Title: Firm Theory: production functions, cost curves and profit maximization
1 Firm Theory production functions cost curves and profit maximization 2 Remarks
Switching gears Theory of the Firm
Embarking on an analysis of the firm.
There are lots of different types of firms.
There are lots of ways to organize entrepreneurial activity.
There are lots of firm objectives.
3 What We Assume
For our analysis we assume that
we have an owner manager
who has a business
with the primary and only objective to maximize economic profit.
4 Whats a Business
A business is an organization producing goods or services also called a firm.
A business or firm is assumed to maximize its profits.
Examples of businesses Microsoft Kinkos the Campus Store (a business within Cornell University).
Examples of organizations that are not businesses in this sense Cornell University as a whole US Department of Defense.
Organizations that produce goods and services but are legally prohibited from using the profit motive are excluded from our formal model of a firm.
5 Whats a Market
A collection of buyers and sellers organized for the purpose of exchanging goods and services for money.
Markets can be global national regional or local depending upon the item being bought and sold.
6 Profit Maximization
profit total revenue - total cost
determined by the level and nature of competition in your market
costs are determined by factor market prices and the firms technology or production function
7 Economic Profits
Economic profits are the difference between total revenue and total costs.
Economic total costs include the opportunity costs of all inputs to the production processin particular the opportunity costs of the owners time and physical capital (equipment and space).
Whenever we talk about profit we mean economic profit.
8 Accounting Profits
Accounting profits are defined as total sales revenue (the same as total revenue in the economic profits definition) minus operating costs (costs of goods sold administrative and sales costs for those who know some accounting).
There are lots of ways to describe production and costs.
You need to understand them all.
total fixed and variable concepts
average and marginal concepts
long run and short run concepts
all related to each other
10 Jonathans New York State Apple Farm
The farm is a business organized to grow and sell apples.
The owner/proprietor Jonathan tries to maximize his profits from the business.
11 The U.S. Apple Market
Americans consume 19 lbs. of apples per person annually for a total consumption of 5 billion lbs.
More than 6 billion lbs. of apples are grown in the US each year (mostly in Washington New York and Michigan).
Only about 234 million lbs. are imported while more than 1.3 billion lbs. are exported.
There are about 1700 apple farms in the State of New York with an average of 96 acres of orchards per farm and about 92000/year in revenue from apple sales.
80 of the New York apple farms are individual or family owned.
Markets like the US apple market are classic examples of competitive product markets.
12 Production Functions
The production function shows the input requirements for each level of production.
For some businesses the production function is relatively simple--a few processes with little substitution.
For some businesses the production function involves thousands of different processes and millions of substitution possibilities.
The production function is the economists summary of the input requirements for each level of production.
13 Jonathans Apple Farm Production Function
The table describes Jonathans inputs for the annual production of apples shown in the first column.
14 Fixed Factors
A fixed factor is one that does not vary as the quantity produced increases or decreases.
Some factors are fixed in the short run (managerial time).
Some factors are fixed in the medium run (cultivated acreage).
No factors are fixed in the long run.
15 Jonathans Fixed Factors
Jonathan has two fixed factors
His cultivated acreage (100 acres)
His own managerial time (1100 hours)
16 Variable Factors
A variable factor is one that must be increased in order to increase output.
The classic variable factor is labor.
Variable factors usually exhibit diminishing marginal productivity--the amount of extra product generated by each additional unit of the input holding other inputs constant declines.
17 Jonathans Variable Factors
Jonathan must vary his labor input to increase his production of apples.
At first this variation is modest going from 50 tons/year to 100 tons/year requires an additional 1200 hours
Going from 200 to 250 tons/year requires an additional 3200 hours.
Jonathan cannot increase the size of his farm his acreage is fixed.
18 Jonathans Marginal Product of Labor
The graph shows how the marginal product of labor rises then falls for Jonathans apple farm. Marginal product is in red.
The marginal product is the extra amount of apple production (pounds/hour worked) that can be produced by an extra hour of work.
Average product (in blue) is the ratio of output to labor used. Average product of labor is usually called labor productivity in the business press.
19 The Average/Marginal Relation
For product curves or any other average/marginal pair of curves
If marginal product is above average product then average product is rising.
If marginal product is below average product then average product is falling.
Therefore marginal product equals average product when average product is at a critical value in this case a maximum.
20 From Production Curves to Cost Curves
By combining the production function and the factor prices we produce the businesss cost curves.
The total cost curve is the amount spent on all fixed and variable costs to produce the indicated output.
The average cost curve is the ratio of total costs to units produced.
21 Marginal Cost
The most important cost concept is marginal cost.
Marginal cost measures the amount by which costs increase as output increases by one unit.
22 7 Short Run Cost Curves
fc fixed costs PK K where K is fixed
vc variable costs PLL(x)
srtc short run total costs fcvc
afc average fixed cost fc/x
avc average variable cost vc/x
sratcshort run average total costsrtc/xafcavc
srmcshort run marginal cost srtc/x vc/x
23 Short Run Cost Curves
Short run cost curves get their shape from the marginal productivity of the variable factor (except the fixed costs of course).
If capital is held constant (short run) then the marginal product of labor gives the short run cost curves their shape.
The levels of cost curves are determined by factor market prices along with technology.
24 Jonathans Input Prices
Each of the entries in this table represents a price that Jonathan must pay for an input.
Notice that he pays for his managerial time because his next best alternative is to earn 12/hour.
He must pay rent for his land.
Jonathan is a wage taker as well as price-taker.
25 Jonathans Cost Curves
When Jonathan faces the technology and input prices shown previously the table shows his cost structure.
26 Graph of Jonathans Cost Curves
The marginal cost of each ton of apples is shown as the red line.
The average total cost curve is shown as the blue line.
Notice that the marginal cost average cost at minimum average cost.
27 Long Run Cost Curves
Describing the long run cost curves requires a description of all of the technological possibilities for operating in the industry.
Now both labor and capital are considered variable.
There are three long run cost curves for the firm
long run total cost lrtc PLL(x) PKK(x)
long run average total cost lratc lrtc/x
long run marginal cost lrmc lrtc/x
The most important one for us is the lratc curve.
Choosing L(x) and K(x) will depend on the prices of capital and labor relative to the marginal products of capital and labor and what x you expect to produce. The bang/buck condition would have to be met. That is at L and K the (mpL/PL ) (mpK/PK)
28 Example 3 Potential Technologies
Suppose there are three different ways for a company System-fixer to do business.
Firm sizes A B and C illustrate the possibilities.
Firm A is small using only 80 in fixed costs.
Firm B uses twice the capital.
Firm C uses three times the capital.
What is the best technology for our system-fixer firm
It depends on how much System-fixer expects to produce and sell in the market.
31 The Firms Long Run Average Total Cost Curve
The firms long run average total cost curve consists of the minimum of the three curves illustrated on the right.
System-fixers long run average total cost curve is size As (blue) until 6 units size Bs (red) from 6 to 10 units and size Cs (brown) from 11 units onward.
The shape of the firms lratc curve will be determined by how the technology behaves.
The lratc is the outer envelope of the possible sratc curves.
32 The Firms Long Run Average Total Cost Curve and MES
MES minimum efficient scale
MES the level of output at the minimum of the firms lratc curve.
When there are economies of scale the lratc is declining.
When there are diseconomies of scale the lratc is increasing.
At MES all the economies of scale are exhausted.
In real world empirical analysis economists often observe a more L-shaped lratc curve.
33 Profit Maximization
Profit () total revenue(tr) - total cost(tc).
Profit depends on the firms output level (x).
So (x) tr(x) - tc(x)
marginal revenue (mr) tr/x
marginal cost (mc) tc/x
34 Profit Maximization
General rules for profit maximization
If x maximizes then
mr mc at x
x is a profit max and not a profit min
at x its worth operating
If using a short-run perspective use short run cost curves.
If using a long-run perspective uselong run cost curves.
35 Running at a Profit
When the market price exceeds the firms average total cost at x the firm is running at a profit.
36 Running at a Loss
When the market price is less than the firms average total cost at x the business is running at a loss.
What should the firm do in the short run
produce x if the firm takes in enough in revenue to cover its variable costs.
shut down and play dead if its revenues at x dont even cover variable costs.
37 Running at a Loss
What should the firm do in the long run
It should plan to go out of business if it does not expect either the market price to rise or its costs to fall or both.
38 Sunk Costs and Avoidable Fixed Costs
In the real world the shut down rule is slightly different.
When the firm actually operates xgt0 it makes sense to only talk about fixed and variable costs.
However when the firm considers shutting down in the short run (when profits are negative at the profit maximizing output level) then they have to take another look at their fixed costs.
Fixed costssunk costs avoidable fixed costs
Now change the shutdown rule to be
produce x if the firm takes in enough in revenue to cover its variable costs avoidable fixed costs otherwise shut down.
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