Question

12.1 Unanswered. 2 attempts left A firm's production function is x = k0.520.5. We have w=12and r=3. Capital is fixed at k=80. The firm's short run supply function is given by x=Ap where p is market price is A is a constant. What is A? Enter a number only, round to two decimal places. Enter a number only, round to two decimal places. If the answer is oo enter 999. If the answer is a range (any range) e.g. (0,2] enter 111. Type your response

Answer 1

0.5 0.9 The supply function is represented by the marginal cost curive. To get marginal cost (Mc) cureve, let us first find total cost as a function of output. x=2005205 -> x=(80) LOS LOS. Los -> (10.5) - - 2 80 Total cost - rok tw l =3*80 +12 (2) = 0 = 240 +0.15 x² = MC = 0.3x. Hence, the marginal cost cureve can also be represented as the supply curve, i.e. p=0.3x = x= 1 = x= 3.33p/ Hence A = 3.33] CCX) In the longreun, firem would minimize cost given output. So, the objective function is: Min rektwe sit. x = h 10.4 lik => Lagrangian's : 2 = 20k+ 201 + 1 [256-40-420-47 Since W = 11 = 20 and 2= 256 First order conditions: - 20-0.47 106.04-0 => 1 - 20 4007904 -0 24 - 20-0.4840440470 ) marzo 20o you — @ 24 - 256-10042004 - 0__ Secondarden conditions : a = -0.46-010) "°2014 to yo ano 32 -0.4(+0.6) 604, 6 yo >> Second order satisfied for minimization Now from Dand@, 2.0 20 509014-2020 2016 => =k - © Using @ in ®, de 2014.40.4-256 - 20:8-256 - l = (256) 0.8 = 1024 . 1=k= 1024 Hence, to preoduce 256 units of output in the ingreun, the firem will hire 1024 labor. L2 079