An individual's preferences are represented by the utility function U(t, c) = 4√t + c, where t is hours of free time and c is units of consumption. The individual's consumption is limited by a feasible frontier described by the equation c = 50 - t^2. To find the optimal choice of free time and consumption, the problem can be simplified by substituting the constraint into the utility function. Which of the following expressions correctly represents the individual's utility as a function of only free time, t?
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Finding an Optimum for a Single-Variable Function using First and Second-Order Conditions
An individual's preferences are represented by the utility function
U(t, c) = 4√t + c, wheretis hours of free time andcis units of consumption. The individual's consumption is limited by a feasible frontier described by the equationc = 50 - t^2. To find the optimal choice of free time and consumption, the problem can be simplified by substituting the constraint into the utility function. Which of the following expressions correctly represents the individual's utility as a function of only free time,t?Interpreting a Simplified Choice Problem
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