## Question from Past Microeconomics Qualifying ExamEdit

**Fall 1999- Section I, Question four, George Mason University**

*True, False, Uncertain.* Determine whether or not each of the following statements are true or false. Explain your reasoning briefly in a paragraph or two. (The explanation is often more important than the answer given). Include a carefully labeled diagram or game matrix if it helps to clarify your answer.

The demand for a factor of production is never upward sloping in a setting where the production function is strictly concave.

## AnswerEdit

True, A function is strictly concave if points on a chord connecting two points of a function lie beneath the function. There is at most one local maximum and the second order condition is negative over the entire domain. These properties lead the strictly concave function to follow the law of diminishing returns. This means that when equal amounts of a variable input are added and all other inputs are held fixed, the resulting increments to output will eventually diminish. Because output decreases with increasing inputs, the demand for any particular factor of production will be downward sloping – the higher the price the less demanded, and the lower the price the more demanded. Each additional unit of input provides a smaller amount of additional output at the margin.

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