Economics 2010 Lecture 11 Organizing Production (II) Production and Costs (The long run) Output and Costs Plant Size and Cost The Production Function Diminishing Returns and Returns to

Scale Short-Run and Long-Run Cost Curves Plant 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 Plant Size and Cost In the long-run, the firm uses the economically-efficient plant size. Long-run costs depend on:

the firm's production function factor prices The Production Function 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 Function Machines Labor 1 4 1 2

10 3 13 4 15 5 16 2 10 15 18

20 21 3 13 18 22 24 25 4 15

21 24 26 27 The Production Function Machines Labor 1 1 4 10 13 2 10 15 18 3 13 18 22

4 15 20 24 5 16 21 25 2 15 21 24 26 27 3

4 The Production Function Machines Labor 1 1 4 10 13 2 10 15 18 3 13 18 22 4 15 20 24 5 16 21 25

2 15 21 24 26 27 3 4 The Production Function

Machines Labor 1 1 4 10 13 2 10 15 18 3 13 18 22 4 15 20 24 5 16 21 25 2 15 21

24 26 27 3 4 The Production Function 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 Function

TP3 is the total product curve with 3 machines TP4 is the total product curve with 4 machines Diminishing Returns and Returns to Scale Contrast

and distinguish between the two related but different concepts of: diminishing marginal returns returns to scale Diminishing Returns and Returns to Scale The

law of diminishing returns When 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 Returns to Scale Returns to scale

When 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 Returns to Scale Returns

to scale can be increasing constant decreasing Diminishing Returns and Returns 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 Returns to Scale Returns

to scale are constant if: The percentage increase in total product equals the percentage increase in all inputs Diminishing Returns and Returns 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 Returns to Scale Machines Labor 1

1 4 10 13 2 10 15 18 3 13 18 22 4 15 20 24 5 16 21 25 2 15 21 24 26 27

3 4 Diminishing Returns and Returns to Scale Machines Labor 1 1 4 10 13 2 10 15 18

3 13 18 22 4 15 20 24 5 16 21 25 2 15 21 24 26 27 3

4 Diminishing Returns and Returns to Scale Machines Labor 1 1 4 10 13 2 10 15 18 3 13 18 22 4 15 20 24

5 16 21 25 2 15 21 24 26 27 3 4

Returns to Scale Increasing 26 22 returns from 1 to 2

Decreasing returns from 2 to 3 and from 3 to 4 4 Short-Run and Long-Run Cost Curves 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 shortrun average cost curves Short-Run and Long-Run 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 Cost Curves ATC1 is the ATC curve for a plant with 1 knitting machine. Short-Run Cost Curves ATC2 is the ATC curve for a plant with 2 knitting machines.

Short-Run Cost Curves ATC3 is the ATC curve for a plant with 3 knitting machines. Short-Run Cost Curves ATC4 is the ATC curve for a plant with 4 knitting machines. Finding the LRAC Curve 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 LRAC Curve 13 sweaters a day cost $7.69 each

on ATC1. Finding the LRAC Curve 13 sweaters a day cost $6.80 each on ATC2. Finding the LRAC Curve 13 sweaters a day cost $7.69 each on ATC3.

Finding the LRAC Curve 13 sweaters a day cost $9.50 each on ATC4. Finding the LRAC Curve 13 sweaters a day cost $6.80 each on ATC2. Least-cost way of producing 13 sweaters a day

Finding the LRAC Curve 18 24 Finding the LRAC Curve Short-Run and Long-Run Cost Curves 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 Curves 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 Curves If

plant size can be varied by tiny amounts, LRAC curve is a smooth, Ushaped curve The SRAC curve for each plant just touches the LRAC curve at a single output level Short-Run and Long-Run Cost Curves Fig. 10.10 shows how

SRAC touches LRAC It also shows economies and diseconomies of scale Short-Run and Long-Run Cost Curves If

the firm produces in the range of economies of scale, it has excess capacity Short-Run and Long-Run Cost Curves If

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