The Cobb-Douglas function and level sets
Here and here I started to discuss topics in optimization. This post is a preparatory step to the next topic: the Lagrange method.
The Cobb–Douglas production function made a big splash in economics. It is still used a lot. In case of just two inputs, capital and labor, its definition is
For simplicity, in the videos below I assume . We discuss the definition, homogeneity and the reason for choosing a multiplicative form.
It is important to realize that the same function is used for modeling preferences. That is, the utility of consuming a pair of goods is measured by the function
Thus, everything that has been said about production functions, applies to utility functions as well.
Level sets, isoquants and indifference curves
Let
Level sets, isoquants and indifference curves define equivalence relations, see the definition and properties here.
The next video explains that isocosts, isoquants and indifference curves are all level sets for certain functions.
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