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Consider a quasiconcave, upper semicontinuous and homogeneous of degree γ function f. This paper shows that the reciprocal of the degree of homogeneity, 1 / γ , can be interpreted as a measure of the degree of concavity of f. As a direct implication of this result, it is also shown that f is harmonically concave if γ ≤ - 1 or γ ≥ 0 , concave if 0 ≤ γ ≤ 1 and logconcave if γ ≥ 0 . Some relevant applications to economic theory are given. For example, it is shown that a quasiconcave and homogeneous production function is concave if it displays nonincreasing returns to scale and logconcave if it displays increasing returns to scale. [ABSTRACT FROM AUTHOR]