Transcript Profit Maximization - University of Hawaii at Manoa

Applied Economics for
Business Management
Lecture #8
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Review
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Homework Set #6
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Continue Production Economic Theory
Lecture Outline
Distinguish between cost equation and cost function
Cost function: C = f(z)
Cost Function
Cost Function
How do we derive the cost function for a competitive
firm given only production information and market
prices?
To derive the cost function, you need the following
information:
i. production function
ii. cost equation
iii. equation of the expansion path
Case of 2 or more inputs
(production function)
(cost equation)
Example
How do we derive the equation of the expansion path?
Recall the expansion path is the locus of least cost
combinations. A least cost combination is where the
isoquant is tangent to the isocost line.
Slope of isoquant = slope of isocost
Example
Example
Equation of the
expansion path
Now use the 3 pieces of information:
Example
Now use the cost equation:
Example
┌Total Fixed Cost
└Total Variable Cost
Example
Using the previous example:
Example
Marginal Cost
Profit Maximization
(using output formulation rather than input formulation)
Previously, we examined profit maximization as finding the
value of inputs where profits are maximized.
Now consider profits in terms of output:
└cost function
Profit Maximization
1st order condition:
So profits are maximized for the output level where
Profit Maximization
2nd order condition:
Profit Maximization
What does this mean?
C″(y) is the slope of the MC function
C″(y) > 0  slope of MC function is positive or MC
function is upward sloping.
Profit Maximization
What does this mean?
Graphically,
Profit Maximization
If the market price for this commodity is p0, then equating
p0 to MC yields the profit maximizing level of output y0.
Note p = MC on the upward sloping portion of the MC
curve (satisfying the 2nd order condition).
Profit Maximization
A familiar example:
We solved earlier:
Profit Maximization: Input
Formulation Method
1st order conditions:
Profit Maximization: Input
Formulation Method
2nd order conditions:
Profit Maximization: Input
Formulation Method
Let’s now check this solution using the input formulation.
1st order conditions:
Profit Maximization: Input
Formulation Method
Profit Maximization: Input
Formulation Method
Profit Maximization: Input
Formulation Method
So the input formulation method finds a profit maximizing
output level to be:
found with the output formulation
Profit Maximization: Input
Formulation Method
Beginning and intermediate microeconomics
courses state that the supply curve for the firm
is that portion of the MC curve above minimum
AVC.
Supply Curve
Recall also that the second order conditions for profit
maximization states that the critical values must lie on
the upward sloping portion of the MC curve.
Supply Curve
Why isn’t the supply curve of the firm the entire MC
function?
2 reasons:
(i) 2nd order conditions for profit max eliminates the
negatively sloped portion of the MC curve
(ii) if p < min AVC  the firm chooses not to produce
since cannot cover all of fixed costs and a portion of
variable costs
Supply Curve
What is the supply function of the firm?
The supply function expresses a relationship between
the price of the product and the quantity supplied of that
product by the firm.
Note that input or factor demand or derived demand is
derived from profit maximization (using the input
formulation in the profit function).
For the firm’s supply function, this too is derived from
profit maximization however by using the output
formulation for profit.
Supply Curve
So we can derived the firm’s supply function from profit
maximization as follows:
From this equation, we solve for y in terms of p
Supply Function
From the firm’s supply function we can derive the
 as p increases, y increases and as p decreases, y
decreases. (These are movements along the firm’s supply
curve.).
Supply Function
Recall we derived the following cost function:
Example
supply function of the firm
Example
What is the elasticity of supply evaluated at the profit
maximizing level?
So if p increases by 10%, the firm is expected to increases
quantities supplied by 40%.
Example