Profit Maximization Profits The objectives of the firm Fixed and variable factors Profit...
-
date post
21-Dec-2015 -
Category
Documents
-
view
227 -
download
2
Transcript of Profit Maximization Profits The objectives of the firm Fixed and variable factors Profit...
![Page 1: Profit Maximization Profits The objectives of the firm Fixed and variable factors Profit maximization in the short and in the long run Returns to scale.](https://reader035.fdocuments.us/reader035/viewer/2022062320/56649d6c5503460f94a4bced/html5/thumbnails/1.jpg)
Profit Maximization
ProfitsThe objectives of the firmFixed and variable factorsProfit maximization in the short and in the long runReturns to scale and profits
![Page 2: Profit Maximization Profits The objectives of the firm Fixed and variable factors Profit maximization in the short and in the long run Returns to scale.](https://reader035.fdocuments.us/reader035/viewer/2022062320/56649d6c5503460f94a4bced/html5/thumbnails/2.jpg)
Competitive Markets
In a competitive market firms take input and output prices as given
Firms are “small” relatively to the market, so that their decisions do not affect market prices
Q: When is this assumption reasonable?
![Page 3: Profit Maximization Profits The objectives of the firm Fixed and variable factors Profit maximization in the short and in the long run Returns to scale.](https://reader035.fdocuments.us/reader035/viewer/2022062320/56649d6c5503460f94a4bced/html5/thumbnails/3.jpg)
Product Homogeneity
A: In markets where firms produce (almost) identical products
When products are homogeneous (agricultural products, raw materials, etc.) no firm can raise its price without losing most of its customers
Differentiated products: a firm can set its price without losing all customers
![Page 4: Profit Maximization Profits The objectives of the firm Fixed and variable factors Profit maximization in the short and in the long run Returns to scale.](https://reader035.fdocuments.us/reader035/viewer/2022062320/56649d6c5503460f94a4bced/html5/thumbnails/4.jpg)
The Objective of the Firm
Q: What is the objective of the firm?
A: The maximization of profits
Q: How are profits defined?
![Page 5: Profit Maximization Profits The objectives of the firm Fixed and variable factors Profit maximization in the short and in the long run Returns to scale.](https://reader035.fdocuments.us/reader035/viewer/2022062320/56649d6c5503460f94a4bced/html5/thumbnails/5.jpg)
Defining Economic Profits
Profits are defined as revenues minus costs
E.g. a firm produces light bulbs using labor and capital
KwLwYp KLb
![Page 6: Profit Maximization Profits The objectives of the firm Fixed and variable factors Profit maximization in the short and in the long run Returns to scale.](https://reader035.fdocuments.us/reader035/viewer/2022062320/56649d6c5503460f94a4bced/html5/thumbnails/6.jpg)
Defining Economic Profits
Labor: suppose that the owner of the firm works in the firm
Q: Should costs take the owner’s labor into account?
A: Yes, we need to take into account the opportunity cost for the owner of not employing his/her labor somewhere else
![Page 7: Profit Maximization Profits The objectives of the firm Fixed and variable factors Profit maximization in the short and in the long run Returns to scale.](https://reader035.fdocuments.us/reader035/viewer/2022062320/56649d6c5503460f94a4bced/html5/thumbnails/7.jpg)
Defining Economic Profits
Q: How should you take into account the cost of using physical capital?
A: Since factor inputs are measured in flows (e.g. labor and machine hours per week), the unit cost of using physical capital should be its rental rate
![Page 8: Profit Maximization Profits The objectives of the firm Fixed and variable factors Profit maximization in the short and in the long run Returns to scale.](https://reader035.fdocuments.us/reader035/viewer/2022062320/56649d6c5503460f94a4bced/html5/thumbnails/8.jpg)
Fixed and Variable Factors
Short run: there are fixed factors that the firm is obliged to employ.
E.g.: firm has signed a contract to lease space in a building for certain number of months. Even if the firm decides not to produce it still has to pay lease.
![Page 9: Profit Maximization Profits The objectives of the firm Fixed and variable factors Profit maximization in the short and in the long run Returns to scale.](https://reader035.fdocuments.us/reader035/viewer/2022062320/56649d6c5503460f94a4bced/html5/thumbnails/9.jpg)
Fixed and Variable Factors
Long run: all factors of production are variable.
Variable factors are factors that the firm employs and pays for only if it decides to produce something. E.g.: labor
In the long run all factors are variable: firm can always decide to use zero inputs and produce zero output, i.e., go out of business.
![Page 10: Profit Maximization Profits The objectives of the firm Fixed and variable factors Profit maximization in the short and in the long run Returns to scale.](https://reader035.fdocuments.us/reader035/viewer/2022062320/56649d6c5503460f94a4bced/html5/thumbnails/10.jpg)
Short Run Profit Maximization
Let’s consider the problem of a consulting firm that has rented 3000sq feet in a building (fixed factor)
It has to decide how many consultants to hire
Production function (output in a year):
lx
6.02.03000 lxy
![Page 11: Profit Maximization Profits The objectives of the firm Fixed and variable factors Profit maximization in the short and in the long run Returns to scale.](https://reader035.fdocuments.us/reader035/viewer/2022062320/56649d6c5503460f94a4bced/html5/thumbnails/11.jpg)
Short Run Profit Maximization
Suppose the salary of a consultant is $70K per year, office space costs $1000 per square foot per year, and the firm sells its consultation services at $100K each
Problem of the firm in the short run:
3000703000100max 6.02.0 ll xx
![Page 12: Profit Maximization Profits The objectives of the firm Fixed and variable factors Profit maximization in the short and in the long run Returns to scale.](https://reader035.fdocuments.us/reader035/viewer/2022062320/56649d6c5503460f94a4bced/html5/thumbnails/12.jpg)
Short Run Profit Maximization
Problem of the firm in the short run:
First order condition:
3000703000100max 6.02.0 ll xx
07030006.0100 16.02.0 lx
![Page 13: Profit Maximization Profits The objectives of the firm Fixed and variable factors Profit maximization in the short and in the long run Returns to scale.](https://reader035.fdocuments.us/reader035/viewer/2022062320/56649d6c5503460f94a4bced/html5/thumbnails/13.jpg)
Short Run Profit Maximization
First order condition:
Interpretation:
7030006.0100 16.02.0 lx
salaryMPp L )(
![Page 14: Profit Maximization Profits The objectives of the firm Fixed and variable factors Profit maximization in the short and in the long run Returns to scale.](https://reader035.fdocuments.us/reader035/viewer/2022062320/56649d6c5503460f94a4bced/html5/thumbnails/14.jpg)
Short Run Profit Maximization
First order condition:
Solve this equation for number of consultants. Then get output and profits :
7030001006.0 16.02.0 lx
37lx 43y K1290
![Page 15: Profit Maximization Profits The objectives of the firm Fixed and variable factors Profit maximization in the short and in the long run Returns to scale.](https://reader035.fdocuments.us/reader035/viewer/2022062320/56649d6c5503460f94a4bced/html5/thumbnails/15.jpg)
Isoprofit Lines
The firm’s profits are given by:
Isoprofit line:
300070100 lxy
3010
7
100
lxy
![Page 16: Profit Maximization Profits The objectives of the firm Fixed and variable factors Profit maximization in the short and in the long run Returns to scale.](https://reader035.fdocuments.us/reader035/viewer/2022062320/56649d6c5503460f94a4bced/html5/thumbnails/16.jpg)
Isoprofit Lines
Isoprofit lines:
Production function:
3010
7
100
lxy
6.02.03000 lxy
y
lx37
43
![Page 17: Profit Maximization Profits The objectives of the firm Fixed and variable factors Profit maximization in the short and in the long run Returns to scale.](https://reader035.fdocuments.us/reader035/viewer/2022062320/56649d6c5503460f94a4bced/html5/thumbnails/17.jpg)
Change in Salary: 70K to 80K
Isoprofit lines:
Production function:
510
8
100
lxy
6.02.03000 lxy
y
lx37
43
27
35
![Page 18: Profit Maximization Profits The objectives of the firm Fixed and variable factors Profit maximization in the short and in the long run Returns to scale.](https://reader035.fdocuments.us/reader035/viewer/2022062320/56649d6c5503460f94a4bced/html5/thumbnails/18.jpg)
Profit Maximization in the Long Run
In the long run the level of inputs is variable:
First order conditions:
ollo xxxx 170100max 6.02.0
706.0100 16.02.0 lo xx
12.0100 6.012.0 lo xx
![Page 19: Profit Maximization Profits The objectives of the firm Fixed and variable factors Profit maximization in the short and in the long run Returns to scale.](https://reader035.fdocuments.us/reader035/viewer/2022062320/56649d6c5503460f94a4bced/html5/thumbnails/19.jpg)
Profit Maximization in the Long Run
First order conditions:
Divide first equation by second:
706.0100 16.02.0 lo xx
12.0100 6.012.0 lo xx
703 l
o
x
x
![Page 20: Profit Maximization Profits The objectives of the firm Fixed and variable factors Profit maximization in the short and in the long run Returns to scale.](https://reader035.fdocuments.us/reader035/viewer/2022062320/56649d6c5503460f94a4bced/html5/thumbnails/20.jpg)
Profit Maximization in the Long Run
First order conditions:
Replace second equation into first:
706.0100 16.02.0 lo xx
lo xx3
70
117
6
3
705
lx
![Page 21: Profit Maximization Profits The objectives of the firm Fixed and variable factors Profit maximization in the short and in the long run Returns to scale.](https://reader035.fdocuments.us/reader035/viewer/2022062320/56649d6c5503460f94a4bced/html5/thumbnails/21.jpg)
Profit Maximization in the Long Run
Find both inputs:
consultants
square feet257113
70ox
117
6
3
705
lx
![Page 22: Profit Maximization Profits The objectives of the firm Fixed and variable factors Profit maximization in the short and in the long run Returns to scale.](https://reader035.fdocuments.us/reader035/viewer/2022062320/56649d6c5503460f94a4bced/html5/thumbnails/22.jpg)
Profit Maximization in the Long Run
Find output and profits:
Ky 2732571170100
1311257 6.02.0 y
![Page 23: Profit Maximization Profits The objectives of the firm Fixed and variable factors Profit maximization in the short and in the long run Returns to scale.](https://reader035.fdocuments.us/reader035/viewer/2022062320/56649d6c5503460f94a4bced/html5/thumbnails/23.jpg)
Factor Demand Curves
In the example above, the firm chooses inputs so that:
salaryxxpMP loL ,
rentxxpMP loO ,
![Page 24: Profit Maximization Profits The objectives of the firm Fixed and variable factors Profit maximization in the short and in the long run Returns to scale.](https://reader035.fdocuments.us/reader035/viewer/2022062320/56649d6c5503460f94a4bced/html5/thumbnails/24.jpg)
Factor Demand Curves
Solve these equations to get factor demand curves:
salaryDx ll
rentDx oo
![Page 25: Profit Maximization Profits The objectives of the firm Fixed and variable factors Profit maximization in the short and in the long run Returns to scale.](https://reader035.fdocuments.us/reader035/viewer/2022062320/56649d6c5503460f94a4bced/html5/thumbnails/25.jpg)
Inverse Factor Demand Curves
Express what the factor price would have to be for factor demand to be at a certain level:
ll xfsalary
oo xfrent
![Page 26: Profit Maximization Profits The objectives of the firm Fixed and variable factors Profit maximization in the short and in the long run Returns to scale.](https://reader035.fdocuments.us/reader035/viewer/2022062320/56649d6c5503460f94a4bced/html5/thumbnails/26.jpg)
Find Factor Demand Curve in the Example
From first order conditions:
Solve for :
llo wxx 16.02.06.0100
ll
o xw
x3
lx
4
5 1
3
60
l
lw
x
![Page 27: Profit Maximization Profits The objectives of the firm Fixed and variable factors Profit maximization in the short and in the long run Returns to scale.](https://reader035.fdocuments.us/reader035/viewer/2022062320/56649d6c5503460f94a4bced/html5/thumbnails/27.jpg)
Find Inverse Factor Demand Curve in the Example
Solve for :
Get:
lw
4
5 1
3
60
l
lw
x
25.0
127
l
lx
w
![Page 28: Profit Maximization Profits The objectives of the firm Fixed and variable factors Profit maximization in the short and in the long run Returns to scale.](https://reader035.fdocuments.us/reader035/viewer/2022062320/56649d6c5503460f94a4bced/html5/thumbnails/28.jpg)
Diagram of Inverse Factor Demand for Consultants
lw
lx11
K70