applied economics for business management
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Applied Economics for Applied Economics for Business ManagementBusiness Management
Lecture #8
Lecture OutlineLecture Outline
Review
Homework Set #6
Continue Production Economic Theory
Cost FunctionCost Function
Distinguish between cost equation and cost function
Cost function: C = f(z)
Cost FunctionCost Function
Case of 2 or more inputsCase of 2 or more inputs
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:
iii. equation of the expansion path
i. production functionii. cost equation
ExampleExample
(production function)
(cost equation)
ExampleExample
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
ExampleExample
Equation of the expansion path
ExampleExample
Now use the 3 pieces of information:
ExampleExample
Now use the cost equation:
ExampleExample
┌Total Fixed Cost└Total Variable Cost
ExampleExample
Using the previous example:
Marginal CostMarginal Cost
Profit MaximizationProfit Maximization
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 MaximizationProfit Maximization
1st order condition:
So profits are maximized for the output level where
Profit MaximizationProfit Maximization
2nd order condition:
Profit MaximizationProfit Maximization
What does this mean? C″(y) is the slope of the MC functionC″(y) > 0 slope of MC function is positive or MC function is upward sloping.
Profit MaximizationProfit Maximization
What does this mean? Graphically,
Profit MaximizationProfit 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: Input Profit Maximization: Input Formulation MethodFormulation Method
A familiar example:We solved earlier:
Profit Maximization: Input Profit Maximization: Input Formulation MethodFormulation Method
1st order conditions:
Profit Maximization: Input Profit Maximization: Input Formulation MethodFormulation Method
2nd order conditions:
Profit Maximization: Input Profit Maximization: Input Formulation MethodFormulation Method
Let’s now check this solution using the input formulation.1st order conditions:
Profit Maximization: Input Profit Maximization: Input Formulation MethodFormulation Method
Profit Maximization: Input Profit Maximization: Input Formulation Method Formulation Method
Profit Maximization: Input Profit Maximization: Input Formulation MethodFormulation Method
So the input formulation method finds a profit maximizing output level to be:
found with the output formulation
Supply CurveSupply Curve
Beginning and intermediate microeconomics courses state that the supply curve for the firm is that portion of the MC curve above minimum AVC.
Supply CurveSupply 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 CurveSupply 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 CurveSupply 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 FunctionSupply Function
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 Supply Function
as p increases, y increases and as p decreases, y decreases. (These are movements along the firm’s supply curve.).
From the firm’s supply function we can derive the
ExampleExample
Recall we derived the following cost function:
ExampleExample
supply function of the firm
ExampleExample
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%.
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