Production, Consumption, and Trade-offs for a Self-Sufficient Individual
A self-sufficient individual's production of goods is characterized by a diminishing marginal product of labor, meaning each additional hour of work adds less to the total output than the previous hour. Explain how this characteristic of production shapes the individual's feasible consumption frontier. In your explanation, discuss the relationship between the amount of free time chosen and the rate at which that free time can be transformed into consumable goods.
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An independent farmer produces and consumes all of their own output. Their production of grain (y) is determined by the hours they work per day (h), according to the function y = 10 * sqrt(h). If the farmer has 24 hours available each day to allocate between work and free time (t), which equation correctly represents their feasible consumption frontier, where consumption is denoted by 'c'?