economics 2010 lecture 11’ organizing production (ii) production and costs (the long run)

Economics 2010Economics 2010

Lecture 11’

Organizing Production (II) Production and Costs

(The long run)

Output and CostsOutput and Costs

Plant Size and CostThe Production FunctionDiminishing Returns and Returns to

ScaleShort-Run and Long-Run Cost

Curves

Plant Size and CostPlant Size and Cost

In the short-run, the firm uses a given plant

Short-run costs depend on the firm's short-run production function factor prices

In the long-run, the firm uses the economically-efficient plant size.

Long-run costs depend on: the firm's production function factor prices

Plant Size and CostPlant Size and Cost

The production function is the relationship between the maximum attainable output and the quantity of all the inputs used

The production function is shown by: a table a total product curve for each plant size

The Production FunctionThe Production Function

The Production FunctionThe Production Function

Machines

Labor 1 2 3 4

1

2

3

4

5

4 10 13 15

10 15 18 21

13 18 22 24

15 20 24 26

16 21 25 27

The Production FunctionThe Production Function

Machines

Labor 1 2 3 4

1 4 10 13 15

2 10 15 18 21

3 13 18 22 24

4 15 20 24 26

5 16 21 25 27

The Production FunctionThe Production Function

Machines

Labor 1 2 3 4

1 4 10 13 15

2 10 15 18 21

3 13 18 22 24

4 15 20 24 26

5 16 21 25 27

The Production FunctionThe Production Function

Machines

Labor 1 2 3 4

1 4 10 13 15

2 10 15 18 21

3 13 18 22 24

4 15 20 24 26

5 16 21 25 27

The Production The Production FunctionFunction

Let us plot these production functions

TP1 is the total product curve with 1 machine

TP2 is the total product curve with 2 machines

The Production The Production FunctionFunction

TP3 is the total product curve with 3 machines

TP4 is the total product curve with 4 machines

Diminishing Returns and Diminishing Returns and Returns to ScaleReturns to Scale

Contrast and distinguish between the two related but different concepts of: diminishing marginal returns returns to scale

The law of diminishing returnsWhen a firm has some fixed inputs, if it

increases the quantity of a variable input, the marginal product of the variable input eventually diminishes

Diminishing Returns and Diminishing Returns and Returns to ScaleReturns to Scale

Returns to scaleWhen a firm increases all its inputs by

the same percentage the resulting change in the firms total product is determined by its returns to scale

Diminishing Returns and Diminishing Returns and Returns to ScaleReturns to Scale

Returns to scale can be increasing constant decreasing

Diminishing Returns and Diminishing Returns and Returns to ScaleReturns to Scale

Returns to scale are increasing if: The percentage increase in total product

exceeds the percentage increase in all inputs (eg, if we double the quantity used of all

inputs, the quantity produced more than doubles)

Diminishing Returns and Diminishing Returns and Returns to ScaleReturns to Scale

Returns to scale are constant if: The percentage increase in total product

equals the percentage increase in all inputs

Diminishing Returns and Diminishing Returns and Returns to ScaleReturns to Scale

Returns to scale are decreasing if: The percentage increase in total product is

less than the percentage increase in all inputs

Diminishing Returns and Diminishing Returns and Returns to ScaleReturns to Scale

Machines

Labor 1 2 3 4

1 4 10 13 15

2 10 15 18 21

3 13 18 22 24

4 15 20 24 26

5 16 21 25 27

Diminishing Returns and Diminishing Returns and Returns to ScaleReturns to Scale

Machines

Labor 1 2 3 4

1 4 10 13 15

2 10 15 18 21

3 13 18 22 24

4 15 20 24 26

5 16 21 25 27

Diminishing Returns and Diminishing Returns and Returns to ScaleReturns to Scale

Machines

Labor 1 2 3 4

1 4 10 13 15

2 10 15 18 21

3 13 18 22 24

4 15 20 24 26

5 16 21 25 27

Diminishing Returns and Diminishing Returns and Returns to ScaleReturns to Scale

Returns to Returns to ScaleScale

Increasing returns from 1 to 2

Decreasing returns from 2 to 3 and from 3 to 4

26

22

4

Short-Run and Long-Run Cost Short-Run and Long-Run Cost CurvesCurves

The long-run average cost (LRAC) curve traces the relationship between the lowest attainable average total cost and output, when both capital and labor inputs can be varied

To see how the LRAC curve is constructed, we begin with some short-run average cost curves

Tom has 4 different plant sizes -- 1, 2, 3, or 4 knitting machines

Each plant has a short-run ATC curve -- just like the ATC curve we've been studying

Short-Run and Long-Run Cost Short-Run and Long-Run Cost CurvesCurves

Short-Run Cost CurvesShort-Run Cost Curves

ATC1 is the ATC curve for a plant with 1 knitting machine.

Short-Run Cost CurvesShort-Run Cost Curves

ATC2 is the ATC curve for a plant with 2 knitting machines.

Short-Run Cost CurvesShort-Run Cost Curves

ATC3 is the ATC curve for a plant with 3 knitting machines.

Short-Run Cost CurvesShort-Run Cost Curves

ATC4 is the ATC curve for a plant with 4 knitting machines.

LRAC is made up of the lowest ATC for each level of output.

Therefore, we want to decide which plant has the lowest cost for producing a given level of output

Suppose that Tom wants to produce 13 sweaters a day

Finding the Finding the LRACLRAC Curve Curve

13 sweaters a day cost $7.69 each on ATC1.

Finding the Finding the LRACLRAC Curve Curve

13 sweaters a day cost $6.80 each on ATC2.

Finding the Finding the LRACLRAC Curve Curve

13 sweaters a day cost $7.69 each on ATC3.

Finding the Finding the LRACLRAC Curve Curve

13 sweaters a day cost $9.50 each on ATC4.

Finding the Finding the LRACLRAC Curve Curve

13 sweaters a day cost $6.80 each on ATC2.

Finding the Finding the LRACLRAC Curve Curve

Least-cost way of producing 13 sweaters a day

Finding the Finding the LRACLRAC Curve Curve

18 24

Finding the Finding the LRACLRAC Curve Curve

There is a relationship between the slope of the LRAC curve and returns to scale

When LRAC curve slopes downward, there are increasing returns to scale

In this situation, there are economies of scale

Short-Run and Long-Run Cost Short-Run and Long-Run Cost CurvesCurves

When LRAC curve slopes upward, there are decreasing returns to scale

In this situation, there are diseconomies of scale

When the LRAC curve is horizontal, there are constant returns to scale

Short-Run and Long-Run Cost Short-Run and Long-Run Cost CurvesCurves

If plant size can be varied by tiny amounts, LRAC curve is a smooth, U-shaped curve

The SRAC curve for each plant just touches the LRAC curve at a single output level

Short-Run and Long-Run Cost Short-Run and Long-Run Cost CurvesCurves

Fig. 10.10 shows how SRAC touches LRAC

It also shows economies and diseconomies of scale

Short-Run and Long-Run Cost Short-Run and Long-Run Cost CurvesCurves

If the firm produces in the range of economies of scale, it has excess capacity

Short-Run and Long-Run Cost Short-Run and Long-Run Cost CurvesCurves

If the firm produces in the range of diseconomies of scale, it has over-utilized capacity

Short-Run and Long-Run Cost Short-Run and Long-Run Cost CurvesCurves