Local returns to scale A local measure of the returns to scale incorporated in a production function is given by the scale elasticity eq,t 5 ∂f 1tk, tl2/∂t # t/q evaluated at t 5 1.

a. Show that if the production function exhibits constant returns to scale, then eq,t 5 1.

b. We can define the output elasticities of the inputs k and l as eq, k 5 ∂f 1k, l2

∂k # k q

, eq, l 5 ∂f 1k, l2

∂l # l q

.

Show that eq, t 5 eq, k 1 eq, l

.

c. A function that exhibits variable scale elasticity is q 5 11 1 k21 l

212 21

.

Show that, for this function, eq, t . 1 for q , 0.5 and that eq, t , 1 for q . 0.5.

d. Explain your results from part

(c) intuitively. Hint: Does q have an upper bound for this production function?