Applied Economics for Business Management Lecture #8

Lecture Outline Review Homework Set #6 Continue Production Economic Theory

Cost Function Distinguish between cost equation and cost function Cost function: C = f(z)

Cost Function

Case 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 function ii. cost equation

Example (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 Equation of the expansion path

Example 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:

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 p 0, then equating p 0 to MC yields the profit maximizing level of output y 0. Note p = MC on the upward sloping portion of the MC curve (satisfying the 2nd order condition).

Profit Maximization: Input Formulation Method 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. 1 st order conditions:

Profit Maximization: Input Formulation Method

So the input formulation method finds a profit maximizing output level to be: found with the output formulation

Supply 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 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)2 nd 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 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  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

Example 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%.