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

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Equation of the expansion path

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Now use the 3 pieces of information:

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Now use the cost equation:

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┌Total Fixed Cost└Total Variable Cost

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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

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Recall we derived the following cost function:

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supply function of the firm

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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%.