Question

Suppose q=L^1/3K^1/6A^1/18. You get to choose the L,K, and A and the cost of these inputs are w, r, and m, respectively.

a- what type of returns to scale does this production function have?

b- write down the lagrange for the cost minimization problem and find the first order conditions.

c- Write down the profit equation in terms of L,K, and A for this firm and find the first order conditions.

d-describe what you would do to find the profit function for this firm

Answer 1

come positiv cau then ro duction functim beme メ+B+Y Now if β+Y = 1 then we sal pwdurtim function exhi bitiny nsfant return t scale exhibits cvasins refum to scau decreosing Yeturn +。.cole in our case, 1 3 <l 13 our productian functionn exhitits decveasiny

we nced to minimise above cot funcfin 1궁 Finding FoC with Yespect t LrfL 44 ' 02 てheJe an G 2 fof ard er 97

Proht function When output hao sening pna。P 6、nding ful with rej pect to L/K 4/ A 8下 213 3 ?)下 6 み1( 1 8 A nu 1 win find value, of L, ka 444 Sn ch thed" H= Sy nam etric Hessian rm atrix with each enty 3x3 レㄴ 17,

new (つ 一ㄍ L ( し57 レ kで NIL ︵ 324 う TUL し冷 116 V 3 Sy L A

2 43 573 36x324 34/1s A 3-9/6 2 3 33 ,リ 더 63 p 3 1x 3メ324

n3 variabl cas iF 'l , t element of Hess, an matriメ< anィ HL such a, | u" ル a n Determinant Fo C then value of vari aiJes For ob toined pvvides maximum functi va lw. Fowe have K A レ113 3 2 AI 6 S/ L G m 2 K of)L*, k*, A" ca n we -I hen after fu b stituting value丿 0