Note: Lecture 11 follows this
Lecture 10: Production and Cost in the Short Run (continued)

1. Short run costs

The assumption that we make at the outset is that firms take input prices as given – changes in any individual firm’s production is assumed to have no effect on the prices it pays for its inputs.

Definitions:
Total Cost (TC) is the full cost of producing any given level of output.

TC = TFC + TVC

Total Fixed Cost (TFC) is the cost of hiring fixed inputs – it does not vary with output.  (This is also sometimes called overhead cost).

TFC = r*K Where: r is the price of a unit of capital and K is the number of units of capital hired.

Total Variable cost (TVC) is the cost of hiring variable inputs – it does vary with output.

TVC = w*L Where: w is the price of a unit of labor and L is the number of units of labor hired.

Average Total Cost (ATC) or Average Cost (AC) is the total cost of producing a certain quantity of output divided by that quantity – it is the cost per unit of output.

ATC = TC /q  Where: q is the quantity of output the firm produces.

Average Fixed Cost (AFC) is the total fixed cost divided by the quantity of output – it is the fixed cost per unit of output.

AFC = TFC/q

Average Variable Cost (AVC) is the total variable cost divided by the quantity of output – it is the variable cost per unit of output.

AVC = TVC/q

Marginal Cost (MC) is the increase in total cost resulting from an increase in the level of output by 1 unit.  (This is sometimes called incremental cost).

MC = change in TC/  change in q

Graphs of the Total Cost curves (insert here):

Notice:  TFC is fixed – it doesn’t change with output.
TVC increases with output – initially it increases at a decreasing rate then it increases at an increasing rate.
TC has the same shape as TVC, it is just scaled up by TFC.

Graphs of the Average and Marginal Cost curves (insert here):
 

Notice:  AVC is u-shaped
ATC is also u-shaped and lies above AVC
MC is also u-shaped and it cuts AVC and ATC at their min points

The relationship between AP and AVC:
The point of diminishing AP (the maximum point on the AP curve) corresponds to the minimum point on the AVC curve.

Graph of AP – Graph of AVC (insert here):

Diminishing AP leads to eventually increasing AVC.

Q. Why?

If labor is the variable input -- as the average productivity of workers falls and the firm wants to produce more output, the average cost of hiring workers increases.

The relationship between MP and MC:
The point of diminishing MP (the maximum point on the MP curve) corresponds to the minimum point on the MC curve.

Graph of MP – Graph of MC (insert here):

Diminishing returns leads to eventually increasing MC.

The relationship between MC and AVC, ATC:
The MC curve cuts the AVC and ATC curves at their minimum points.

When MC is below AVC (ATC) it is pulling the average down – AVC (ATC) falling.
When MC is above AVC (ATC) it is pulling the average up – AVC (ATC) rising.

Definition:
The capacity of a firm is the level of output that corresponds to the minimum of the SRAC curve.  It is the largest output that can be produced without encountering rising average cost per unit.

A firm producing to the left of the minimum point on the SRAC curve is said to be producing at excess capacity.

2. Shifts in the SR cost curves

The analysis of short run costs has so far assumed that input prices were held constant.  A change in the prices of inputs will shift the curves.

a. A change in the price of a variable input.
Graph (insert here):
 

An increase in the price of the variable input will: increase TVC – increase TC – increase AVC – increase ATC – increase MC.

An increase in the price of a variable input will shift the cost curves (AVC, ATC, MC) up.
A decrease in the price of a variable input will shift the cost curves (AVC, ATC, MC) down.

b. A change in the price of a fixed input.
Graph (insert here):
 

An increase in the price of the fixed input will: increase TFC – increase TC – increase AFC – increase ATC.

An increase in the price of the fixed input will shift the cost curves (AFC, ATC) up.
A decrease in the price of the fixed input will shift the cost curves (AFC, ATC) down.

3. A note on the SR cost curves

A SR cost curve shows how costs vary with output for a given quantity of the fixed input, for example for the size of plant.

There is thus a different SR cost curve for each quantity of the fixed input, once again in terms of plant size that means a different SR cost curve for each size of plant.

It a firm expands its plant size, it will move from one set of SR cost curves to another.
 
 
 

Lecture 11: Production and Cost in the LR

1. Introduction

In the SR, when at least one of the firm’s inputs is fixed, the only way for the firm to increase output is to increase its use of the variable input.

In the LR, when all inputs can be varied, there are many different ways to produce a given output.  For example, a firm could use more capital and less labor, or it could use more labor and less capital, or it could use roughly equal amounts of capital and labor.  In the LR the firm has decide what level of output to produce and what method to use to produce it.

There are two types of efficiency that are relevant to the firm’s decision making:

Technical efficiency: the firm uses a method of production that does not waste any of its inputs.

Economic efficiency:  of all the technically efficient methods, the firm uses the one that produces the desired output at the lowest possible cost.
 

2. Profit maximization and cost minimization in the LR

Any profit maximizing firm will in the LR choose the method of  production that allows it to produce output at the lowest possible cost.

Profit maximization implies cost minimization in the LR.

How does the firm choose the combination of inputs that minimizes cost?

The firm will substitute one input for another as long as the MP per $1 spent on that input is greater than the MP per $1 spent on the other input.

If a firm can get more extra output from an additional $1 spent on labor than from an additional $1 spent on capital, for example, it will lower costs by using more labor and less capital.

If L = labor and K= capital, and PL is the price of a unit of labor and PK is the price of a unit of capital then the cost minimizing combination of L and K will satisfy the following:

MPK/PK = MPL/PL
 

How does the firm change the combination of inputs when input prices change?

When relative prices of the inputs change, methods of production will change.  Relatively more of the cheaper input and relatively less of the more expensive input will be used.

This is important for understanding why production methods change over time and vary across countries.

For example:  In the U.S. production has become more capital intensive over time in response to rising wages relative to capital costs.

3. Long Run Costs

When all inputs can be varied, there is a least cost method of producing every level of output.

Graph of LRAC (insert here):
 

Note: At qm the firm attains its lowest per unit cost of production for given technology and factor prices.

Definition:
The Long Run Average Cost (LRAC) curve is the boundary between the cost levels that are attainable with known technology and factor prices and those that are unattainable.

The LRAC curve is U-shaped:

a. Decreasing costs: 0 to qm
An expansion of output permits a reduction of costs per unit.
Technologies that have this property are said to exhibit economies of scale or increasing returns to scale (IRTS).

Eg. With IRTS a doubling of all the inputs leads to a more than doubling of output.

IRTS is found when there are gains from specialization in the division of labor.

b. Constant costs: q1 to q2 (graph of a flat bottom to LRAC)
An expansion of output has no effect on cost per unit.
Technologies that have this property are said to exhibit constant returns to scale (CRTS)

Eg. With CRTS a doubling of all the inputs leads to a doubling of output.

Within the range of CRTS there is no cost advantage associated with plant size 1or plant size 2 or any plant size in between.

c. Increasing costs: qm and above
An expansion of output leads to an increase in cost per unit.
Technologies that have this property are said to exhibit diseconomies of scale or decreasing returns to scale (DRTS).

Eg. With DRTS a doubling of all the inputs leads to a doubling of output.

DRTS tends to occur when the firm becomes so large that it is difficult to manage.

4. Relationship between SR and LR costs

Each SRATC curve shows the lowest cost of producing any output when at least one of the inputs is fixed.

The LRAC curve shows the lowest cost of producing any output when all inputs can be varied.

Graph of the SRATCs and LRAC (insert here):
 

Notice: No SRATC curve can fall below the LRAC curve since the LRAC is the lowest cost of producing each possible output.

The SRATCs curves are tangent to the LRAC curve at the outputs for which the quantity of the fixed input is optimal.

Graph of the LRAC as the “lower envelope” of the SR curves (insert here):

        0 to q1: Use plant size 1 (cost per unit is lower than plant size 2)
        q1 to q2: Use plant size 2 (cost per unit is lower than plant size 1 and plant size 3)
        and so on ……..

Shifts in the cost curves:

A rise in input prices will shift the whole family of SRATC curves and the LRAC curve upward.  A decrease in input prices or an improvement in technology will shift the curves downward.

5. The Very Long Run and Technology

In the VLR technology can change and shift the LRAC curve downward.

Definitions:
Technological change refers to all changes in the techniques of production.

Invention is the creation of something new, such as a new production technique or a new product.

Innovation is the introduction of an invention into the methods of production.

Note: innovation is costly and risky.  Which inventions tend to make it to the market?

Types of technological change (pp. 196-197)
a. process innovation
b. product innovation
c. improved inputs

Firms’ choices in the VLR:
A firm can respond to what is perceives as a long term increase in the price of an input in one of two ways:
1. Substitute away from the relatively more expensive input using existing production techniques.
2. Invest in research and develop a new production technique that innovates away from that input.