Lecture 12 - University of Minnesota Twin Cities

Report
Exam 1-Results
•
•
Exam score
(max =
8+12+16= 36)
Exam %
(max 100)
# of students % of students
≥ 31
≥ 87
3
10
28-30
77 - 86
10
34
24-27
67 - 76
12
41
≤ 23
≤ 66
4
14
Average total score: 26.8 (74%)
– Average score Part A: 4.7 (58%)
– Average score Part B: 9.1 (76%)
– Average score Part C: 13 (81%)
Answer key will be posted today and we’ll go over the test in Discussion on Friday
Lecture 11: Introduction to the
Theory of the Firm
Production in the short run
Theory of the firm (1)
• Firm=producer=supplier=seller
• How do firms decide how and how much to
produce in order to maximize profit?
• Firm’s decision has two components:
– Production—how to combine inputs to produce
outputs?
– Cost – how do costs vary with output?
Theory of the firm (2)
• The firm’s decision will depend on:
– Time frame: short-run versus long-run
– Market structure:
• Perfect competition
• Imperfect competition
• Monopoly
Parallels with consumer theory
Consumer
Producer
Bundle of goods
Input mix
Utility function
Marginal utility
Production
function
Marginal product
Indifference curve
Isoquant
MRS
MRTS
Production Process or Function: The relationship that
describes how inputs are combined to produce outputs
Prices and money do
not appear here.
Production is a
physical process
Categories of inputs or factors of production
• Labor
– Workers
– Management/entreprenuership
• Capital
– Physical capital - machinery, equipment, buildings
• Land is sometimes a separate input category, especially
for agriculture
– Materials - Inputs like energy, chemicals, plastic,
and other materials
Categories of outputs or products
• Goods
– Pizzas, cars, buildings, clothes, computers,
paintings
• Services
– Pizza delivery, medical exams, cleaning service,
income tax preparation, rock concert
• Both goods and services are outputs of
production processes
In Class Assignment 1
• Name 3 inputs, at least 1 labor and 1 capital,
required to produce a:
– McDonald’s Happy Meal
– Bicycle
– Divorce decree
– Vikings game
– University of Minnesota graduate
– BBQ in your back yard
In Class Assignment 1 –
some examples of inputs
• Name 3 inputs, at least 1 labor and at least 1
capital, required to produce a:
– McDonalds Happy Meal (ingredients, equipment,
workers, building)
– Bicycle (parts, workers, equipment, building)
– Divorce (lawyers, judge, office supplies, buildings)
– Vikings game (players, stadium, referees)
– University of Minnesota graduate (buildings, teachers,
students)
– BBQ in your back yard (backyard, food, grill)
In Class Assignment Follow Up
• Which inputs would you need more of to go
from producing 1 to producing 10 units?
Inputs that might change if production
goes from 1 to 10 units
• McDonalds Happy Meal -- ingredients,
equipment, workers (per hour), building
• bicycle -- parts, workers, equipment, building
• Divorce (lawyers, judge, office supplies,
buildings)
• Vikings game –players, stadium, referees (if on
different days)
• University of Minnesota graduate (buildings,
teachers, students)
• BBQ in your back yard (backyard, food, grill)
Production function
• Q = f (K, L) where Q is output; K is capital and L
is labor
Production surface =
amount of Q
produced with
different
combinations of K
and L
Q
Q2
K
Q1
L
Common functional forms for
production functions
• Cobb‐Douglas : Q = K0.7L0.5
• Quadratic : Q= 10L– L2+6K–0.3K2
Example: Cobb Douglas
• Q = K0.7L0.5
– If K=10 and L=20, Q=10.7x 20.5= 22.4
L
K
5
10
15
20
25
5
6.9
9.8
11.9
22.0
15.4
10
11.2
15.8
19.4
22.4
25.1
15
14.9
21.1
25.8
29.8
33.3
20
18.2
25.7
31.5
36.4
40.7
25
22.4
30.1
36.9
42.6
47.6
Example: Cobb Douglas
• Q = K0.7L0.5
• When both inputs increase…
L
K
5
10
15
20
25
5
6.9
9.8
11.9
22.0
15.4
10
11.2
15.8
19.4
22.4
25.1
15
14.9
21.1
25.8
29.8
33.3
20
18.2
25.7
31.5
36.4
40.7
25
22.4
30.1
36.9
42.6
47.6
Example: Cobb Douglas
• Q = K0.7L0.5
• When only one input increases…
L
K
5
10
15
20
5
6.9
9.8
11.9
22.0
15.4
10
11.2
15.8
19.4
22.4
25.1
15
14.9
21.1
25.8
29.8
33.3
20
18.2
15.8 -11.2
25.7 =4.6
31.5
36.4
40.7
25
22.4
30.1
42.6
47.6
36.9
25
25.1-22.4
=2.7
• Law of diminishing returns: if other inputs are
fixed, the increase in output from an increase
in the variable input must eventually decline.
Law of diminishing returns
• Q = K0.7L0.5
Change in Q when L goes from
K
5 to 10
10 to 15
15 to 20
20 to 25
5
2.9
4.6
6.2
7.5
7.7
2.2
3.6
4.7
5.8
6.8
1.8
3.0
4.0
4.9
5.7
1.6
2.7
3.5
4.3
5.0
10
15
20
25
Example: Quadratic
• Q= 10L– L2+6K–0.3K2
L
K
3
6
9
12
3
36.3
39.3
24.3
-8.7
6
46.2
49.2
34.2
1.2
9
50.7
53.7
38.7
5.7
12
49.8
52.8
37.8
4.8
Example: Quadratic
• Q= 10L– L2+6K–0.3K2
L
K
3
6
9
12
3
36.3
39.3
24.3
-8.7
6
46.2
49.2
34.2
1.2
9
50.7
53.7
38.7
5.7
12
49.8
52.8
37.8
4.8
Example: Quadratic
• Q= 10L– L2+6K–0.3K2
L
K
3
6
9
12
3
36.3
39.3
24.3
-8.7
6
46.2
49.2
34.2
1.2
9
50.7
53.7
38.7
5.7
12
49.8
52.8
37.8
4.8
Question: Why might total output
decline when more inputs are added?
Typical production function with one
input
Production technology
• “Production technology” describes the
maximum quantity of output a firm can
produce from a given quantities of inputs.
Production function with 1 input
Production technology
• Example: There are two restaurants selling
identical sandwiches and pizzas. Firm 1 uses a
conventional oven while firm 2 uses a
“improved” oven. Their production functions
are:
– Firm 1: Q1 = 50K.5L.5
– Firm 2: Q2=100K.5L.5
– For the same K and L, Firm 2 will produce more Q
Technical change
• Technical change: an advance in technology
that allows more output to be produced with
the same level of inputs. Examples:
– Ovens that cook faster
– Higher-yielding seed varieties
– Faster, smaller computers
The Effect of Technological Progress in Food
Production
(Q= food production, L = labor)
Production in the short and long run
• Refers to the time required to change inputs,
holding technology constant
– Not the same as technical change
• Long run: the shortest period of time required to
alter the amounts of all inputs used in a
production process
– Defined by the input that takes longest to change
• Short run: the longest period of time during
which at least one of the inputs used in a
production process cannot be varied
• If the long run is 5 years, the short run is less than 5
years
Fixed and variable inputs
• Variable input: an input that can be varied in
the short run
• Fixed input: an input that cannot vary in the
short run
• Short and long run, and fixed and variable
inputs vary for different products and
producers
Short and Long Run Production with 2 inputs
Short run
< # of units
(hours, days,
weeks, years)
Long run
> # of units
(hours, days,
weeks, years)
Input 1
Variable
Variable
Input 2
Fixed
Variable
In Class assignment 2: Fill in the following table for:
1) McDonald’s Happy Meal and a University of
Minnesota graduate
Short run
< # of units
(hours, days,
weeks, years)
Long run
> # of units
(hours, days,
weeks, years)
Input 1
Variable
Variable
Input 2
Fixed
Variable
In Class Answer
1) McDonald’s Happy Meal
Short run
Long run
< 1 year (hours,
> 1 year
days, weeks,
(hours, days,
years)
weeks, years)
Ingredients
(lbs/day) or
workers (per
hour)
Restaurant
Variable
Variable
Fixed
Variable
Fill in the following table for:
University of Minnesota graduate
Short run
Long run
< 2 years (hours,
> 2 years
days, weeks,
(hours, days,
years)
weeks, years)
Teachers
(per
semester)
Classrooms
Variable
Variable
Fixed
Variable
Short-run (SR) production
• Production with at least one fixed input
• Q= f(K , L) where Q is total output, K is the fixed input,
and L is variable input
• In SR, firm decides how much L to use given K.
• Two key measures that firms can use to make decisions
about how much L to use are:
– Average product of labor: output per unit of labor
• APL = Q/L
– Marginal product of labor: the additional output produced
from one addition unit of labor
• MPL = ∂Q/∂L
Examplecalculating AP and MP at a point
• From previous example of Q = K0.7L0.5
– If K =10 and L=20, Q=10.7x 20.5= 22.4
• What are APL and MPL at that point?
• APL = Q/L
– Plug in values of K and L to get 22.4/20 = 1.12
• MPL= ∂Q/∂L = .5K.7L -.5
– Plug in values for K and L: (.5)(10.7 )(20-.5 )=
(.5)(5)(.22) = .55
• Q = K0.7L0.5
– If K =10 and L=20, Q=10.7x 20.5= 22.4
• What are APL and MPL at that point?
• APL = Q/L= 22.4/20 = 1.12
• MPL= ∂Q/∂L = .5K.7L -.5 = (.5)(5)(.22) = .56
If L increases, will the APL go up or down?
It will go down because if each additional unit is
contributing less than the average (.56 < 1.12) , the
average has to go down
Example- Calculating AP and MP in short
run when K is fixed
• Q = K0.7L0.5
• If K is fixed at 10 and L is variable, what are
APL and MPL?
– APL = Q/L= (10.7L .5)/L = 5L.5/L
– MPL= ∂Q/∂L = .5K.7L -.5 = (.5)(5) L -.5 = 2.5L -.5
If L increases, will the APL go up or down?
It depends…
In class # 3 – Graph Q on one graph and MPL
and APL on another, on the hand out
L (person
hours)
Q (meals)
0
0
1
MP L
AP L
2
6
2.00
2
14
12
7.00
3
28
14
9.33
4
43
15
10.75
5
59
16
11.80
6
72
13
12.00
7
80
8
11.43
8
80
0
10.00
9
72
-8
8.00
Relationship between MP and AP
curves
• When the marginal product curve lies above
the average product curve, the average
product curve must be rising
• When the marginal product curve lies below
the average product curve, the average
product curve must be falling.
• The two curves intersect at the maximum value
of the average product curve.
Application of average v marginal:
How should the police department allocate
officers to maximize arrests per hour?
Number
of
police
West Philadelphia
(Arrests per hour)
TP
AP
MP
City Center
(Arrests per hour)
TP
AP
MP
0
0
0
0
0
100
40
40
40
45
45
45
200
80
40
40
80
40
35
300
120
40
40
105
35
25
400
160
40
40
120
30
15
500
200
40
40
125
25
5
They should send 400 to West Philadelphia and
100 to City Center. Total arrests: 160+45+205
Number
of
police
West Philadelphia
(Arrests per hour)
TP
AP
MP
City Center
(Arrests per hour)
TP
AP
MP
0
0
0
0
0
100
40
40
40
45
45
45
200
80
40
40
80
40
35
300
120
40
40
105
35
25
400
160
40
40
120
30
15
500
200
40
40
125
25
5

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