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

 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 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 Function

Machines Labor

The Production Function Machines Labor

The Production Function Machines Labor

The Production Function Machines Labor

The Production Function  Let us plot these production functions  TP 1 is the total product curve with 1 machine  TP 2 is the total product curve with 2 machines

The Production Function  TP 3 is the total product curve with 3 machines  TP 4 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

 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 Diminishing Returns and Returns to Scale

Machines Labor Diminishing Returns and Returns to Scale

Machines Labor Diminishing Returns and Returns to Scale

Returns to Scale  Increasing returns from 1 to 2  Decreasing returns from 2 to 3 and from 3 to

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 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 Curves

Short-Run Cost Curves ATC 1 is the ATC curve for a plant with 1 knitting machine.

Short-Run Cost Curves ATC 2 is the ATC curve for a plant with 2 knitting machines.

Short-Run Cost Curves ATC 3 is the ATC curve for a plant with 3 knitting machines.

Short-Run Cost Curves ATC 4 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 LRAC Curve

13 sweaters a day cost $7.69 each on ATC 1. Finding the LRAC Curve

13 sweaters a day cost $6.80 each on ATC 2. Finding the LRAC Curve

13 sweaters a day cost $7.69 each on ATC 3. Finding the LRAC Curve

13 sweaters a day cost $9.50 each on ATC 4. Finding the LRAC Curve

13 sweaters a day cost $6.80 each on ATC 2. Finding the LRAC Curve Least-cost way of producing 13 sweaters a day

Finding the LRAC Curve 18 24

Finding the LRAC 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 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, 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 Curves

 Fig 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 Short-Run and Long-Run Cost Curves