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LONG-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. Cost Minimization.

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Long run costs
LONG-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.


Cost minimization
Cost 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.


Q3

Q2

Q1

Some isoquants: Q1 < Q2 < Q3

capital

(K)

labor (L)


Marginal rate of technical substitution
Marginal Rate of Technical Substitution

  • 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) = -KL, output constant.

  • MRTS is (minus) the slope of an isoquant.


Problem
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?




capital inputs:

(K)

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

C"/ PK

labor (L)

C"/ PL


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

capital

(K)

C"/ PK

Q*

labor (L)

C"/ PL


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

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

capital

(K)

C*/ PK

C"/ PK

Q*

C*/ PL

labor (L)

C"/ PL


Finding the long run total cost curve
Finding the Long-run Total Cost Curve production?

  • 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.


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

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

capital

(K)

C*/ PK

K*

Q'

Q*

C*/ PL

L*

labor (L)


Use these points to start plotting the LRTC curve. production?

capital

(K)

C'/ PK

C*/ PK

K*

Q'

Q*

C*/ PL

L*

labor (L)


Sketch in the lrtc curve

LRTC production?

Sketch in the LRTC curve.

TC

C'

C*

Q*

Q'

Q



The long run average cost curve
The Long-run Average Cost Curve and marginal cost curves.

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.


Sr and lr average costs
SR and LR Average Costs and marginal cost curves.

  • 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.



Each small U-shaped fixed costs, then each plant size for a firm will give us a different set of short-run cost curves.

curve is a SAC curve.

  • 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:

$/Q

LRAC

The LRAC

curve.

Q

Average costs for a

typical firm.





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

LRAC shows

economies of

scale here.

$/Q

LRAC

Q

Average costs for a

typical pizza firm.


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

LRAC shows

diseconomies of

scale here.

$/Q

LRAC

Q

Average costs for a

typical pizza firm.




$/Q at large outputs.

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

LRAC

Q

Electric power generation

in a local market


  • 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.


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