Really need help answering these set of questions

Determine whether the following statements are true or false and explain. a. Given a production function f(L, K) = LUK 1"], the corresponding longrun output expansion path gets steeper as a grows larger. b. A rm currently employs ve units of capital. When the rm adds a sixth unit of capital, it is able to reach a lower average cost for a greater quantity of output. That implies the rm exhibits increasing returns to scale at the output level of 6 units. c. Since the production function f1 (L, K) = 2K0'3L0'7 has constant returns to scale, the production function f2(L, K) = 2K0'3L0'7 1 also has constant returns to scale (:1. Just as the utility functions U1(.'L'1,$2) = rst?\" and U2(a:1,a:2) = alnwl + (1 00112932 (0: is a constant between 0 and 1) represent the same preferences, the production functions f1 (L, K) = LO'K1_\" and f2 (L, K) = alnL + (1 (1)an also represent the same production technology. 6. In a constant-cost industry where all the rms are identical, suppose the xed cost equals zero even in the short run and free entry and exit is allowed only in the long run, then each rm's short-run prot is always no less than its long-run prot