Chapter 3: Production and Costs

3.1 Production Function

Production Function: A relationship between inputs used and output produced by a firm. It shows the maximum quantity of output that can be produced for various quantities of inputs.

General form: q = f(L, K)

Where:

q = output
L = labor
K = capital

Key features:

Defined for a given technology
Represents efficient use of inputs
If technology improves, we get a new production function

Example Production Function

q = K × L

Where q is wheat produced, K is land in hectares, L is hours of work per day.

Numerical Example

Labor\Capital	1	2	3	4	5	6
0	0	0	0	0	0	0
1	1	3	7	10	12	13
2	3	10	18	24	29	33
3	7	18	30	40	46	50
4	10	24	40	50	56	57
5	12	29	46	56	58	59
6	13	33	50	57	59	60

Isoquant

Isoquant: A curve showing all possible combinations of two inputs that yield the same maximum possible level of output.

Properties:

Negatively sloped (when marginal products are positive)
Convex to the origin
Higher isoquant represents higher output level

3.2 The Short Run and the Long Run

Short Run: A period where at least one factor of production (labor or capital) cannot be varied and remains fixed.

Long Run: A period where all factors of production can be varied.

Key differences:

Aspect	Short Run	Long Run
Factor variability	At least one fixed factor	All factors variable
Cost structure	Fixed and variable costs	All costs variable
Time period	Shorter	Longer

3.3 Total Product, Average Product and Marginal Product

3.3.1 Total Product (TP)

Total Product: The relationship between a variable input and output when all other inputs are held constant.

3.3.2 Average Product (AP)

Average Product: Output per unit of variable input.

Formula: AP_L = TP_L/L

3.3.3 Marginal Product (MP)

Marginal Product: Change in output per unit change in input when all other inputs are held constant.

Formula: MP_L = ΔTP_L/ΔL

Numerical Example

Labor	TP	MP_L	AP_L
0	0	-	-
1	10	10	10
2	24	14	12
3	40	16	13.33
4	50	10	12.5
5	56	6	11.2
6	57	1	9.5

3.4 The Law of Diminishing Marginal Product and the Law of Variable Proportions

Law of Diminishing Marginal Product (Law of Variable Proportions): As more and more units of a variable input are employed, marginal product initially increases, but after reaching a certain level of employment, it starts falling.

Reasons:

Initially, factor proportions become more suitable for production
After a point, the production process becomes too crowded with the variable input

3.5 Shapes of Total Product, Marginal Product and Average Product Curves

TP Curve: Positively sloped, initially increases at increasing rate, then at decreasing rate

MP Curve: Inverse 'U'-shaped

AP Curve: Inverse 'U'-shaped

Relationship between MP and AP:

When MP > AP, AP is rising
When MP < AP, AP is falling
MP curve cuts AP curve from above at its maximum point

3.6 Returns to Scale

Returns to Scale: How output changes when all inputs are changed proportionally.

Three types:

Increasing Returns to Scale (IRS): Output increases by more than the proportional increase in inputs
Constant Returns to Scale (CRS): Output increases by the same proportion as inputs
Decreasing Returns to Scale (DRS): Output increases by less than the proportional increase in inputs

Cobb-Douglas Production Function

q = x₁^αx₂^β

Returns to scale:

If α + β = 1 → CRS
If α + β > 1 → IRS
If α + β < 1 → DRS

3.7 Costs

3.7.1 Short Run Costs

Total Fixed Cost (TFC): Cost of fixed inputs that doesn't change with output

Total Variable Cost (TVC): Cost of variable inputs that changes with output

Total Cost (TC): Sum of TFC and TVC

Formula: TC = TVC + TFC

Average Costs:

Short Run Average Cost (SAC): Total cost per unit of output

Formula: SAC = TC/q

Average Variable Cost (AVC): Total variable cost per unit of output

Formula: AVC = TVC/q

Average Fixed Cost (AFC): Total fixed cost per unit of output

Formula: AFC = TFC/q

Relationship: SAC = AVC + AFC

Short Run Marginal Cost (SMC): Change in total cost per unit change in output

Formula: SMC = ΔTC/Δq

Numerical Example

Output (q)	TFC (Rs)	TVC (Rs)	TC (Rs)	AFC (Rs)	AVC (Rs)	SAC (Rs)	SMC (Rs)
0	20	0	20	-	-	-	-
1	20	10	30	20	10	30	10
2	20	18	38	10	9	19	8
3	20	24	44	6.67	8	14.67	6
4	20	29	49	5	7.25	12.25	5
5	20	33	53	4	6.6	10.6	4
6	20	39	59	3.33	6.5	9.83	6

Shapes of Short Run Cost Curves

TFC Curve: Horizontal straight line

TVC Curve: Starts from origin, increases with output

TC Curve: Vertical sum of TFC and TVC curves

AFC Curve: Rectangular hyperbola (downward sloping)

AVC Curve: 'U'-shaped

SAC Curve: 'U'-shaped

SMC Curve: 'U'-shaped

Relationships:

SMC curve cuts AVC curve from below at AVC's minimum point
SMC curve cuts SAC curve from below at SAC's minimum point
When SMC < AVC, AVC is falling
When SMC > AVC, AVC is rising

3.7.2 Long Run Costs

Long Run Average Cost (LRAC): Cost per unit of output when all inputs are variable

Formula: LRAC = TC/q

Long Run Marginal Cost (LRMC): Change in total cost per unit change in output in the long run

Formula: LRMC = ΔTC/Δq

Shapes of Long Run Cost Curves

LRAC Curve: 'U'-shaped

Downward sloping part corresponds to IRS
Minimum point corresponds to CRS
Upward sloping part corresponds to DRS

LRMC Curve: 'U'-shaped

Cuts LRAC curve from below at its minimum point
When LRMC > LRAC, LRAC is falling
When LRMC > LRAC, LRAC is rising

Chapter Summary

Production function shows maximum output for different input combinations
Short run has fixed factors; long run has all variable factors
Total product is output from variable input with others fixed
AP and MP curves are inverse 'U'-shaped
Law of diminishing returns explains falling MP after a point
Returns to scale: IRS, CRS, DRS
Short run costs include fixed and variable components
Short run cost curves are 'U'-shaped
Long run cost curves are also 'U'-shaped
SMC cuts AVC and SAC at their minimum points
LRMC cuts LRAC at its minimum point

Labor\Capital	1	2	3	4	5	6
0	0	0	0	0	0	0
1	1	3	7	10	12	13
2	3	10	18	24	29	33
3	7	18	30	40	46	50
4	10	24	40	50	56	57
5	12	29	46	56	58	59
6	13	33	50	57	59	60

Labor\Capital	1	2	3	4	5	6
0	0	0	0	0	0	0
1	1	3	7	10	12	13
2	3	10	18	24	29	33
3	7	18	30	40	46	50
4	10	24	40	50	56	57
5	12	29	46	56	58	59
6	13	33	50	57	59	60

Labor\Capital	1	2	3	4	5	6
0	0	0	0	0	0	0
1	1	3	7	10	12	13
2	3	10	18	24	29	33
3	7	18	30	40	46	50
4	10	24	40	50	56	57
5	12	29	46	56	58	59
6	13	33	50	57	59	60