![]() ![]() Douglas preferences are easy to use and therefore commonly used. This can be particularly useful when performing linear regressions. We consider a consumer with Cobb-Douglas preferences. However, we will often transform this function by taking the natural log, which allows us to transform exponents into coefficients: The general form of a Cobb-Douglas function over two goods is ![]() The Cobb-Douglas functional form was first proposed as a production function in a macroeconomic setting, but its mathematical properties are also useful as a utility function describing goods which are neither complements nor substitutes. Cobb-Douglas function with U10 and 0.5 and 0.5. The tangency condition yields: x2 x1 p1 p2 (2.4) Rearranging, p1x1 p2x2. 2.2 Example: Symmetric Cobb Douglas Suppose u(x1 x2) x1x2. ![]() Table 1 shows how the agent’s utility (the numbers in the boxes) varies with the number of x1 and x2 consumed. Preferences and Utility Functions 4.11 The Cobb-Douglas Utility Function 1.1 Example Suppose there are two goods, x1 and x2. Example of Cobb Douglas Production Function The Cobb Douglas production function : y F(K, L) K' L1-' where 0<'<1 has all the properties we assumed in the H-O Model. ![]()
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