Question

Consider the production function of a firm employing two inputs capital (K) and labour
(L) as = (, ). Suppose the unit price of labour is while that of capital is and the
firm wishes to minimize its cost of production (with no other cost), = + subject
to the output = (, ) The firm using Lagrange multiplier method gets following first
order conditions for the problem:
−
′ = 0 (1)
−
′ = 0 (2)
− (, ) = 0 (3)
a) Assuming that (, ) is a
2
function, find the conditions under which K, L and λ
may be expressed as differentiable functions of of w, r and Y.
b) Using results in part (a) above, find expressions for
,

and
. × =
c) Assume that = 1 and = 2 and draw the level curves of the function, (, ) =



at heights 1 and 2. × =
d) Now consider the function, (, ) = ln (, ) with = 1 and = 2 and draw the
level curves at heights 1 and 2. How does your answer compare with that in part (a)
above?

Answer 1

Answer:

now brother this question is too long to be answered