Question

A firm has a production technology y=K9/11,1/11 where K is capital, and Lis labour. It wants to find its cost function when the wage rate is w = 3, the price of capital is v= 2. (a) Write Lagrangean for the optimization problem that the firm wants to solve. Lagrangean= (b) Find the first order conditions. 09=0, is the FOC for 1, 2-) =0, is the FOC for K, and 3 - 1 DE=0, is the FOC for L. Now solve the FOC K= B and L= (c) Check the second order conditions. Use J to denote, and enter in the order J, K, L. Be sure to use capital letters for J, K, L, The Bordered Hessian is sin(a) (To input your answer, right-click on the box below to bring up the symbols bar, select the button with a square made out of 9 smaller squares and select the appropriate size of matrix. If the correct size is not shown, select n xm and set the dimensions yourself. And be careful about order of operations when entering answers. Use extra brackets as long as they are matched.) The determinant of the Bordered Hessian is negative O zero O positive and this means that the solution is in determinate. We cannot say if it is a maximum, a minimum, or neither. O a minimum. O a maximum

Please Do all, if not, just B and C

Answer 1

Sol - Given that, Production technology ia., y = K L where, ki is Capital Lisa Labour * To find its Cost function = ? from past (a): V V + 7 ok K i L +7 Lagwangean 1) - fak+ 3L + / -k", 1" + - akt3L from Part (b) in we know that, KKY first order function is, * dL - -2-2, 4K Ľ") -0 FOC for K. der K L - y B FOC for a = 0 d? - 3-2 (who 1 * ), FOC For L :0

-22 7 = -2 K 9 L 3-** (***) 20 -2+ q " - 0 (***)-3 À propose 22 ho qiu -10% 33 % -1% same me then From from 0 and Ô Left hand side is Rh Right hand are equal., the - 33 -22 - Y -10) K 92" in L 27 L = 2k L = 24 the above value in equ. ① Put

* ( ਵੰਸ਼ ) : 1 ਵਿੱਚ 1 ਉਹ ਪੀ ਆ ,", ਯਾਰ ਰ੫ ॥ * K £ / = ਅ . N ੧) " , ਮੈਂ ) w . 33 33L • "/b 33

from Past (0) in The Bordered Hessian is, 2* a L Н . ƏKƏL akal -24*)*)** * * * * * * - [*# (4) ] - 10% % -3% % H 18 2 % Tail K 311-1071 ^ L : -92 121 12 -% ka -10% -102 % Talk 2% L - 992 lova -2% L -4 k det (H) >0 The Booded Hessian determines it is a positive art hence it means the solution is minimum ,

from Second order Condition is , 18 % -13), You Ľ" 18 33 (11,2 - ** (3)(2+4)* . • ()** 54 i The Leading principal number is. dºL a >o