# Lecture 13 - Lecture 13 Costs II ye have eaten up the...

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Dr. Steven Waters Econ 380 Page 1 of 5 Lecture 13 Costs II … ye have eaten up the vineyard; the spoil of the poor is in your houses. What mean ye that ye beat my people to pieces, and grind the faces of the poor? Isaiah 3:14-15 The Economics Outline 1. Changing Input Prices 2. Long-Run Cost Functions 3. Short-Run Cost Functions The Mathematics Outline 1. Homogeneity 2. Algebra & Calculus Cost Functions and Homogeneity The total cost function is homogeneous of degree one in input prices . Consider what happens when input prices both increase by the same proportion, t . Initial Total Cost function: wL vK TC + = Increase by proportion, t : TC t wL vK t L tw K tv = + = + ) ( ) ( ) ( Thinking about the cost minimizing bundle combination, the slope of the isoquant at the cost minimizing point is - w/v even after the proportional increase in v and w . Hence, the same amount of K and L will minimize costs but costs will just be at a higher level. Because the total cost function is homogeneous of degree one in all input prices, the Average Cost function and the Marginal Cost function will also be homogeneous of degree one in input prices. To see this, consider the following:

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Lecture 13 - Lecture 13 Costs II ye have eaten up the...

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