slide 1Long-run costs

LONG-RUN COSTSLONG-RUN COSTS

In the long-run there are no fixed inputs, and therefore no fixed costs. All costs are variable.

Another way to look at the long-run is that in the long-run a firm can choose any amount of fixed costs it wants for making short-run decisions.

slide 2Long-run costs

Cost MinimizationCost Minimization

Suppose a firm has a production function with two variable inputs, labor (L), and capital (K).

Q = f(L, K)

This production function can be represented by an isoquant map.

slide 3Long-run costs

capital

(K)

labor (L)

Q1

Q2

Q3

Some isoquants: Q1 < Q2 < Q3

slide 4Long-run costs

Marginal Rate of Technical Marginal Rate of Technical SubstitutionSubstitution

The Marginal Rate of Technical Substitution of L or K is the amount of K it takes to make up for the loss of one unit of L, output constant.

MRTS (L for K) = -KL, output constant.

MRTS is (minus) the slope of an isoquant.

slide 5Long-run costs

Problem

The firm is told it has to produce a particular output level, say, Q*.

The firm can buy L and K at fixed known prices,

PL and PK.

How should the firm choose L and K if it must produce Q* at minimum cost?

slide 6Long-run costs

The firm's total cost is its expenditure on all of its inputs:

C = PL L + PKK

For a given value of C, the above expression is known as an "isocost" line, or "cost constraint".

slide 7Long-run costs

The firm's cost contraint can be rewritten as

K = (C/ PK ) - (PL /PK ) L

and drawn on the same set of axes as the firm's isoquants.

slide 8Long-run costs

capital

(K)

labor (L)

C"/ PK

C"/ PL

The slope of the isocost line is (PL /PK )

slide 9Long-run costs

capital

(K)

labor (L)

C"/ PK

C"/ PL

Q*

If Q* is to be produced, what's the lowest possible cost of

production?

slide 10Long-run costs

capital

(K)

labor (L)

C"/ PK

C"/ PL

Q*

Exactly C* is the minimum cost of producing Q*.

What's the rule? How much L and K are used?

C*/ PK

C*/ PL

slide 12Long-run costs

Finding the Long-run Total Cost Curve

The Long-Run Total Cost Curve shows the minimum cost of producing any output when all inputs are variable.

In this case the number of inputs is two.

We show how to find a couple of points on the firm's LRTC curve.

slide 13Long-run costs

capital

(K)

labor (L)

Q*

Q* and C* are one point of the firm's LRTC curve.

What's the cost of producing Q' (>Q*)?

C*/ PK

C*/ PL

K*

L*

Q'

slide 14Long-run costs

capital

(K)

labor (L)

Q*

Use these points to start plotting the LRTC curve.

C*/ PK

C*/ PL

K*

L*

Q'

C'/ PK

slide 15Long-run costs

Sketch in the LRTC curve.

Q

TC

C'

C*

Q'Q*

LRTC

slide 16Long-run costs

From this LRTC curve you can find the corresponding average and

marginal cost curves.

slide 17Long-run costs

The Long-run Average Cost Curve

The long-run average cost curve shows the minimum average cost at each output level when all inputs are variable, that is, when the firm can have any plant size it wants.

There is a relationship between the LRAC curve and the firm's set of short-run average cost curves.

slide 18Long-run costs

SR and LR Average Costs

Economists use the term “plant size” to talk about having a particular amount of fixed inputs. Choosing a different amount of plant and equipment (plant size) amounts to choosing an amount of fixed costs.

Economists want you to think of fixed costs as being associated with plant and equipment. Bigger plants have larger fixed costs.

slide 19Long-run costs

If each plant size is associated with a different amount of fixed costs, then each plant size for a firm will give us a different set of short-run cost curves.

Choosing a different plant size (a long-run decision) then means moving from one short-run cost curve to another.

slide 20Long-run costs

Economists usually assume that plant size is infinitely divisible (variable). In the case of finely divisible plant size, the LRAC curve might look like this:

LRAC

Each small U-shaped

curve is a SAC curve.

The LRAC

curve.

$/Q

QAverage costs for a

typical firm.

slide 21Long-run costs

In the preceding graph, each short-run cost curve corresponds to a particular amount of fixed inputs.

As the fixed input amount increases in the long run, you move to different SR cost curves, each one corresponding to a particular plant size.

slide 22Long-run costs

Notice in the graphs of LRAC curves presented so far that the curves have been drawn to be U-shaped. That is, when output is increasing LRAC at first falls, and then eventually rises.

The overall shape of the long-run average cost curve depends on the technology of production.

slide 23Long-run costs

For example, advantages implicit in large scale production (with large plants) may allow firms to produce large outputs at lower cost per unit.

On the other hand, firms may get so big that ever increasing managerial and monitoring costs may cause unit costs to rise.

slide 24Long-run costs

LRAC

$/Q

QAverage costs for a

typical pizza firm.

LRAC shows

economies of

scale here.

ECONOMIES OF SCALE: When output increases, long-run average costs decline.

slide 25Long-run costs

LRAC

$/Q

QAverage costs for a

typical pizza firm.

LRAC shows

diseconomies of

scale here.

DISECONOMIES OF SCALE: When output increases, long-run average costs increase.

slide 26Long-run costs

For the U-shaped long-run average cost curve, there are economies of scale over small outputs, and diseconomies of scale at larger outputs.

slide 27Long-run costs

Not all firms necessarily suffer from diseconomies of scale at large outputs.

When a firm has economies of scale over a range of outputs big enough to supply the total market demand, that firm is called a natural monopoly.

slide 28Long-run costs

Naturally monopolies have long-run average cost curves that look like this:

$/Q

Q

LRAC

Electric power generation

in a local market

slide 29Long-run costs

As we will see, firms in perfect competition must have U-shaped long-run average cost curves.

One conclusion from this is that only certain industries can be expected to be perfectly competitive. And a crucial factor is the technology of production, since that is what determines the shape of the long-run average cost curve.