increase by a particular amount?
RTS = [%Q]/[%(all inputs)]
1% increase in inputs => more than 1% increase in output, increasing returns to scale.
1% increase in inputs => 1% increase in output
constant returns to scale.
1% increase in inputs => a less than 1% increase in output, decreasing returns to scale.

38. Example 1: Q1 = 500L1+400K1
Q1 * = 500(L1)+400(K1)
Q1 *= 500L1+400K1
Q1 *= (500L1+400K1)
Q1 *= Q1
So this production function exhibits CONSTANT returns to scale. Ie: if inputs double (=2), outputs double.

39. Example 2: Q1 = AL1K1
Q2 = A(L1)(K1)
= + AL1K1
= +Q1
so returns to scale will depend on the value of +.
+ = 1 … CRS
+ <1 … DRS
+ >1 … IRS

40. Why are returns to scale important?
If an industry faces DECREASING returns to scale, small factories make sense
-It is easier to have small firms in this industry
If an industry faces INCREASING returns to scale, large factories make sense
-Large firms have an advantage; natural monopolies

41. Notes:
• The marginal product of a single factor may diminish while the returns to scale do not
Marginal product deals with a SINGLE input increasing, while returns to scale deals with MULTIPLE inputs increasing
• Returns to scale need not be the same at different levels of production

42. 6.6 Special Production Functions
1. Linear Production Function:
Q = aL + bK
MRTS constant
Constant returns to scale
Inputs are PERFECT SUBSTITUTES:
-Ie: 10 CD’s are a perfect substitute for 1 DVD for storing data.

43. K
Example: Linear Production Function
Q = Q1
Q = Q0 L

44. Special Production Functions
-ie: 2 pieces of bread and 1 piece of cheese make a grilled cheese sandwich: Q=min (c, 1/2b)

45. Cheese
Example: Fixed Proportion Production Function 2
Q = 2 1
Q = 1
Bread

46. Special Production Functions
Cobb-Douglas Production Function:
Q = aLK
if  +  > 1 then IRTS
if  +  = 1 then CRTS
if  +  < 1 then DRTS
smooth isoquants
MRTS varies along isoquants

47. K
Example: Cobb-Douglas Production Function
Q = Q1
Q = Q0 L

48. Constant Elasticity of Substitution Production Function:
Q = [aL+bK]1/
Where  = (-1)/
if  = 0, we get Leontief case
if  = , we get linear case
if  = 1, we get the Cobb-Douglas case
General form of other functions

49. 6.8 Technological Progress
Definition: Technological progress shifts isoquants inward by allowing the firm to achieve more output from a given combination of inputs (or the same output with fewer inputs).
Neutral technological progress shifts the isoquant corresponding to a given level of output inwards, but leaves the MRTSL,K unchanged along any ray from the origin

50. Example: “neutral technological progress”K
Q = 100 before
Q = 100 after
MRTS remains same
K/L L

51. Technological Progress
Labor saving technological progress results in a fall in the MRTSL,K along any ray from the origin
Slope decreases along origin ray
Since MRTSL,K=MPL/MPK, MPk increases more than MPL
ie: better robots, computers, machines

52. Example: Labor Saving Technological ProgressK
Q = 100 before
Q = 100 after
MRTS gets smaller
K/L L

53. Technological Progress
Capital saving technological progress results in a rise in the MRTSL,K along any ray from the origin.
Slope increases along origin ray
Since MRTSL,K=MPL/MPK, MPk increases less than MPL
ie: higher education, higher skilled workers

54. Example: “capital saving technological progress”K
Q = 100 before
Q = 100 after
MRTS gets larger
K/L L

55. Technological Progress

56. Chapter 6 Key Concepts Inputs and Production Technical Efficiency
Marginal Product
Law of Diminishing Returns
Average Product
Isoquants
Marginal rate of technical substitution
Returns to Scale
Special production functions
Technological Progress