Error Analysis in a Utility Calculation
A farmer's satisfaction is described by the utility function U(c, t) = c * t, where 'c' is units of consumption and 't' is hours of free time. The farmer has 24 hours per day, which can be spent on work (h) or free time (t). The farmer's production is determined by the function: Production = 4h. Under their contract, they must pay a fixed rent of 36 units. The farmer determines that their optimal choice is to work 8 hours per day.
Another student presents the following calculation to find the farmer's final utility:
- Optimal work hours (h) = 8
- Free time (t) = 24 - 8 = 16
- Total Production = 4 * 8 = 32
- Consumption (c) = 32 - 36 = -4
- Final Utility = c * h = (-4) * 8 = -32
Identify the specific conceptual error in the student's final calculation step (Step 5) and explain what the correct calculation should have been, based on the provided utility function.
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