MICROECONOMICS�
Production
The Firm’s Problem
�
Production Technology
�
Production Functions
Cobb-Douglas Isoquants
L
K
Perfect Complements in Production
L
K
4
8
14
2
4
7
K = 2L
Marginal Products
MPL and the production function
Y
output
L
labor
1
MPL
1
MPL
1
MPL
As more labor is added, MPL falls
Slope of the production function equals MPL
Example: Diminishing Marginal Products
and
Both marginal products are diminishing.
Cobb-Douglas:
Marginal Rate of Technical Substitution
Marginal Rate of Technical Substitution
L
K
Y=100
The slope is the rate at which labor must be given up as capital’s level is increased so as not to change the output level. The slope of an isoquant is its marginal rate of technical substitution.
Returns to scale
Initially Y1 = F (K1 , L1 )
Scale all inputs by the same factor z:
K2 = zK1 and L2 = zL1
(e.g., if z = 1.2, then all inputs are increased by 20%)
What happens to output, Y2 = F (K2, L2 )?
Returns to scale
Formally: starting with F(K,L) = Y
Returns to scale: Example 1
constant returns to scale for any z > 0
Returns to scale: Example 2
increasing returns to scale for any �z > 1
Firms and Their Production Decisions�
The Short Run versus the Long Run
short run Period of time in which quantities of capital production factor cannot be changed. It requires new investment. It is assumed that capital is fixed in short run.
long run Amount of time needed to make all production inputs variable
Production with One Variable Input (Labor)
Average and Marginal Products
average product Output per unit of a particular input.
marginal product Additional output produced as an input is increased by one unit.
Average product of labor
Output/labor input = Y/L
Marginal product of labor
Change in output/change in labor input = ∆Y/ ∆ L
The Relationship Between Average and Marginal Product Curves
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The Slopes of the Product Curve
PRODUCTION WITH ONE VARIABLE INPUT
The total product curve in (a) shows the output produced for different amounts of labor input.
The average and marginal products in (b) can be obtained (using the data in Table) from the total product curve.
At point A in (a), the marginal product is 20 because the tangent to the total product curve has a slope of 20.
At point B in (a) the average product of labor is 20, which is the slope of the line from the origin to B.
The average product of labor at point C in (a) is given by the slope of the line 0C.
20
The Slopes of the Product Curve
PRODUCTION WITH ONE VARIABLE INPUT
To the left of point E in (b), the marginal product is above the average product and the average is increasing; to the right of E, the marginal product is below the average product and the average is decreasing.
As a result, E represents the point at which the average and marginal products are equal, when the average product reaches its maximum.
At D, when total output is maximized, the slope of the tangent to the total product curve is 0, as is the marginal product.
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The Firm’s Problem
Firm Profits in General
Profit Maximization by a Competitive Firm
Profit Maximization by a Competitive Firm
Profit Maximization and Returns to Scale
Profit Maximization and Returns to Scale
Profit Maximization and CRS
The Firm’s Problem
The Nature of Cost
29
Measures of Short-Run Cost
30
Fixed versus Sunk Costs
31
Because a sunk cost cannot be recovered, it should not influence the firm’s decisions.
For example, consider the purchase of specialized equipment for a plant. Suppose the equipment can be used to do only what it was originally designed for and cannot be converted for alternative use. The expenditure on this equipment is a sunk cost. Because it has no alternative use, its opportunity cost is zero. Thus it should not be included as part of the firm’s economic costs.
It is important to understand the characteristics of production costs and to be able to identify which costs are fixed, which are variable, and which are sunk.
Computers (Lenovo, Dell, etc): mostly variable costs
Software: mostly sunk costs
Pizzas: mostly fixed costs
SUNK, FIXED, AND VARIABL E COSTS: COMPUTERS, SOFTWARE, AND PIZZAS
Fixed Costs and Variable Costs
Shutting Down
Shutting down doesn’t necessarily mean going out of business.
By reducing the output of a factory to zero, the company could eliminate the costs of raw materials and much of the labor. The only way to eliminate fixed costs would be to close the doors, turn off the electricity, and perhaps even sell off or scrap the machinery.
Fixed or Variable?
How do we know which costs are fixed and which are variable?
Over a very short time horizon—say, a few months—most costs are fixed. Over such a short period, a firm is usually obligated to pay for contracted shipments of materials.
Over a very long-time horizon—say, ten years—nearly all costs are variable. Workers and managers can be laid off (or employment can be reduced by attrition), and much of the machinery can be sold off or not replaced as it becomes obsolete and is scrapped.
34
From Total Product to Total Variable Cost
Cost
Q
TC(Q) = TVC + TFC
TVC(Q)
FC
0
DIMINISHING MARGINAL RETURNS AND MARGINAL COST
Diminishing marginal returns means that the marginal product of labor declines as the quantity of labor employed increases.
As a result, when there are diminishing marginal returns, marginal cost will increase as output increases.
Five Other Measures of Short-Run Cost
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TA FIRM’S COSTS
RATE OF OUTPUT (UNITS PER YEAR) | FIXED COST (DOLLARS PER YEAR) | VARIABLE COST (DOLLARS PER YEAR) | TOTAL COST (DOLLARS PER YEAR) | MARGINAL COST (DOLLARS PER UNIT) | AVERAGE FIXED COST (DOLLARS PER UNIT) | AVERAGE VARIABLE COST (DOLLARS PER UNIT) | AVERAGE TOTAL COST (DOLLARS PER UNIT) |
Blank Cell | (FC) (1) | (VC) (2) | (TC) (3) | (MC) (4) | (AFC) (5) | (AVC) (6) | (ATC) (7) |
0 | 50 | 0 | 50 | — | — | — | — |
1 | 50 | 50 | 100 | 50 | 50 | 50 | 100 |
2 | 50 | 78 | 128 | 28 | 25 | 39 | 64 |
3 | 50 | 98 | 148 | 20 | 16.7 | 32.7 | 49.3 |
4 | 50 | 112 | 162 | 14 | 12.5 | 28 | 40.5 |
5 | 50 | 130 | 180 | 18 | 10 | 26 | 36 |
6 | 50 | 150 | 200 | 20 | 8.3 | 25 | 33.3 |
7 | 50 | 175 | 225 | 25 | 7.1 | 25 | 32.1 |
8 | 50 | 204 | 254 | 29 | 6.3 | 25.5 | 31.8 |
9 | 50 | 242 | 292 | 38 | 5.6 | 26.9 | 32.4 |
10 | 50 | 300 | 350 | 58 | 5 | 30 | 35 |
11 | 50 | 385 | 435 | 85 | 4.5 | 35 | 39.5 |
Average Costs
$/output unit
AFC(y)
y
0
AFC(y) → 0 as y → ∞
$/output unit
y
AVC(y)
MC(y)
ATC(y)
Marginal Cost-Average Cost Relationships
41
COST IN THE SHORT RUN
The Shapes of the Cost Curves
In (a) total cost TC is the vertical sum of fixed cost FC and variable cost VC.
In (b) average total cost ATC is the sum of average variable cost AVC and average fixed cost AFC.
Marginal cost MC crosses the average variable cost and average total cost curves at their minimum points.
COST IN THE SHORT RUN
The Shapes of the Cost Curves
The Average-Marginal Relationship
Consider the line drawn from origin to point A in (a). The slope of the line measures average variable cost (a total cost of $175 divided by an output of 7, or a cost per unit of $25).
Because the slope of the VC curve is the marginal cost , the tangent to the VC curve at A is the marginal cost of production when output is 7. At A, this marginal cost of $25 is equal to the average variable cost of $25 because average variable cost is minimized at this output.
LONG-RUN COST OF PRODUCTION
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Cost Minimization
Isoquant
Isoquants
L
K
Isocost
Isocost Lines
RK + WL ≡ c’
RK + WL ≡ c”
c’ < c”
K
L
Slope = -R/W.
Cost Minimization
K
L
All input bundles yielding Y’ units�of output. Which is the cheapest?
F(K,L) ≡ Y’
K
L
All input bundles yielding Y’ units�of output. Which is the cheapest?
F(K,L) ≡ Y’
K
L
All input bundles yielding Y’ units�of output. Which is the cheapest?
F(K,L) ≡ Y’
K
L
All input bundles yielding Y’ units�of output. Which is the cheapest?
F(K,L) ≡ Y’
K*
L*
K
L
F(K,L) ≡ Y’
K*
L*
At an interior cost-minimizing input bundle:�(a) F(K,L) ≡ Y’ and�(b) slope of isocost = slope of isoquant; i.e.
Cost Minimization
�
Minimized Cost Function
�
Cost in the Long Run
INPUT SUBSTITUTION WHEN AN INPUT PRICE CHANGES
Facing an isocost curve C1, the firm produces output q1 at point A using L1 units of labor and K1 units of capital.
When the price of labor increases, the isocost curves become steeper.
Output q1 is now produced at point B on isocost curve C2 by using L2 units of labor and K2 units of capital.
$/output unit
y
AVC(y)
MC(y)
ATC(y)
Average Variable Costs
Economies of Scale and Diseconomies of Scale
61
The Long Run and Short Run Revisited
Summary:
62
Short- and Long-Run Average Cost Curves
63
The Assumptions of Perfect Competition
64
Profit Maximization
Short-Run Profit Maximization �
66
The Firm’s Supply Decision
MC(y)
ATC(y)
y
p
The firm’s�supply curve
$
Qf
ATC
AVC
MC
Pe = MR
Qf*
ATC
Pe
Profit = (Pe - ATC) × Qf*
Should this Firm Sustain Short Run Losses or Shut Down?
$
Qf
ATC
AVC
MC
Pe = MR
Qf*
ATC
Pe
Profit = (Pe - ATC) × Qf* < 0
Loss
Operating at a Loss in the Short-Run
70
Shutdown Decision Rule
Decision rule:
Firm’s Short-Run Supply Curve: MC Above Min AVC
$
Qf
ATC
AVC
MC
Qf*
P min AVC
8-72
A Competitive Firm’s Short-Run Supply Curve
73
Short-Run Market Supply Curve
Firm 1
Firm 2
5
10
20
30
Market
Q
Q
Q
P
P
P
15
18
25
43
S1
S2
SM
8-74
Short-Run Industry Equilibrium
Market demand
Short-run industry�supply
pse
Yse
Y
Short-run equilibrium price clears the�market and is taken as given by each firm.
y1
y2
y3
ATC
ATC
ATC
MC
MC
MC
y1*
y2*
y3*
pse
Firm 1
Firm 2
Firm 3
y1
y2
y3
ATC
ATC
ATC
MC
MC
MC
y1*
y2*
y3*
pse
Firm 1
Firm 2
Firm 3
Firm 1 wishes�to remain in�the industry.
Firm 2 wishes�to exit from�the industry.
Firm 3 is�indifferent.
Π1 > 0
Π2 < 0
Π3 = 0
Long-Run Industry Supply
S2(p)
Mkt. Demand
ATC(y)
MC(y)
y
A “Typical” Firm
The Market
p
p
Y
Suppose the industry initially contains�only two firms.
Mkt.�Supply
S2(p)
Mkt. Demand
ATC(y)
MC(y)
y
A “Typical” Firm
The Market
p
p
Y
p2
p2
Then the market-clearing price is p2.
S2(p)
Mkt. Demand
ATC(y)
MC(y)
y
A “Typical” Firm
The Market
p
p
Y
p2
p2
y2*
Then the market-clearing price is p2.�Each firm produces y2* units of output.
S2(p)
Mkt. Demand
ATC(y)
MC(y)
y
A “Typical” Firm
The Market
p
p
Y
p2
p2
y2*
Π > 0
Each firm makes a positive economic�profit, inducing entry by another firm.
S2(p)
S3(p)
Mkt. Demand
ATC(y)
MC(y)
y
A “Typical” Firm
The Market
p
p
Y
p2
p2
Market supply shifts outwards.
y2*
S2(p)
S3(p)
Mkt. Demand
ATC(y)
MC(y)
y
A “Typical” Firm
The Market
p
p
Y
p2
p2
Market supply shifts outwards.�Market price falls.
y2*
S2(p)
S3(p)
Mkt. Demand
ATC(y)
MC(y)
y
A “Typical” Firm
The Market
p
p
Y
p3
Each firm produces less.
y3*
p3
S2(p)
S3(p)
Mkt. Demand
ATC(y)
MC(y)
y
A “Typical” Firm
The Market
p
p
Y
p3
Each firm produces less.�Each firm’s economic profit is reduced.
y3*
p3
Π > 0
S3(p)
Mkt. Demand
ATC(y)
MC(y)
y
A “Typical” Firm
The Market
p
p
Y
p3
Each firm’s economic profit is positive.�Will another firm enter?
y3*
p3
Π > 0
S4(p)
S3(p)
Mkt. Demand
ATC(y)
MC(y)
y
A “Typical” Firm
The Market
p
p
Y
p3
Market supply would shift outwards again.
y3*
p3
S4(p)
S3(p)
Mkt. Demand
ATC(y)
MC(y)
y
A “Typical” Firm
The Market
p
p
Y
p3
Market supply would shift outwards again.�Market price would fall again.
y3*
p3
S4(p)
S3(p)
Mkt. Demand
ATC(y)
MC(y)
y
A “Typical” Firm
The Market
p
p
Y
p4
Each firm would produce less again.
y4*
p4
S4(p)
S3(p)
Mkt. Demand
ATC(y)
MC(y)
y
A “Typical” Firm
The Market
p
p
Y
p4
Each firm would produce less again. Each�firm’s economic profit would be negative.
y4*
Π < 0
p4
S4(p)
S3(p)
Mkt. Demand
ATC(y)
MC(y)
y
A “Typical” Firm
The Market
p
p
Y
p4
Each firm would produce less again. Each�firm’s economic profit would be negative.�So the fourth firm would not enter.
y4*
Π < 0
p4
Long-Run Industry Supply
S(p)
Mkt. Demand
ATC(y)
MC(y)
y
A “Typical” Firm
The Market
p
p
Y
p’
y*
p’
A long-run competitive equilibrium occurs when three conditions hold:
Output Response to a Change in Input Prices
Question: What is the impact of a change in input price, holding product price constant?
1) ATC and MC will shift
2) Firm will adjust output until MC=MR
96
How a Firm Responds to Input Prices Changes
97
The Long-Run Industry Supply Curve
98
The Long-Run Industry Supply Curve
99
CONSTANT-, INCREASING-, AND DECREASING-COST INDUSTRIES: COFFEE, OIL, AND AUTOMOBILES
You have been introduced to industries that have constant, increasing, and decreasing long-run costs.
The supply of coffee is extremely elastic in the long run. The reason is that land for growing coffee is widely available and the costs of planting and caring for trees remains constant as the volume grows. Thus, coffee is a constant-cost industry.
The oil industry is an increasing cost industry because there is a limited availability of easily accessible, large-volume oil fields.
Finally, a decreasing-cost industry. In the automobile industry, certain cost advantages arise because inputs can be acquired more cheaply as the volume of production increases.
The Industry’s Long-Run Supply Curve
Constant-Cost Industry
constant-cost industry Industry whose long-run supply curve is horizontal.
LONG-RUN SUPPLY IN A CONSTANT COST INDUSTRY
In (b), the long-run supply curve in a constant-cost industry is a horizontal line SL. When demand increases, initially causing a price rise, the firm initially increases its output from q1 to q2, as shown in (a). But the entry of new firms causes a shift to the right in industry supply. Because input prices are unaffected by the increased output of the industry, entry occurs until the original price is obtained (at point B in (b)).
The long-run supply curve for a constant-cost industry is, therefore, a horizontal line at a price that is equal to the long-run minimum average cost of production.
The Industry’s Long-Run Supply Curve
Increasing-Cost Industry
increasing-cost industry Industry whose long-run supply curve is upward sloping.
LONG-RUN SUPPLY IN A CONSTANT COST INDUSTRY
In (b), the long-run supply curve in an increasing-cost industry is an upward-sloping curve SL. When demand increases, initially causing a price rise, the firms increase their output from q1 to q2 in (a). In that case, the entry of new firms causes a shift to the right in supply from S1 to S2.
Because input prices increase as a result, the new long-run equilibrium occurs at a higher price than the initial equilibrium.
In an increasing-cost industry, the long-run industry supply curve is upward sloping.