Cobb-Douglas utility function is a mathematical formula used to represent the preferences of an individual or household towards consumption of goods and services. It was first introduced by Paul Douglas and Charles Cobb in 1928.
The general form of the Cobb-Douglas utility function is given as:
U(x1, x2,....xn) = Ax1^a1x2^a2....xn^an
where U represents the level of satisfaction, x1, x2,...xn represents the quantities of n goods consumed, A is a constant and a1, a2,...an are the parameters that measure the marginal utility or satisfaction obtained from consuming each good.
The key features of the Cobb-Douglas utility function are that it exhibits constant returns to scale, it is homogeneous of degree one, and its parameters satisfy the property of adding up to 1.
The Cobb-Douglas function is widely used in economics and has numerous applications in areas such as consumer theory, production theory, and international trade. It is commonly used in empirical studies to estimate demand or production functions and has been found to be a good fit for data on real-world consumption patterns.
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