Question

Complete parts A-C. Show work.

1. The "firm's problem" in a 2 input Cobb-Douglas world can be expressed as follows: min C(L,K) = wL + rK s.t. Qo= L°K® Where a, B, w, r, & Qo are positive and assumed constant. Using this information, please answer the following questions. a. Find this Labor and Capital demand functions for this firm. Show all work. (3 pts) b. Using your results from part "a.", show that the curvature of C(Q) depends on the returns to scale of the production function and identify the RTS conditions which would make C(Q) convex, concave, and linear. Show work/explain. (3 pts) c. Show that, in the short run, C(Q) will have a fixed variable component. Show work/explain. (3 pts)

Answer 1

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of (&+B) > 1 then d²c (IRS → Increasing Retums) Lo Concave Cost funch d02 202 2tß >1 CRS + Constant Retume d2 =0, Libels technology Ane In short Run Let K is fixed at E, 80 8= (LL) is then L - FQ7V ✓ Blo Short Run then c(Q) = Whatok SRG (8) = wro 7/7 ok [ KB ] variable fixed component LEBT thao component