Econ 101: Principles of Microeconomics
Chapter 12 - Behind the Supply Curve - Inputs and Costs
Fall 2010
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Outline
1
The Production Function
2
Marginal Cost and Average Cost
3
Short-Run versus Long-Run Costs
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Ch. 12 Behind the Supply Curve
Overview
In this chapter we turn our attention to the firm.
A firm is an organization that produces goods or services for sale.
We will begin by characterizing the relationship between the firm’s
inputs and the quantity of outputs it produces.
The production function describes the relationship between the
quantity of inputs and the quantity of outputs that the firm produces.
Basic characteristics of the production function has implications for
the cost structure for the firm, which in turn has implications for the
firm’ ultimate supply function.
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The Production Function
The Short Run and the Long Run
It is useful to categorize firms’ decisions into
- Long-run decisions–involves a time horizon long enough for a firm to
vary all of its inputs
- Short-run decisions–involves any time horizon over which at least one
of the firm’s inputs cannot be varied
To guide the firm over the next several years, manager must use the
long-run view
To determine what the firm should do next week, the short run view
is best.
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The Production Function
Production in the Short Run
In the short-run, the firm’s inputs can be divided into one of two
categories
1
Fixed inputs
- These are inputs whose quantity is constant for some period of time
(regardless of how much output is produced).
- Typically, fixed inputs will include land and machinery, though they can
also include certain types of labor (due to contracts).
2
Variable inputs
- These are inputs whose quantity the firm can vary, even in the short
run.
- Examples of variable inputs often include labor, energy, fuel, etc.
When firms make short-run decisions, there is nothing they can do
about their fixed inputs; i.e., they are stuck with whatever quantity
they have.
However, they can make choices about their variable inputs.
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The Production Function
Total Product
To fix ideas, suppose we have a firm whose only variable input is labor
All other inputs (capital, land, raw materials, etc.) we will assume for
now are fixed.
Total product is the maximum quantity of output that can be
produced from a given combination of inputs.
The total product curve shows how the quantity of output depends on
the quantity of variable input, for a given quantity of the fixed input.
We would generally expect the total product curve to be increasing;
i.e., as the quantity of the variable input increases, we would expect
total output to increase.
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The Production Function
Consider John’s Woodworking Shop Again
Units of Labor
0
1
2
3
4
5
6
7
8
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Total Product
0
10
35
80
160
193
218
239
257
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The Production Function
The Total Product Curve
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Ch. 12 Behind the Supply Curve
The Production Function
Marginal Product
Notice that the Total Product curve is always increasing in this case,
but that it’s slope is not the same throughout.
- Initial the slope is increasing
- but eventually it starts to flatten out.
The slope of the Total Product Curve is the Marginal Product of
labor.
Formally,
Marginal Product of Labor (MPL) =
=
Change in Quantity of Output
Change in Quantity of Labor
∆Q
∆L
Tells us the rise in output produced when one more worker is hired
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The Production Function
Units of Labor
0
Total Product
0
Marginal Product
10
1
10
25
2
35
45
3
80
80
4
160
33
5
193
25
6
218
21
7
239
18
8
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Ch. 12 Behind the Supply Curve
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The Production Function
The Marginal Product Curve
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The Production Function
Marginal Returns To Labor
As more and more workers are hired, the MPL is at first increasing
- This is known as increasing returns to labor
- This is typically due to the returns to specialization
- It can also arise due to minimum labor requirements for equipment.
Eventually, however, the MPL starts to decline
- This is known as diminishing returns to labor
- This arises as the gains from specialization are exhausted and
- The constraints caused by the fixed inputs start to bind
This pattern of MPL (and for other inputs) is thought to hold for
most industries.
Consider the problem of a woodworking shop.
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Marginal Cost and Average Cost
Production and Firm Costs
Understanding the nature of a firm’s production function is important
in that it has implications for the firm’s costs.
In the short run, the firm’s costs can be divided into two broad
categories:
1
Total Fixed costs (TFC): These are costs that do not depend upon the
quantity of output produced.
- These costs are typically associated with fixed inputs.
- Examples of fixed costs might be the rent paid for the firm’s building or
equipment rentals.
2
Total Variable costs (TVC): These are costs that depend on the
quantity output produced.
- As the name suggests, these are costs associated with the variable
inputs.
- In the case of John’s Woodworking shop, the TVC = w × L where w
denotes the wage rate.
Total Costs = TFC + TVC.
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Marginal Cost and Average Cost
John’s Cost Structure
Suppose that John has a TFC of $5000 and pays a wage rate of
$1200 per week
Units of
Labor
0
1
2
3
4
5
6
7
8
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Total
Output
0
10
35
80
160
193
218
239
257
Total Fixed
Cost (TFC)
$5000
$5000
$5000
$5000
$5000
$5000
$5000
$5000
$5000
Total Variable
Costs (TVC)
$0
$1200
$2400
$3600
$4800
$6000
$7200
$8400
$9600
Ch. 12 Behind the Supply Curve
Total
Costs (TC)
$5000
$6200
$7400
$8600
$9800
$11000
$12200
$13400
$14600
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Marginal Cost and Average Cost
The Cost Curves
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Marginal Cost and Average Cost
Marginal and Average Cost Curves
While the breakdown of Total Cost into Total Fixed and Total
Variable Costs is helpful, two other measures of cost will be even
more useful:
1
2
Marginal Cost: Measures the additional cost of producing one more
unit of a good or service.
Average Cost: Measures the average cost per unit of the good or
service (i.e., the costs averaged over all of the output produced by the
firm).
Understanding the distinction between these two concepts will be key
to finding the optimal level of production for the firm.
We’ll start with average cost
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Marginal Cost and Average Cost
Average Costs
There are three types of average costs
1 Average Fixed Costs (AFC) = Total Fixed Costs divided by Output
TFC
AFC =
(1)
Q
Since the numerator is fixed, AFC will decline as output increases.
2 Average Variable Costs (AVC) = Total Variable Costs divided by
Output
TVC
AVC =
(2)
Q
- Since TVC is initial slowing down as output increases (with increasing
returns to labor), AVC will initially fall as output increases.
- As TVC starts to increase more rapidly with output (with diminishing
returns to labor), AVC will start to increase with output.
3
Average Total Costs (ATC) = Total Costs divided by Output
TC
ATC =
= AFC + AVC
Q
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Marginal Cost and Average Cost
John’s Average Costs
Units of Labor
1
2
3
4
5
6
7
8
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Total Product
10
35
80
160
193
218
239
257
AFC
$500.00
$142.86
$62.50
$31.25
$25.91
$22.94
$20.92
$19.46
Ch. 12 Behind the Supply Curve
AVC
$120.00
$68.57
$45.00
$30.00
$31.09
$33.03
$35.15
$37.35
ATC
$620.00
$211.43
$107.50
$61.25
$56.99
$55.96
$56.07
$56.81
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Marginal Cost and Average Cost
The Average Cost Curves
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Marginal Cost and Average Cost
Marginal Costs
Another way of looking at the firm’s cost structure is to look at its
Marginal Costs; i.e., how it’s costs increase as output increases.
Formally:
∆TC
MC =
(4)
∆Q
If we look at John’s Woodworking Shop we have
Output
0
10
35
80
160
193
218
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Total Cost
5000
6200
7400
8600
9800
11000
12200
13400
14600
∆Q
∆TC
MC
10
25
45
80
33
25
21
18
1200
1200
1200
1200
1200
1200
1200
1200
120
48
27
15
36
48
57
67
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Marginal Cost and Average Cost
Adding in the MC Curve
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Marginal Cost and Average Cost
Patterns in the MC and AC Curves
Notice that the MC curve is
- Initially declining- this is due to increasing returns to labor
- Eventually increasing- this is due to diminishing returns to labor
The minimum-cost output, Q min , is the quantity at which the average
total cost is lowest.
- This is at the bottom of the ATC curve.
- and occurs where ATC=MC
At outputs less than Q min , ATC > MC and ATC is falling.
At outputs greater than Q min , ATC < MC and ATC is rising.
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Short-Run versus Long-Run Costs
Production Costs in the Long Run
Up until now, we have been focussing on the short-run, with some of
the firm’s inputs held fixed.
In the long run, costs behave differently
Firm can adjust all of its inputs in any way it wants
In the long run, there are no fixed inputs or fixed costs; i.e. all inputs
and all costs are variable
Firm must decide what combination of inputs to use in producing any
level of output
The firms goal is to earn the highest possible profit
To do this, it must follow the least cost rule; i.e., to produce any given
level of output the firm will choose the input mix with the lowest cost
This yields a Long-Run Average Total Cost Curve; i.e., the
relationship between the output and the ATC when fixed costs are
chosen to minimize total cost for each level of output.
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Short-Run versus Long-Run Costs
Consider John’s Woodworking Shop
Suppose that in our first production function, we assumed that John
had only one set of tools (e.g., 1 table saw, 1 drill press, and 1 router
table).
We’ll call this one unit of capital
The tools (and the space to house his tools) constitute fixed costs for
John in the short-run.
In the long-run, John must decide whether or not he wants to expand
his capital stock
The trade-off is that additional capital will avoid worker congestion,
but imposes a large fixed cost on the firm.
At low levels of production, having just one set of tools is not a binding
constraint and John would rather avoid the additional capital costs.
At higher levels of production, additional capital will avoid congestion
problems and the capital costs are spread out over more units of
production.
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Short-Run versus Long-Run Costs
Different Levels of Capital
Labor
Units of Labor
0
1
2
3
4
5
6
7
8
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Units of Capital
Capital = 1 Capital = 2 Capital = 3
0
0
0
10
10
10
35
39
39
80
92
101
160
184
202
193
284
314
218
397
439
239
443
571
257
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Short-Run versus Long-Run Costs
The Corresponding ATC Figures are Given by
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Ch. 12 Behind the Supply Curve
Short-Run versus Long-Run Costs
John’s Capital Stock Choice
The level of capital stock John chooses depends on his expected level of
output
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Short-Run versus Long-Run Costs
If Capital Stock Can be Varied Continuously, We Get
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Short-Run versus Long-Run Costs
Returns to Scale
LRATC curves for industries usually exhibit three basic phases:
1
Increasing Returns to Scale: Output range with declining LRATC
This is also known as economies of scale
Economies of scale often arise due to the gains from specialization.
The greatest opportunities for increased specialization occur when a
firm is producing at a relatively low level of output
Economies of scale can also arise due to minimum size requirements for
certain types of equipment.
2
Constant Returns to Scale: Output range with constant LRATC
Over some range of production, size may not matter and firms of the
same size will be equally cost-effective.
3
Decreasing Returns to Scale: Output range with increasing LRATC
This is also known as diseconomies of scale
As output continues to increase, most firms will reach a point where
bigness begins to cause problems
This is true even in the long run, when the firm is free to increase its
plant size as well as its workforce
Diseconomies of scale are more likely at higher output levels
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Short-Run versus Long-Run Costs
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Ch. 12 Behind the Supply Curve