Micro 8 - Cost Function of Microeconomics

Lecture in UGM

1. Cost Function & Minimization
Prepared by Dea Yustisia
Universitas Gadjah Mada
2025
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2. Costs
”An economist is a person who,
when invited to give a talk at a
banquet, tells the audience there’s
no such thing as a free lunch.”

3. What are Costs?: Total Revenue, Total Cost, Profit
We assume that the firm’s goal is to maximize profit.
Total revenue minus total
cost
Profit= Total revenue -
Total costTR = P×Q
The amount a firm receives from the sale of
its output
The market value of the inputs a firm uses
in production
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4. What are Costs?: Total Costs and Opportunity Costs
Total costs
TC = Opportunity costs
Definition
The cost of something is what you
give up to get it.
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5. Coz Firm’s Cost of Production Include:
Explicit costsrequire an outlay of money,e.g., paying wages to
workers.
Implicit costsdo not require a cash outlay,e.g., theopportunity
costof the owner’s time or the wage forgone coz of doing business.
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6. What are Costs?: Total Revenue, Total Cost, Profit
Example: Explicit vs. Implicit Costs
You need$100,000 to start your business.
Assume: the interest rate is 5% and you have savings of$40,000.
Alternative 1:borrow$100,000
explicit cost =$5000 interest on loan→total cost =$5000
Alternative 2:use$40,000 of your savings, and borrow the other
$60,000
explicit cost =$3000 (5%) interest on the loan
implicit cost =$2000 (5%) foregone interest you could have earned on
your$40,000
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7. What are Costs?: Total Revenue, Total Cost, Profit
total cost = 3000 + 2000 =$5000
In both cases, total (exp + imp) costs =$5000.
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8. Profit: Accounting Profit vs Economic Profit
The overall goal of most firms is to maximize profits or the firm’s
value
Accounting profit
What shows up on the firm’s income
statement and is typically reported to
the manager by the firm’s accounting
department.
Total amount of money taken in
from sales (total revenue)
minus the dollar cost of
producing goods or services
(total cost).
Accounting profit= TR−TC
Economic profit
The difference between total revenue
and the cost ofopportunity cost.
Economic profit
= TR−cost of opportunity cost
Opportunity cost
The explicit (accounting) cost of
a resource plus the implicit cost
of giving up its best alternative.
Opportunity cost = accounting
cost (explicit) + implicit cost
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9. Profit: Accounting Profit vs Economic Profit
Accounting profit:πA= TR−TCexplicitEconomic profit:π= TR−TC = TR−TCexplicit−TCimplicit
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10. What are Costs?: Accounting Profit vs Economic Profit
Accounting Profit vs Economic Profit
Comparison between the two types of profit and their different
components.
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11. Example of Accounting Cost vs Economic Cost
Suppose you own a building in New York that you use to run a small
pizzeria. Food supplies are your only accounting costs (TC) which cost
about$20,000. At the end of the year, your revenues were$100,000.
Thus, your accounting profits are:
Accounting profit= TR - TC =$100,000 -$20,000 =$80,000.
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12. Accounting vs Economic Profit
Theseaccounting profitsmay probably overstate youreconomic profits
because the costs include only accounting costs.
The costs do not include the time you spent running the business.
Accounting costs do not account for economic costs.
Profit Formulas
Accounting profit:πA= TR−TCexplicit
Economic profit:π= TR−TC = TR−TCexplicit−TCimplicit
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13. Implicit Cost of Time
First, the costs do not include the time you spent running the
business.
Example:You could have worked for someone else for$30,000 a year,
instead of running a pizzeria business.
Thus, the wage that you earned as a worker =$30,000 = your opportunity
cost of time = the implicit cost of running the pizzeria→This fact
reflects aneconomic cost (or opportunity cost).
The costs do not include the time you
spent running the business.
Accounting costs do not account for
economic cost.
Profit Formulas
Accounting profit:
πA= TR−TCexplicit
Economic profit:
π= TR−TC =
TR−TCexplicit−TCimplicit
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14. Accounting Costs vs Economic Costs
Second, accounting costs do not account economic cost.
Example:If you do not run the pizzeria, you could have rented your
building. Let’s say, the rental value of the building is$100,000 per year.
Thus, the costs of running the pizzeria include:
the costs of supplies =$20,000
the wage that you earned as a worker =$30,000
the rental value of the building =$100,000
THUS, the economic cost (or opportunity cost) of running the
pizzeria is$150,000.
Let’s say your TR if you run the pizzeria is$100,000, then you actually
lost$50,000 by running the pizzeria→your economic profits were
negative (−$50,000).
The costs do not include the time you
spent running the business.
Accounting costs do not account
economic cost.
Profit Formulas
Accounting profit:
πA= TR−TCexplicit
Economic profit:
π= TR−TC =
TR−TCexplicit−TCimplicit
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15. Andrew’s Party Shop: Profit Calculation
Andrew operates a small shop specializing in party favors.
Owns the building, supplies his own labor and money capital.
No explicit rental or wage costs.
Given:
Previous income from renting the store:$1,000 per month
Previous job as store manager:$2,500 per month
Interest sacrificed on U.S. Treasury bonds:$1,000 per month
Monthly revenue from the shop:$10,000
Monthly expenses for labor and supplies:$6,000
Calculate Andrew’s monthly accounting and economic profits!
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16. Step 1: Accounting Profit Calculation
Formula
Accounting Profit = Revenue - Explicit Costs
Calculation:
Accounting Profit = 10,000−6,000 = 4,000
Result:Andrew’s accounting profit is$4,000 per month.
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17. Step 2: Economic Profit Calculation
Formula
Economic Profit = Revenue - (Explicit Costs + Implicit Costs)
Implicit Costs:
Rent = 1,000,Salary = 2,500,Interest = 1,000
Total Implicit Costs = 1,000 + 2,500 + 1,000 = 4,500
Calculation:
Economic Profit = 10,000−(6,000 + 4,500) =−500
Result:Economic profit = -$500 per month (loss).
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18. Adam’s Grocery Store Case Study
Adam is the owner of a small grocery store in a busy section of Boulder,
Colorado. Adam’s annual revenue is$200,000, and his total cost for
running his business is$180,000 per year. A supermarket chain wants to
hire Adam as its general manager for$60,000 per year.
Question (a):What is the implicit cost to Adam of owning and
managing the grocery store?
Question (b):What is Adam’s accounting profit?
Question (c):What is Adam’s economic profit?
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19. Answer to (a): Implicit Cost Calculation
Definition of Implicit Cost
Implicit costs are the opportunity costs of using resources that the owner
already owns.
Given:Adam’s foregone salary as a potential supermarket general
manager is$60,000.
Answer:Therefore, the implicit cost to Adam of owning and managing his
grocery store is:
Implicit Cost = $60,000
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20. Answer to (b): Accounting Profit Calculation
Formula for Accounting Profit
Accounting Profit = Revenue - Explicit Costs
Given:Adam’s revenue is$200,000, and his explicit costs are$180,000.
Calculation:
Accounting Profit = 200,000−180,000 = 20,000
Answer:Adam’s accounting profit is$20,000 per year.
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21. Answer to (c): Economic Profit Calculation
Formula for Economic Profit
Economic Profit = Revenue - (Explicit Costs + Implicit Costs)
Calculation:
Economic Profit = 200,000−(180,000 + 60,000) =−40,000
Answer:Adam’s economic profit is -$40,000 per year (a loss).
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22. Economists versus Accountants
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23. Production and Costs: The Production Function
Production function
Relationship between
Quantity of inputs used to make a good (K, L)
And the quantity of output of that good (Q)
It can be represented by:
(a)
(b)
(c)
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24. Production and Costs: The Production Function
Production function
Relationship between
Quantity of inputs used to make a good (K, L)
And the quantity of output of that good (Q)
It can be represented by:
(a)equation
(b)
(c)
The PF in the form of Equation
Assumption:
A production process that utilizes two inputs, capital and labor, to produce
output.
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25. Production and Costs: The Production Function
Mathematically, the PF is denoted as:
Q=F(K,L)
Q= the level of output.
K= the quantity of capital input.
L= the quantity of labor input.
the maximum amount of output that can be produced with K units of
capital and L units of labor
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26. Production and Costs: The Production Function
The PF in the form of
Example:Farmer Jack grows wheat.
He has 5 acres of land.
He can hire as many workers as he wants.
L Q
(no. of workers) (bushels of wheat)
0 0
1 1000
2 1800
3 2400
4 2800
5 3000
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27. Production and Costs: The Production Function
The Production Function in the form of Graph
Relationship between quantity of inputs used to make a good and
the quantity of output of that good.
Diminishing marginal product
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28. The Production Function: Diminishing Marginal Product
One of the Ten Principles of Economics introduced in Chapter 1 is
that rational people think at the margin.
”Marginalism”is the key to understanding the decisions a firm makes
about how many workers to hire and how much output to produce.
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29. The Production Function: Marginal Product
Example of marginalism:Marginal product
Increase in output that arises from an additional unit of input (K or L)
Thus, there are 2 types of MP i.e.:
Marginal Product of Labor (MPL)
Marginal Product of Capital (MPK)
MP is the slope of the production function
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30. The Production Function: Marginal Product Notation and
Formula
Notation “marginal” = ∆ (delta) = “change in. . . ”
Examples:
∆Q= change in output, ∆L= change in labor
Formula: Marginal product of labor (MPL) =
∆Q
∆L
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31. Example 1: Total Marginal Product of Labor
Explanation
MPLequals the slope of the Production Function (PF).
Notice thatMPLdiminishes asL(number of workers) increases.
This explains why the PF gets flatter asLincreases.
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32. Example 1: Total Marginal Product of Labor
Total Marginal Product Labor
L Q ∆L ∆Q MPL
(workers)
(bushels of
wheat)
0 0 - - -
1 1000 1 1000 1000
2 1800 1 800 800
3 2400 1 600 600
4 2800 1 400 400
5 3000 1 200 200
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33. Example 1: MPL as Slope of Production Function
MPL = Slope of Production Function
MPL diminishes as L increases, explaining the flattening of the
production function curve.
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34. The Production Function: Diminishing Marginal Product
Why MPL Is Important
Recall one of the Ten Principles:Rational people think at the margin.
When Farmer Jack hires an extra worker,
his costs rise by the wage he pays the worker
his output rises byMPL
Comparing MPL helps Jack decide whether he would benefit
from hiring the worker.
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35. Why MPL Diminishes
Farmer Jack’s output rises by a smaller and smaller amount for each
additional worker. Why?
As Jack adds workers, the average worker has less land to work
with and will be less productive.
In general,MPLdiminishes asLrises whether the fixed input is land
or capital (equipment, machines, etc.).
Diminishing marginal product:the marginal product of an input
declines as the quantity of the input increases (other things equal).
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36. Example 2: A Production Function and Total Cost:
Caroline’s Cookie Factory
EXAMPLE 2: A Production Function and Total Cost: Caroline’s Cookie Factory
Number of
Workers
Output
(cookies per
hour)
Marginal
Product of
Labor
Cost of
Factory
Cost of
Workers
Total Cost of
Inputs
0 0 - $30 $0 $30
1 50 50 30 10 40
2 90 40 30 20 50
3 120 30 30 30 60
4 140 20 30 40 70
5 150 10 30 50 80
6 155 5 30 60 90
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37. Understanding Marginal Product of Labor (MPL)
Why MPL Is Important and Why MPL Diminishes
Recall one of the Ten Principles:Rational people think at the margin.
When Farmer Jack hires an extra worker:
His costs rise by the wage he pays the worker.
His output rises byMPL.
Comparing MPL helps Jack decide whether he would benefit
from hiring the worker.
Farmer Jack’s output rises by a smaller amount for each additional
worker. This is because:
As Jack adds workers, the average worker has less land to work with
and becomes less productive.
In general,MPLdiminishes asL(number of workers) rises, especially
when other inputs (like land or equipment) are fixed.
Diminishing marginal product:The marginal product of an input
declines as the quantity of the input increases (holding other inputs
constant).
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38. Marginal Product of Capital (MPK)
Understanding the Marginal Product of Capital (MPK)
Definition:The Marginal Product of Capital (MPK) is the increase
in output resulting from an additional unit of capital, holding other
inputs constant.
Formula:MPK =
∆Q
∆K
∆Q: Change in output
∆K: Change in capital input
Interpretation:MPK represents how much additional output can be
produced with one more unit of capital.
Diminishing Returns to Capital:Similar to labor, as more capital is
added, the MPK tends to decrease when other inputs are fixed.
Example:If adding a machine increases production by 100 units,
MPK = 100.
Importance of MPK:Helps firms decide whether investing in more
capital (like equipment) will be beneficial.
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39. The Production Function: Diminishing Marginal Product
EXAMPLE 1: Farmer Jack’s Costs
Farmer Jack must pay$1000 per month for the land, regardless of
how much wheat he grows.
The market wage for a farm worker is$2000 per month.
So Farmer Jack’s costs are related to how much wheat he produces.
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40. Total Cost and Marginal Cost
Marginal Cost (MC):is the increase in Total Cost from producing
one more unit.
Formula:
MC=
∆TC
∆Q
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41. The Production Function: Diminishing Marginal Product
EXAMPLE 1: Farmer Jack’s Costs
L Q Cost of Land Cost of Labor Total Cost
(no. of
workers)
(bushels of wheat)
0 0 $1,000 $0 $1,000
1 1,000 $1,000 $2,000 $3,000
2 1,800 $1,000 $4,000 $5,000
3 2,400 $1,000 $6,000 $7,000
4 2,800 $1,000 $8,000 $9,000
5 3,000 $1,000 $10,000 $11,000
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42. EXAMPLE 1: Farmer Jack’s Total Cost Curve
Q (bushels of wheat) Total Cost
Q Total Cost
0 $1,000
1000 $3,000
1800 $5,000
2400 $7,000
2800 $9,000
3000 $11,000
Total Cost and Quantity of Wheat
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43. EXAMPLE 1: Total and Marginal Cost
MC =
∆TC
∆Q
Q(bushels of
wheat)
Total Cost ∆TC ∆Q
Marginal Cost
(MC)
0 $1,000 - - -
1,000 $3,000 $2,000 1000 $2.00
1,800 $5,000 $2,000 800 $2.50
2,400 $7,000 $2,000 600 $3.33
2,800 $9,000 $2,000 400 $5.00
3,000 $11,000 $2,000 200 $10.00
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44. EXAMPLE 1: The Marginal Cost Curve
Q TC MC
0 $1,000 $2.00
1,000 $3,000 $2.50
1,800 $5,000 $3.33
2,400 $7,000 $5.00
2,800 $9,000 $10.00
3,000 $11,000 $10.00
Marginal Cost Curve
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45. The Various Measures of Cost
From data on a firm’s total cost, we can derive several related
measures of cost, which will turn out to be useful when we analyze
production and pricing decisions in future chapters.
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46. Fixed and Variable Costs
Fixed costs (FC): cost that do not vary with the quantity of output
produced.
For Farmer Jack,FC= $1000 for his land.
Other examples: cost of equipment, loan payments, rent.
Variable costs (VC): cost that vary with the quantity produced.
For Farmer Jack,VC= wages he pays workers.
Other example: cost of materials.
Total cost (TC) = FC + VC
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47. The Various Measures of Cost
Average fixed cost,AFC
Fixed cost divided by the quantity of output.
AFC=
FC
Q
Average variable cost,AVC
Variable cost divided by the quantity of output.
AVC=
VC
Q
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48. Fixed Cost vs Sunk Cost
Fixed Costs:
Incurred while the firm is operating—regardless of output level.
Examples: salaries of executives, office rent, insurance, plant
maintenance.
Avoidableif the firm shuts down.
Sunk Costs:
Already incurred andcannot be recovered.
Examples: R&D for a drug, investment in highly specialized
machinery.
Irrelevantfor future decisions—cost is gone regardless of what
happens next.
Why It Matters:
Fixed costsaffect future decisions (e.g., shutdown or not).
Sunk costsshould be ignored when making forward-looking choices.
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49. Sunk, Fixed, and Variable Costs: Case Examples
Let’s explore examples from different industries:
Computers
Software
Pizzerias
Textbooks
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50. Computers & Software
Computers (e.g., Dell, HP)
Most costs arevariable: components like chips and labor.
Fewfixed costs; components often outsourced.
Sunk costsare minimal.
Success relies on scale and cost efficiency.
Software (e.g., Microsoft)
High sunk costs: time spent on coding, R&D, marketing.
Low variable costs: copying and packaging.
Low fixed costs.
High uncertainty—sales depend on product success.
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51. Pizzerias & Textbooks
Pizzerias
High fixed costs: ovens, rent, utilities.
Low variable costs: ingredients like sauce and cheese.
Profit margins are squeezed despite high pizza prices.
Textbooks
Mostly sunk costs: writing, editing, typesetting.
Low variable costper copy (5–10).
Market price often unrelated to production cost.
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52. EXAMPLE 2
Our second example is more general, applies to any type of firm
producing any good with any types of inputs.
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53. EXAMPLE 2: Costs
QFCVCTC
0$100$0$100
110070170
2100120220
3100160260
4100210310
5100280380
6100380480
7100520620
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54. EXAMPLE 2: Marginal Cost
QTCMC
0$100$70
117050
222040
326050
431070
5380100
6480140
7620200
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55. Example 2: Average Fixed Cost
QFCAFC
0$100n/a
1$100$100
2$10050
3$10033.33
4$10025
5$10020
6$10016.67
7$10014.29
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56. EXAMPLE 2: Average Variable Cost
QVCAVC
0$0n/a
170 70
212060
316053.33
421052.50
528056.00
638063.33
752074.29
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57. EXAMPLE 2: Average Total Cost
QTC ATC AFC AVC
0$100n/a n/a n/a
1170170 100 70
2220110 50 60
326086.6733.3353.33
431077.502552.50
5380 76 2056.00
6480 8016.6763.33
762088.5714.2974.29
Average total cost (ATC)equals
total cost divided by the quantity of
output:
ATC=
TC
Q
Also,
ATC=AFC+AVC
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58. EXAMPLE 2: Average Total Cost
QTC ATC
0$100n/a
1170170
2220110
326086.67
431077.50
5380 76
6480 80
762088.57
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59. EXAMPLE 2: The Various Cost Curves Together
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60. Why the previous curves differ from the curve in the book?
Average Cost and Marginal
Cost Curves
The figure shows average
total cost (ATC), average
fixed cost (AFC), average
variable cost (AVC), and
marginal cost (MC) for
Caleb’s Coffee Shop.
Features of these curves:
1
Marginal cost rises with
the quantity of output.
2
ATC curve is U-shaped.
3
MC curve crosses ATC at
its minimum point.
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61. The Various Measures of Cost
Typical cost curves
Marginal cost eventually rises with the quantity of output
Average-total-cost curve is U-shaped
Marginal-cost curve crosses the average-total-cost curve at the
minimum of average total cost
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62. Example 2: ATC and MC
WhenMC<ATC,ATCis
falling.
WhenMC>ATC,ATCis
rising.
TheMCcurve crosses theATC
curve at theATCcurve’s
minimum.
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63. Active Learning 3: Calculating Costs
Fill in the blank spaces of this table.
QVCTCAFCAVCATC MC
0 $50n/an/a n/a$10
110 $10$60.00
23080 1540.0030
3 11016.672036.67
410015012.50 37.50
5150 3040.00
62102608.333543.3360
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64. Active Learning 3: Answers
First, deduceFC= $50and useFC+VC=TC.
QVCTCAFC AVCATC MC
0$0$50n/a n/a n/a$10
11060$50.00$10$60.0020
2308025.001540.0030
36011016.672036.6740
410015012.502537.5050
515020010.003040.0060
62102608.333543.33
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65. Costs in the Short Run & Long Run
Short run:Some inputs arefixed(e.g., factories, land). The costs of
these inputs areFC.
Long run:All inputs arevariable(e.g., firms can build more
factories, or sell existing ones).
In the long run,ATCat anyQis cost per unit using the most efficient
mix of inputs for thatQ(e.g., the factory size with the lowestATC).
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66. Short-Run Costs
Recall that the short run is a period of time in which some inputs can
be varied, while other inputs are fixed.
Short run cost measuresall assume labor is variable and capital is
fixed:
Fixed cost (F): a cost that doesn’t vary with the level of output (e.g.,
expenditures on land or production facilities).
Variable cost (VC): production expense that changes with the level of
output produced (e.g., labor cost, materials cost).
Total cost (C): sum of variable and fixed costs (C=VC+F).
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67. Short-Run Cost Curves
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68. Production Functions and the Shape of Cost Curves
The SR production function,Q=f(L,K), determines the shape of a
firm’s cost curves.
We can writeQ=g(L) because capital is fixed in the SR.
Amount ofLneeded to produceQisL=g
−1
(q).
If the wage paid to labor iswand labor is the only variable input,
then variable cost isVC=wL.
VC is a function of output:V(Q) =wL=w g
−1
(Q).
Total cost is also a function of output:
C(Q) =V(Q) +F=w g
−1
(Q) +F.
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69. Production Functions and the Shape of Cost Curves
Shape of the MC curve:
MC=
dV(Q)
dQ
=w
dL
dQ
MC moves in the opposite direction
ofMPL
MC=
w
MPL
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70. Production Functions and the Shape of Cost Curves
Shape of the AC curve:
Driven by diminishing marginal
returns to labor in the AVC curve
AVC=
VC
Q
=
wL
Q
AVC=
w
APL
AC moves in the opposite direction
ofAPL
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71. Effects of Taxes on Costs
A$10 per unit tax increases firm
costs, shifting up both AC and MC
curves.
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72. Industry Context
Aluminum is widely used in airplanes, packaging, and construction.
Production begins with bauxite refining, then smelting via electric
current.
Electricity and alumina account for60% of per-ton costs.
Plants operate in shifts (2-shift typical, 3-shift incurs higher cost).
Short-run cost analysis focuses on existing capacity (no new plant
build).
This example is based on Kenneth S. Corts, “The Aluminum Industry in 1994, Harvard Business School Case N9-799-129, April
1999.
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73. Short-Run Cost Structure
At≤600 tons/day:
Total cost =$1140/ton.
Constant cost components: electricity, alumina, raw materials.
At>600 tons/day:
Third shift required→labor, maintenance, freight increase 50%.
New total cost =$1300/ton.
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74. Short-Run Cost Structure
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75. AVC Formula When Output
>
600 Tons/Day
Total Variable Cost:
TVC= 1140·600 + 1300(q−600) = 1300q−96,000
Average Variable Cost (AVC):
AVC= 1300−
96,000
q
AVC remains constant at$1140 forq≤600.
Forq>600, AVC increases due to higher third-shift costs.
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76. AVC Formula When Output>600 Tons/Day
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77. Implications for SR Cost Management
Smelters must evaluate cost increases before scaling beyond 600
tons/day.
Third shift increases marginal and average costs sharply.
At 900 tons/day, plant hits full capacity→AVC and MC become
very steep.
Understanding short-run variable costs helps avoid inefficiencies.
Key Insight:SR cost analysis helps determine the efficient operating
range before diseconomies of scale set in.
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78. Short-Run Cost Summary
Costs of inputs thatcan’t be adjustedarefixedand costs of inputs
thatcan be adjustedarevariable.
Shapes of SR cost curves (VC, MC, AC) are determined by the
production function.
When a variable input has diminishing marginal returns, VC and C
become steep as output increases.
Thus, AC, AVC, and MC curves rise with output.
When MC lies below AVC and AC, it pulls both down; when MC lies
above AVC and AC, it pulls both up.
MC intersects AVC and AC at their minimum points.
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79. Long-Run Costs
Recall that the long run is a period of time in which all inputs can be
varied.
In the LR, firms can change plant size, build new equipment, and
adjust inputs that were fixed in the SR.
We assume LR fixed costs are zero (F= 0).
In LR, firm concentrates onC,AC, andMCwhen it decides how
much labor (L) and capital (K) to employ in the production process.
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80. Long-Run Costs and Input Choice
Isocost linesummarizes all combinations of inputs that require the
same total expenditure.
If the firm hiresLhours of labor at a wage ofwper hour, total labor
cost iswL.
If the firm rentsKhours of machine services at a rental rate ofrper
hour, total capital cost isrK.
Cost is fixed at a particular level along a given isocost line:
C=wL+rK
Rewrite the isocost equation for easier graphing:
K=
C
r
−
w
r
L
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81. Isocost Lines
Three properties of isocost lines:
1
The firm’s costs,C, and input prices determine where the isocost line
hits the axes.
2
Isocosts farther from the origin have higher costs than those closer to
the origin.
3
The slope of each isocost is the same and is given by the relative prices
of the inputs.
dK
dL
=−
w
r
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82. Cost Minimization
Three equivalent approaches to minimizing cost:
1
Lowest-isocost rule: Pick the bundle of inputs where the lowest
isocost line touches the isoquant associated with the desired level of
output.
2
Tangency rule: Pick the bundle of inputs where the desired isoquant
is tangent to the budget line.
MRTS=−
w
r
3
Last-dollar rule: Pick the bundle of inputs where the last dollar spent
on one input yields as much additional output as the last dollar spent
on any other input.
MPL
MPK
=
w
r
Or rewrite as
MPL
w
=
MPK
r
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83. The Shape of LR Cost Curves
The LR AC curve may be U-shaped
Not due to downward-sloping AFC or diminishing marginal returns,
both of which are SR phenomena, as it is for SR AC.
Shape is due to economies and diseconomies of scale.
A cost function exhibitseconomies of scaleif the average cost of
production falls as output expands.
Doubling inputs more than doubles output, so AC falls with higher
output.
A cost function exhibitsdiseconomies of scaleif the average cost of
production rises as output expands.
Doubling inputs less than doubles output, so AC rises with higher
output.
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84. Cost Minimization with Varying Output Levels
Firms select input combinations to minimize costs for different output
levels.
Input prices: Labor (w= $10/hour), Capital (r= $20/hour).
Cost function:
C= 10L+ 20K
Isocost lines and isoquants determine the optimal input mix.
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85. Interpreting the Expansion Path
Each point of tangency between an isocost and isoquant represents
the cost-minimizing combination.
Example:
Point A (Output = 100):L= 50,K= 25, Cost =$1000
Point B (Output = 200):L= 100,K= 50, Cost =$2000
Point C (Output = 300):L= 150,K= 75, Cost =$3000
The firm’s expansion path is a straight line through these points.
Slope of expansion path:
∆K
∆L
=
50−25
100−50
=
1
2
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86. Figure: Expansion Path Illustration
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87. Figure: Expansion Path Illustration
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88. Duality
Aspect Cost MinimizationOutput Maximiza-
tion
Objective Minimize cost for a
given outputq0
Maximize output for a
given budgetTC
Constraint F(K,L) =q0 wL+rK=TC
Function Optimized TC=wL+rK F(K,L)
Lagrangian Φ = wL+rK−
λ(F(K,L)−q0)
Φ =F(K,L)−µ(wL+
rK−TC)
Optimal Condition
MPK
r
=
MPL
w
MPK
r
=
MPL
w
Economic InterpretationUse inputs with the
highest productivity
per dollar
Allocate budget to
maximize output
Final Result Most cost-efficient
combination ofKand
L
Most output-efficient
combination ofKand
L
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89. Economies, Constant, and Diseconomies of Scale
Economies of scale
Long-run average total cost falls as the quantity of output increases
Increasing specialization among workers
Constant returns to scale
Long-run average total cost stays the same as the quantity of output
changes
Diseconomies of scale
Long-run average total cost rises as the quantity of output increases
Increasing coordination problems
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90. Lower Costs in the Long Run
Because a firm cannot varyKin the SR
but it can in the LR, SR cost is at least
as high as LR cost.
... and even higher if the ”wrong”
level ofKis used in the SR.
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91. How ATC Changes as the Scale of Production Changes
Economies of scaleoccur when increasing production allows greater
specialization: workers more efficient when focusing on a narrow task.
More common whenQis low.
Diseconomies of scaleare due to coordination problems in large
organizations. E.g., management becomes stretched, can’t control
costs.
More common whenQis high.
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92. Example 3: LRATC with 3 Factory Sizes
Firm can choose from 3 factory sizes:S,M,L.
Each size has its ownSRATCcurve.
The firm can change to a different factory size
not in the short run.
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93. SR and LR Cost Curves
Short-Run Average and Marginal
Costs (SRAC and SRMC):In the
short run, costs are influenced by fixed
inputs, causing SRAC and SRMC
curves to be steeper.
Long-Run Average Cost (LRAC):In
the long run, all inputs are variable,
leading to a flatter LRAC as firms can
adjust all factors to minimize costs.
Relationship Between Curves:SRMC
curves intersect SRAC at their minimum
points. LRAC represents the lowest
achievable cost as production scales.
Figure:Universitas Gadjah Mada 93 / 106

94. Short-Run vs. Long-Run Total Cost
Short-run total cost exceeds long-run total cost except for the output
level where the short-run input level restriction is the long-run input
level choice.
This implies that the long-run total cost curve always has one point in
common with any particular short-run total cost curve.
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95. Short-Run and Long-Run Total Cost Curves
A short-run total cost curve always has one point in common with the
long-run total cost curve, and is elsewhere higher than the long-run
total cost curve.
cs(y) represents the short-run total cost curve.
c(y) represents the long-run total cost curve.
F=w2x
′
2
indicates the fixed cost in the short run.
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96. Cost of Producing Multiple Goods
If a firm produces multiple goods, the cost of one good may depend
on the output level of the other.
Outputs are linked if a single input is used to produce both.
There areeconomies of scopeif it is cheaper to produce goods jointly
than separately.
Measure:
SC=
C(q1,0) +C(0,q2)−C(q1,q2)
C(q1,q2)
C(q1,0) = cost of producingq1units of good 1 by itself
C(0,q2) = cost of producingq2units of good 2 by itself
C(q1,q2) = cost of producing both goods together
SC>0 implies it is cheaper to produce the goods jointly.
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97. Cost of Producing Multiple Goods
Production possibilities frontier (PPF)
bows away from the origin if there are
economies of scope.
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98. Example of Economies of Scope
For example, a restaurant
produces both hamburgers and
sandwiches. The cost of
separately producing 1,000,000
hamburgers is$0.50 each.
Likewise, if 4,000,000
sandwiches are produced
separately, the cost is$0.30
each.
If 1,000,000 hamburgers and
4,000,000 sandwiches are
produced together (by using the
same preparation and storage
facility), the total cost is
$1,500,000.
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99. Example of Economies of Scope - Calculation
To determine the economies of
scope:
1
DetermineC(qa) =
1,000,000×0.50 = 500,000
2
DetermineC(qb) =
4,000,000×0.30 = 1,200,000
3
Determine
C(qa+qb) = 1,500,000
Economies of Scope Formula:
SC=
C(qa,0) +C(0,qb)−C(qa,qb)
C(qa,qb)
SC=
500,000 + 1,200,000−1,500,000
1,500,000
= 13.33%
The cost of producing hamburgers
and sandwiches together is 13.33%
less than the cost of producing them
separately.
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100. Economies of Scope vs. Economies of Scale
Economies of Scopeare often
confused witheconomies of scale.
The former refers to the decrease in
the average total cost of production
when there is an increasingvariety of
goods produced.
Economies of scope: Savings in
cost due to the increased
production of distinct products
using the same operations.
Economies of scope reduce the
average cost of producing
multiple products.
Economies of Scalerefer to the
cost savings achieved from increasing
thescale of production of a single
good.
Economies of scale: Savings in
cost due to the increased
production of the same product.
Economies of scale reduce the
average cost of producing one
product.
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101. Learning by Doing/Learning Curve
Learning by Doing:
Efficiency improves as firms
produce more over time,
reducing average costs.
Economies of Scale:
Increased production decreases
average costs by spreading
fixed costs over larger output.
Combined Effect:Both
learning by doing and
economies of scale contribute
to lowering costs as output
rises.
Figure:
(b) Economies of Scale and Learning
by Doing
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102. Summary
In the short run, firms face fixed and variable costs.
In the long run, all costs are variable, allowing firms to adjust their
production scale.
Economies of scale lead to lower average total costs as production
increases, while diseconomies of scale lead to higher costs.
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103. Summary
Implicit costsdo not involve a cash outlay, yet are as important as
explicit costs to firms’ decisions.
Accounting profitis revenue minus explicit costs.
Economic profitis revenue minus total (explicit + implicit) costs.
Theproduction functionshows the relationship between output and
inputs.
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104. Summary
Marginal product of laboris the increase in output from a one-unit
increase in labor, holding other inputs constant.
Marginal productdiminishes as the input increases. As output rises,
the production function flattens, and the total cost curve steepens.
Variable costsvary with output;fixed costsdo not.
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105. Summary
Marginal cost(MC) is the increase in total cost from an extra unit
of production, typically upward-sloping.
Average variable cost(AVC) is variable cost divided by output.
Average fixed cost(AFC) is fixed cost divided by output and
decreases as output increases.
Average total cost(ATC), sometimes called ”cost per unit,” is total
cost divided by output and is usually U-shaped.
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106. Summary
TheMC curveintersects theATC curveat the minimum average
total cost.
WhenMC<ATC,ATCfalls asQrises.
WhenMC>ATC,ATCrises asQrises.
In thelong run, all costs are variable.
Economies of scale:ATCfalls asQrises.
Diseconomies of scale:ATCrises asQrises.
Constant returns to scale:ATCremains constant asQrises.
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