Explaining the Shape of the Feasible Frontier
A student's production function, which relates hours of study to their final grade, is concave. This means that each additional hour of study produces a smaller increase in the final grade than the previous hour. Explain in detail why this property of the production function results in a feasible frontier (showing the trade-off between the final grade and free time) that is also concave (bowed outwards from the origin).
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A student's feasible frontier for a final grade versus hours of free time per day is a downward-sloping curve that is bowed outwards from the origin (concave). This frontier is derived from a production function that converts hours of study into a final grade. What does the shape of this feasible frontier imply about the underlying production function?
From Production Function to Feasible Frontier
A production function describes how an input (e.g., hours of study) is converted into an output (e.g., final grade). This relationship determines the shape of the feasible frontier, which illustrates the trade-off between that output and an alternative (e.g., hours of free time). Match each property of the production function with its direct geometric consequence for the feasible frontier.
A manufacturing firm uses labor and coal as its primary inputs. The cost of labor is Ā£10 per worker, and the price of coal is Ā£20 per ton. If the firm chooses a production technique that requires 2 workers and 3 tons of coal, what is the total cost of these inputs?
Impact of a New Technology on Production Possibilities
If a student's production function for converting study hours into exam points exhibits constant marginal returns, their feasible frontier, which shows the trade-off between exam points and free time, will be a straight line.
Deriving the Feasible Frontier's Shape
A production process that converts hours of an input into units of an output exhibits diminishing marginal returns. This means each additional hour of input generates less additional output than the previous hour. This production process is used to derive a feasible frontier showing the trade-off between the output and free time. Which of the following best describes the geometric shape of this feasible frontier?
Explaining the Shape of the Feasible Frontier
A new production process is developed where, due to specialization, each additional hour of labor is more productive than the previous one. This process is used to derive a feasible frontier showing the trade-off between the goods produced and an individual's free time. What will be the geometric shape of this feasible frontier?