cost curves

Short and Long Run Short and Long Run

COST CURVESCOST CURVES

CostsCosts

CostsCosts

Total Cost Total Cost -- the sum of all costs incurred the sum of all costs incurred in productionin production

TC = FC + VCTC = FC + VC Average CostAverage Cost – the cost per unit – the cost per unit

of outputof output AC = TC/OutputAC = TC/Output

Marginal CostMarginal Cost – the cost of one more or – the cost of one more or one fewer units of productionone fewer units of production

MCMC = TC= TCnn – TC – TCn-1n-1 units units

Types of Cost CurvesTypes of Cost Curves

A A total cost curvetotal cost curve is the graph of a is the graph of a firm’s total cost function.firm’s total cost function.

A A variable cost curvevariable cost curve is the graph of is the graph of a firm’s variable cost function.a firm’s variable cost function.

An An average total cost curveaverage total cost curve is the is the graph of a firm’s average total cost graph of a firm’s average total cost function.function.

Types of Cost CurvesTypes of Cost Curves

An An average variable cost curveaverage variable cost curve is the is the graph of a firm’s average variable graph of a firm’s average variable cost function.cost function.

An An average fixed cost curveaverage fixed cost curve is the is the graph of a firm’s average fixed cost graph of a firm’s average fixed cost function.function.

A A marginal cost curvemarginal cost curve is the graph of is the graph of a firm’s marginal cost function.a firm’s marginal cost function.

Types of Cost CurvesTypes of Cost Curves

How are these cost curves related to How are these cost curves related to each other?each other?

How are a firm’s long-run and short-How are a firm’s long-run and short-run cost curves related?run cost curves related?

Fixed, Variable & Total Cost Fixed, Variable & Total Cost FunctionsFunctions

F is the total cost to a firm of its F is the total cost to a firm of its short-run short-run fixed inputsfixed inputs. F, the firm’s . F, the firm’s fixed costfixed cost, does , does not vary with the firm’s output level.not vary with the firm’s output level.

ccvv(y) is the total cost to a firm of its (y) is the total cost to a firm of its variable inputsvariable inputs when producing y output when producing y output units. cunits. cvv(y) is the firm’s (y) is the firm’s variable costvariable cost function.function.

ccvv(y) depends upon the levels of the fixed (y) depends upon the levels of the fixed inputs.inputs.

Fixed, Variable & Total Cost Fixed, Variable & Total Cost FunctionsFunctions

c(y) is the total cost of all inputs, c(y) is the total cost of all inputs, fixed and variablefixed and variable, when producing y , when producing y output units. c(y) is the firm’s output units. c(y) is the firm’s total total costcost function; function;

c y F c yv( ) ( ).

y

$

F

y

$

cv(y)

y

$

F

cv(y)

y

$

F

cv(y)

c(y)

F

c y F c yv( ) ( )

Av. Fixed, Av. Variable & Av. Av. Fixed, Av. Variable & Av. Total Cost CurvesTotal Cost Curves

The firm’s total cost function isThe firm’s total cost function is

For y > 0, the firm’s average total For y > 0, the firm’s average total cost function iscost function is

c y F c yv( ) ( ).

AC yFy

c yy

AFC y AVC y

v( )( )

( ) ( ).

Av. Fixed, Av. Variable & Av. Av. Fixed, Av. Variable & Av. Total Cost CurvesTotal Cost Curves

What does an average fixed cost What does an average fixed cost curve look like?curve look like?

AFC(y) is a rectangular hyperbola so AFC(y) is a rectangular hyperbola so its graph looks like ...its graph looks like ...

AFC yFy

( )

$/output unit

AFC(y)

y0

AFC(y) 0 as y

Av. Fixed, Av. Variable & Av. Av. Fixed, Av. Variable & Av. Total Cost CurvesTotal Cost Curves

In a short-run with a fixed amount of In a short-run with a fixed amount of at least one input, the Law of at least one input, the Law of Diminishing (Marginal) Returns must Diminishing (Marginal) Returns must apply, causing the firm’s average apply, causing the firm’s average variable cost of production to variable cost of production to increase eventually.increase eventually.

$/output unit

AVC(y)

y0

$/output unit

AFC(y)

AVC(y)

y0

Av. Fixed, Av. Variable & Av. Av. Fixed, Av. Variable & Av. Total Cost CurvesTotal Cost Curves

And ATC(y) = AFC(y) + AVC(y)And ATC(y) = AFC(y) + AVC(y)

$/output unit

AFC(y)

AVC(y)

ATC(y)

y0

ATC(y) = AFC(y) + AVC(y)

$/output unit

AFC(y)

AVC(y)

ATC(y)

y0

AFC(y) = ATC(y) - AVC(y)

AFC

$/output unit

AFC(y)

AVC(y)

ATC(y)

y0

Since AFC(y) 0 as y ,ATC(y) AVC(y) as y

AFC

$/output unit

AFC(y)

AVC(y)

ATC(y)

y0

Since AFC(y) 0 as y ,ATC(y) AVC(y) as y

And since short-run AVC(y) musteventually increase, ATC(y) must eventually increase in a short-run.

Marginal Cost FunctionMarginal Cost Function

Marginal cost is the rate-of-change of Marginal cost is the rate-of-change of variable production cost as the variable production cost as the output level changes. That is,output level changes. That is,

MC yc yyv( )( ).

$/output unit

y

AVC(y)

MC(y)

$/output unit

y

AVC(y)

MC(y)

MC y AVC yAVC yy

( ) ( )( )

0

The short-run MC curve intersectsthe short-run AVC curve frombelow at the AVC curve’s minimum.

$/output unit

y

AVC(y)

MC(y)

ATC(y)

CostsCosts

Short runShort run – Diminishing marginal – Diminishing marginal returns results from adding returns results from adding successive quantities of variable successive quantities of variable factors to a fixed factorfactors to a fixed factor

Long runLong run – Increases in capacity can – Increases in capacity can lead to increasing, decreasing or lead to increasing, decreasing or constant returns to scaleconstant returns to scale

Short-Run & Long-Run Total Short-Run & Long-Run Total Cost CurvesCost Curves

The firm’s long-run total cost curve The firm’s long-run total cost curve consists of the lowest parts of the consists of the lowest parts of the short-run total cost curves. short-run total cost curves. The long-The long-run total cost curve is the run total cost curve is the lower lower envelopeenvelope of the short-run total cost of the short-run total cost curves.curves.

Short-Run & Long-Run Average Short-Run & Long-Run Average Total Cost CurvesTotal Cost Curves

For any output level y, the long-run For any output level y, the long-run total cost curve always gives the total cost curve always gives the lowest possible total production cost.lowest possible total production cost.

Therefore, the long-run av. total cost Therefore, the long-run av. total cost curve must always give the lowest curve must always give the lowest possible av. total production cost.possible av. total production cost.

The long-run av. total cost curve must The long-run av. total cost curve must be the lower envelope of all of the be the lower envelope of all of the firm’s short-run av. total cost curves.firm’s short-run av. total cost curves.

Short-Run & Long-Run Marginal Short-Run & Long-Run Marginal Cost CurvesCost Curves

For any output level y > 0, the long-For any output level y > 0, the long-run marginal cost of production is the run marginal cost of production is the marginal cost of production for the marginal cost of production for the short-run chosen by the firm.short-run chosen by the firm.

y

$/output unit

ACs(y;x2)

ACs(y;x2)ACs(y;x2)

MCs(y;x2) MCs(y;x2)

MCs(y;x2)

MC(y), the long-run marginalcost curve.

Short-Run & Long-Run Marginal Short-Run & Long-Run Marginal Cost CurvesCost Curves

AC(y)

$/output unit

y

SRACs

Short-Run & Long-Run Marginal Short-Run & Long-Run Marginal Cost CurvesCost Curves

AC(y)

$/output unit

y

SRMCs

Short-Run & Long-Run Marginal Short-Run & Long-Run Marginal Cost CurvesCost Curves

AC(y)

MC(y)$/output unit

y

SRMCs

For each y > 0, the long-run MC equals theMC for the short-run chosen by the firm.