An economics student is solving for an individual's optimal choice between consumption (c) and free time (t). The individual's willingness to trade is MRS = 40 / t and the technical possibility of trading is MRT = 4 / √(20 - t). The student's work is presented below:
Step 1: Set MRS = MRT → 40 / t = 4 / √(20 - t)
Step 2: Simplify the equation → 10 / t = 1 / √(20 - t), which rearranges to 10 * √(20 - t) = t
Step 3: Square both sides → 100 * (20 - t) = t^2
Step 4: Expand and rearr
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An economics student is solving for an individual's optimal choice between consumption (
c) and free time (t). The individual's willingness to trade isMRS = 40 / tand the technical possibility of trading isMRT = 4 / √(20 - t). The student's work is presented below:Step 1: Set MRS = MRT →
40 / t = 4 / √(20 - t)Step 2: Simplify the equation →10 / t = 1 / √(20 - t), which rearranges to10 * √(20 - t) = tStep 3: Square both sides →100 * (20 - t) = t^2Step 4: Expand and rearr