To fully analyze an economic choice problem involving Cobb-Douglas preferences, it is necessary to compute both the Marginal Rate of Substitution (MRS) and the Marginal Rate of Transformation (MRT). This allows for finding the optimal choice by equating MRS and MRT. As noted in 'Extension 5.9', this calculation is a key step in solving the problem for such utility functions.

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Figure E5.7 is a graph that visually represents the feasible frontier and a set of indifference curves for a scenario where Angela has Cobb-Douglas preferences. The figure highlights that the points on different indifference curves where the slope matches that of the feasible frontier occur at different values of free time ($t$). This visual aid is part of an example used to determine the Pareto efficiency curve. The feasible frontier in the graph is derived from the production function $f(h) = (48h - h^2)/40$, while Angela's indifference curves are based on a Cobb-Douglas utility function where the parameter $\alpha$ is set to 8/13.

Figure E5.7 - Indifference Curves and Feasible Frontier for Cobb-Douglas Preferences

To cite the ebook, use The CORE Econ Team 2023 The Economy 2.0: Microeconomics Open access e-text https://core-econ.org/the-economy/.

To cite a unit, use The CORE Econ Team 2023 The Economy 2.0: Microeconomics Open access e-text https://core-econ.org/the-economy/ Unit [unit number] (url).

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